text:
Statistics/Hypothesis Testing

Introduction
In previous chapters, we have discussed two methods for, namely and. Estimating unknown parameters is an important area in statistical inference, and in this chapter we will discuss another important area, namely, which is related to. Indeed, the concepts of and  are closely related, as we will demonstrate.

Basic concepts and terminologies
Before discussing how to hypothesis testing, and  the "goodness" of a hypothesis test, let us introduce some basic concepts and terminologies related to hypothesis testing first.

There are two terms that classify hypotheses:

Sometimes, it is not immediately clear that whether a hypothesis is simple or composite. To understand the classification of hypotheses more clearly, let us consider the following example.

In hypothesis tests, we consider two hypotheses:

A general form of $$H_0$$ and $$H_1$$ is $$H_0:\theta\in\Theta_0$$ and $$H_1:\theta\in\Theta_1$$ where $$\Theta_1=\Theta_0^c$$, which is the of $$\Theta_0$$ (with respect to $$\Theta$$), i.e., $$\Theta_0^c=\Theta\setminus\Theta_0$$ ($$\Theta$$ is the parameter space, containing all possible values of $$\theta$$). The reason for choosing the complement of $$\Theta_0$$ in $$H_1$$ is that $$H_1$$ is the complementary hypothesis to $$H_0$$, as suggested in the above definition.

We have mentioned that exactly one of $$H_0$$ and $$H_1$$ is assumed to be true. To make a decision, we need to which hypothesis should be regarded as true. Of course, as one may expect, this decision is not perfect, and we will have some errors involved in our decision. So, we cannot say we "prove that" a particular hypothesis is true (that is, we cannot be that a particular hypothesis is true). Despite this, we may "regard" (or "accept") a particular hypothesis as true (but prove it as true) when we have  that lead us to make this decision (ideally, with small errors ).

Now, we are facing with two questions. First, what evidences should we consider? Second, what is meant by "sufficient"? For the first question, a natural answer is that we should consider the observed, right? This is because we are making hypothesis about the population, and the samples are taken from, and thus closely related to the population, which should help us make the decision.

To answer the second question, we need the concepts in. In particular, in hypothesis testing, we will construct a so-called or  to help us determining that  we should reject the  hypothesis (i.e., regard $$H_0$$ as false),  and hence (naturally) regard $$H_1$$ as true ("accept" $$H_1$$) (we have assumed that exactly one of $$H_0$$ and $$H_1$$ is true, so when we regard one of them as false, we should regard another of them as true). In particular, when we do reject $$H_0$$, we will act as if, or accept $$H_0$$ as true (and thus should also reject $$H_1$$ since exactly one of $$H_0$$ of $$H_1$$ is true).

Let us formally define the terms related to hypothesis testing in the following.

Typically, we use (a statistic for conducting a hypothesis test) to specify the rejection region. For instance, if the random sample is $$X_1,\dotsc,X_n$$ and the test statistic is $$\overline X$$, the rejection region may be, say, $$R=\{\mathbf x:\overline x<2\}$$ (where $$x_1,\dotsc,x_n$$ and $$\overline x$$ is observed value of $$X_1,\dotsc,X_n$$ and $$\overline X$$ respectively). Through this, we can directly construct a hypothesis test: when $$\mathbf x\in R$$, we reject $$H_0$$ and accept $$H_1$$. Otherwise, if $$\mathbf x\in R^c$$, we accept $$H_0$$. So, in general, to specify the rule in a hypothesis test, we just need a. After that, we will apply the test on testing $$H_0$$ against $$H_1$$. There are some terminologies related to the hypothesis tests constructed in this way:

As we have mentioned, the decisions made by hypothesis test should not be perfect, and errors occur. Indeed, when we think carefully, there are actually of errors, as follows:

We can illustrate these two types of errors more clearly using the following table. We can express $$H_0:\theta\in\Theta_0$$ and $$H_1:\theta\in\Theta_0^c$$. Also, assume the rejection region is $$R=R(\mathbf X)$$ (i.e., the rejection region with "$$x$$" replaced by "$$X$$"). In general, when "$$R$$" is put together with "$$X$$", we assume $$R=R(\mathbf X)$$.

Then we have some notations and expressions for of making type I and II errors: (let $$X_1,\dotsc,X_n$$ be a random sample and $$\mathbf X=(X_1,\dotsc,X_n)$$)
 * The probability of making a type I error, denoted by $$\alpha(\theta)$$, is $$\mathbb P_{\theta}(\mathbf X\in R)$$ if $$\theta\in\Theta_0$$.
 * The probability of making a type II error, denoted by $$\beta(\theta)$$, is $$\mathbb P_{\theta}(\mathbf X\in R^c)=1-\mathbb P_{\theta}(\mathbf X\in R)$$ if $$\theta\in\Theta_0^c$$.

Notice that we have a common expression in both $$\alpha(\theta)$$ and $$\beta(\theta)$$, which is "$$\mathbb P_{\theta}((X_1,\dotsc,X_n)\in R)$$". Indeed, we can also write this expression as $$\mathbb P_{\theta}((X_1,\dotsc,X_n)\in R)=\begin{cases}\alpha(\theta),&\theta\in\Theta_0;\\1-\beta(\theta),&\theta\in\Theta_0^c.\end{cases}$$ Through this, we can observe that this expression contains all informations about the probabilities of making errors, given a hypothesis test with rejection $$R$$. Hence, we will give a special name to it:

Ideally, we want to make both $$\alpha(\theta)$$ and $$\beta(\theta)$$ arbitrarily small. But this is generally impossible. To understand this, we can consider the following extreme examples: We can observe that to make $$\alpha(\theta)$$ ($$\beta(\theta)$$) to be very small, it is inevitable that $$\beta(\theta)$$ ($$\alpha(\theta)$$) will increase consequently, due to accepting (rejecting) "too much". As a result, we can only try to minimize the probability of making one type of error, holding the probability of making another type of error.
 * Set the rejection region $$R$$ to be $$S=\{\mathbf x\}$$, which is the set of all possible observations of random samples. Then, $$\pi(\theta)=1$$ for each $$\theta\in\Theta$$. From this, of course we have $$\beta(\theta)=0$$, which is nice. But the serious problem is that $$\alpha(\theta)=1$$ due to the mindless rejection.
 * Another extreme is setting the rejection region $$R$$ to be the empty set $$\varnothing$$. Then, $$\pi(\theta)=0$$ for each $$\theta\in\Theta$$. From this, we have $$\alpha(\theta)=0$$, which is nice. But, again the serious problem is that $$\beta(\theta)=1$$ due to the mindless acceptance.

Now, we are interested in knowing that type of errors should be controlled. To motivate the choice, we can again consider the analogy of legal principle of presumption of innocence. In this case, type I error means proving an innocent guilty, and type II error means acquitting a guilty person. Then, as suggested by Blackstone's ratio, type I error is more serious and important than type II error. This motivates us to control the probability of type I error, i.e., $$\alpha(\theta)$$, at a specified small value $$\alpha^*$$, so that we can control the probability of making this more serious error. After that, we consider the tests that "control the type I error probability at this level", and the one with the smallest $$\beta(\theta)$$ is the "best" one (in the sense of probability of making errors).

To describe "control the type I error probability at this level" in a more precise way, let us define the following term.

So, using this definition, controlling the type I error probability at a particular level $$\alpha$$ means that the size of the test should not exceed $$\alpha$$, i.e., $$\sup_{\theta\in\Theta_0}\pi(\theta)\le\alpha$$ (in some other places, such test is called a.

For now, we have focused on using to conduct hypothesis tests. But this is not the only way. Alternatively, we can make use of $$p$$-value.

The following theorem allows us to use $$p$$-value for hypothesis testing.

Evaluating a hypothesis test
After discussing some basic concepts and terminologies, let us now study some ways to evaluate goodness of a hypothesis test. As we have previously mentioned, we want the probability of making type I errors and type II errors to be small, but we have mentioned that it is generally impossible to make both probabilities to be arbitrarily small. Hence, we have suggested to control the type I error, using the size of a test, and the "best" test should the one with the smallest probability of making type II error, after controlling the type I error.

These ideas lead us to the following definitions.

Using this definition, instead of saying "best" test (test with the smallest type II error probability), we can say "a test with the most power", or in other words, the "most powerful test".

Constructing a hypothesis test
There are many ways of constructing a hypothesis test, but of course not all are good (i.e., "powerful"). In the following, we will provide some common approaches to construct hypothesis tests. In particular, the following lemma is very useful for constructing a MP test with size $$\alpha$$.

Neyman-Pearson lemma
Even if the hypotheses involved in the Neyman-Pearson lemma are simple, with some conditions, we can use the lemma to construct a UMP test for testing null hypothesis against  alternative hypothesis. The details are as follows: For testing $$H_0:\theta\le\theta_0\quad\text{vs.}\quad H_1:\theta>\theta_0$$ For testing $$H_0:\theta\ge\theta_0\quad\text{vs.}\quad H_1:\theta<\theta_0$$, the steps are similar. But in general, there is no UMP test for testing $$H_0:\theta=\theta_0\quad\text{vs.}\quad H_1:\theta\ne\theta_0$$.
 * 1) Find a MP test $$\varphi$$ with size $$\alpha$$, for testing $$H_0:\theta=\theta_0\quad\text{vs.}\quad H_1:\theta=\theta_1>\theta_0$$ using the Neyman-Pearson lemma, where $$\theta_1$$ is an arbitrary value such that $$\theta_1>\theta_0$$.
 * , then the test $$\varphi$$ has the greatest power for $$\theta\in\Theta_1=\{\vartheta:\vartheta>\theta_0\}$$. So, the test $$\varphi$$ is a UMP test with size $$\alpha$$ for testing $$H_0:\theta=\theta_0\quad\text{vs.}\quad H_1:\theta>\theta_0$$
 * , then it means that the size of the test $$\varphi$$ is still $$\alpha$$, even if the null hypothesis is changed to $$H_0:\theta\le\theta$$. So, after changing $$H_0:\theta=\theta_0$$ to $$H_0:\theta\le \theta_0$$ and not changing $$H_1$$ (also adjusting the parameter space) for the test $$\varphi$$, the test $$\varphi$$ still satisfies the "MP" requirement (because of not changing $$H_1$$, so the result in step 2 still applies), and also the test $$\varphi$$ will satisfy the "size" requirement (because of changing $$H_0$$ in this way). Hence, the test $$\varphi$$ is a UMP test with size $$\alpha$$ for testing $$H_0:\theta\le\theta_0\quad\text{vs.}\quad H_1:\theta>\theta_0$$.

Of course, when the condition in step 3 holds but that in step 2 does not hold, the test $$\varphi$$ in step 1 is a UMP test with size $$\alpha$$ for testing $$H_0:\theta\le\theta_0\quad\text{vs.}\quad H_1:\theta=\theta_1$$ where $$\theta_1$$ is a constant (which is larger than $$\theta_0$$, or else $$H_1$$ and $$H_0$$ are not disjoint). However, the hypotheses are generally not in this form.

Now, let us consider another example where the underlying distribution is discrete.

Likelihood-ratio test
Previously, we have suggested using the Neyman-Pearson lemma to construct MPT for testing simple null hypothesis against simple alternative hypothesis. However, when the hypotheses are composite, we may not be able to use the Neyman-Pearson lemma. So, in the following, we will give a general method for constructing tests for any hypotheses, not limited to simple hypotheses. But we should notice that the tests constructed are not necessarily UMPT.

Relationship between hypothesis testing and confidence intervals
We have mentioned that there are similarities between hypothesis testing and confidence intervals. In this section, we will introduce a theorem suggesting how to construct a hypothesis test from a confidence interval (or in general, confidence ), and vice versa.

title: Statistics/Hypothesis Testing


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Basics of fine-art photography/Creating works in necrophoto

Necrophoto (photography related to death) is a neologism used by the author of textbook to designate a genre where the objects of photography are burial places, ritual (funeral) paraphernalia, remains of people, mummies, relics, and everything that is related to death and subsequent events/processes.

If the age of the subject is several hundred years old, photographic works can be attributed to the intersection of two genres: the one described in this article and "archaeological photography".

General information
This theme has been used in the history of photographic art since the invention of the camera. However, to this day, “photography associated with death” does not have a stable classification, and has not taken one of the places in the hierarchy of genres. The encyclopedia reports only about "Post-mortem photography", where the subject of the shooting are deceased people, which "posing", like the living; however, topic is limited to the indicated scope and does not include what is listed in the preamble of this article.

Ways of implementation
The genre of "necrophoto" can serve both documentary and artistic purposes, depending on the choice of the author. Since this textbook is directly related to art, the emphasis will be on the artistic side of the issue.

In my opinion, the combination of necrophoto and travel photography is the most interesting.

The traditions of the world associated with the funeral ritual and other actions accompanying the death of fellow tribesmen (such as mummification, etc.) are worthy of being captured. For example, the Ma'nene Festival in Indonesia, during which aborigines temporarily remove the bodies of long-dead relatives from the ground in order to return them to their graves after a short “communication”; or Merry Cemetery in Romania, there are many examples. The attitude towards death among the natives, the so-called exotic countries, is fundamentally different from the perception of this fatality by Europeans, therefore, the photographs taken by you will arouse interest among compatriots upon your return.

As for the choice of space for actions, transport and ways of moving, the Internet and your own imagination will help you, and 15 examples from the practice of the author of this article can be seen in the gallery below.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Wikijunior:Raspberry Pi/Raspberry Pi Make a Graphical User Interface (GUI)

Laura Sach @codeboom – CC-BY-SA 4.0

This workshop explores creating easy Python graphical interfaces with the  library.

itself is an alternative to the Tkinter graphical interface library which is included with Python.

Setup and installation
You can install the  library by running the   command from the Terminal which is the recommended way:

Alternatively, there is a Microsoft Windows installer from the website: https://lawsie.github.io/guizero/

Your first GUI

 * 1) From the Programming menu, open up Python 3
 * 2) Click on File > New File to create a blank window where you will write your code
 * 3) Add the following source code below to your file.
 * 4) Save the file, then press F5 to run the code. You should see a basic GUI!

Let's look at what the lines of code do:

Tells Python we want to use App and Text from

Creates the app (the box bit) and puts the words "My first GUI" in the title.

Creates the  (the word "Hello!" in the grey part) and adds it to the app. Whenever we create something new in  we always add it to the app so that it appears on the screen.

Display the app, and run a loop to update it in case anything changes. This line is always last.

Jazzing up the text
This text is a bit boring! You can change the size, colour and font of the text by adding some additional parameters.

Find this line of code.

Add another parameter to change the colour to red (note the American spellling).

You can add more parameters by putting commas between them, like this:

Pictures
Pictures must be in GIF format to be displayed on the GUI. All code for items to display on the GUI must go between these two lines of code.

 * Import the class –
 * Make sure you have a GIF picture saved in the same folder as your Python file
 * Add this line of code to your app (replace cat.gif with the filename of your picture)

Sadly,  can't display animated GIFs. 😟

Buttons
You can add a button like this:

Import the class by adding to the top line.

At the top of your program, just after the  statement, write a function which will be called when the button is pressed. Our example function is called  but you can call it whatever you like (don't put spaces or punctuation in the name though).

Make sure that the print line is indented by pressing the tab key – this is important!

Add the button code between the two lines of app code as for the picture.

Run your program by pressing F5. Click the button and look in the Python shell – you should see a message saying.

Challenge – Cat name generator

When you press the button, your randomly generated "cat name" will appear below.

 * 1) Change your GUI so that it looks like this. You should be able to work out how to do this by changing the code you already have. You can use your own picture!
 * 2) Add the line   at the top of your program so that we can randomly choose a cat name.
 * 3) Add this code below your button to create some text. This is where the cat name will be displayed, but we don’t know what it is yet so we will just put   for now.

Find the line of code  in your existing program. Replace the line of code  with this code to randomly choose your cat's first name from the list. Add some more different names if you like!

Write another line of code underneath this one to randomly pick a last name for your cat. Make sure to start this line with  so we can tell which is which.

Now add a line of code to join them together and set the result inside the  text you created earlier.

Save and run your program, then press the button to discover your cat alter ego!

What's next?
The official website for  has documentation for creating graphical user interface (GUI) apps. The authors have designed it to be used in "advanced projects": https://lawsie.github.io/guizero/

The Raspberry Pi Foundation has published a free PDF book for  called Create Graphical User Interfaces with Python (2020) by Martin O'Hanlon and Laura Sach: https://magpi.raspberrypi.org/books/create-guis


text: User:Gat lombard

title: User:Gat lombard


text:
User:Itsblair/Collections/LaTeX Wikibook

LaTeX Wikibook

 * Getting Started
 * Introduction
 * Installation
 * Installing Extra Packages
 * Basics

 * Common Elements
 * Document Structure
 * Text Formatting
 * Paragraph Formatting
 * Colors
 * Fonts
 * List Structures
 * Special Characters
 * Internationalization
 * Rotations
 * Tables
 * Title Creation
 * Page Layout
 * Importing Graphics
 * Floats, Figures and Captions
 * Hyperlinks
 * Labels and Cross-referencing

 * Mechanics
 * Errors and Warnings
 * Lengths
 * Counters
 * Boxes
 * Rules and Struts

 * Technical Texts
 * Mathematics
 * Advanced Mathematics
 * Theorems
 * Chemical Graphics
 * Algorithms
 * Source Code Listings
 * Linguistics

 * Special Pages
 * Indexing
 * Glossary
 * Bibliography Management
 * More Bibliographies

 * Special Documents
 * Letters
 * Presentations
 * Teacher's Corner
 * Curriculum Vitae

 * Creating Graphics
 * Introducing Procedural Graphics
 * MetaPost
 * Picture
 * PGF/TikZ
 * PSTricks
 * Xy-pic
 * Creating 3D graphics

 * Programming
 * Macros
 * Plain TeX
 * Creating Packages
 * Themes

 * Miscellaneous
 * Modular Documents
 * Collaborative Writing of LaTeX Documents
 * Export To Other Formats

 * Help and Recommendations
 * FAQ
 * Tips and Tricks

 * Appendix
 * Authors
 * Links
 * Package Reference
 * Sample LaTeX documents
 * Index
 * Command Glossary


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LMIs in Control/Click here to continue/Applications of Linear systems/LMI based State-Feedback Control Design for a Wind Generating Power Plant

LMI-Based Sliding Mode Robust Control for a Class of Multi-Agent Linear Systems

The System
The state-space representation:

 * $$ \dot{x}(t)= Ax_i(t) + Bu_i(t)+ di,$$ i=1,⋯,N  .(1)

where $$x_i(t)$$∈$$R^{n}$$, $$u_i$$ ∈ $$R_n$$ are the state and control input of the $$i^{th}$$ agent, $$d_i$$∈$$R^{ n \times 1 }$$ is disturbance term, A and $$B$$∈ $$R^{n \times n}$$ are constant matrices and the initial state is defined by $$x_i(0)$$. The control targets are $$x_i$$→$$x_i^{y}$$, for i=1,...,N. $$x_i^{y}$$ is an ideal instruction.

Assumption. This study deals with the information exchange among agents is modeled by an undirected graph. We assume that the communication topology is connected.

The Design of Controllers
We define the tracking error as $$z_i(t)= x_i(t)-x_i^{y}(t)$$, then

 * $$\dot{z}_i(t)$$= $$\dot{x}_i(t) - \dot{x}_i^{y}(t)$$ = $$Ax_i(t)+Bu_i(t)+d_i - \dot{x}_i^{y}(t)$$  .(2)

Design the tracking error as a sliding mode function, we give the design of control law as

 * $$u_i(t)=F_i(t)x_i(t)+u_i^{y}(t)+u_i^{s}(t)$$   .(3)

Where $$F_i(t)$$ is a state feedback gain matrix which can be obtained by designing LMI.
 * Take forward-feedback control term:
 * $$u_i^{y}(t)=-F_i(t)x_i^{y}(t)-B^{-1}(t)A_i(t)x_i^{y}(t)+B^{-1}(t)\dot{x}_i^{y}(t)$$,

 * Sliding mode robust term:
 * $$u_i^{s}=-B^{-1}$$[$$\eta_isgn(z_i)], \eta_i$$∈$$R^{n x 1}$$,$$d_i^{j}-\eta_i^{j}<0$$ or$$ d_i{j}+\eta_i^{j}>0$$ ,
 * and $$\eta_isgn(zi)=[\eta_i^{1}sgnz_i^{1},...,\eta_i^{n}sgnz_i^{n}]^{T}$$.

The LMI
Theorem 1. Assume that
 * $$A^{T}P_i+M_i^{T}+P_iA+M_i<0$$ is true for any i=1,...,N,   .(4)
 * where $$F_i=(P_iB)^{-1}M_i$$,

then the closed-loop system consisting of (1) and (3) is asymptotic stability.

Implementation
We focus on the multi-agent linear system, without loss of generality, we assume that the system has three agents and B is the unit matrix.

According to (1),
 * B=$$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$$, $$A=\begin{bmatrix}-2.4 & 9.2 & 0 \\ 1 & -1 & 1 \\0 & -16.3 & 3\end{bmatrix}$$

the ideal matrix is [ sin(t)  cos(t)  sin(t) ], the interference matrix is
 * $$d_1=\begin{bmatrix}50 sin(t) \\ 50 cos(t) \\ 50sin(t) \end{bmatrix}$$, $$d_2=\begin{bmatrix}40 sin(t) \\ 40 cos(t) \\ 40sin(t) \end{bmatrix}$$,$$d_3=\begin{bmatrix}50 sin(t) \\ 50 cos(t) \\ 50sin(t) \end{bmatrix}$$,

corresponding to the ideal matrix. Solving LMI (4), let
 * $$P_1=\begin{bmatrix}10000 & 0 & 0 \\ 0 & 10000 & 0 \\0 & 0 & 10000\end{bmatrix}$$,
 * $$P_2=\begin{bmatrix}100000 & 0 & 0 \\ 0 & 100000 & 0 \\0 & 0 & 100000\end{bmatrix}$$,
 * $$P_3=\begin{bmatrix}5000000 & 0 & 0 \\ 0 & 5000000 & 0 \\0 & 0 & 5000000\end{bmatrix}$$,

respectively. Due to (3), let

 * $$\eta1=\begin{bmatrix}50 \\ 50  \\ 50) \end{bmatrix}$$,$$\eta2=\begin{bmatrix}40  \\ 40  \\ 40) \end{bmatrix}$$,$$\eta3=\begin{bmatrix}50  \\ 50  \\ 50) \end{bmatrix}$$

replacing switching function with saturation function and choosing the boundary layer as Δ=0.05. We give simulations are in the following (Figures 1-3).

 * It is clear that from three figures the closed-loop system with disturbance is asymptotic stability, hence, the proposed method is effective.

Conclusion
The multi-agent linear system was studied in this paper. Based on linear matrix inequality technology and sliding mode control, the forward-feedback control term was given. Sufficient conditions for the closed-loop system were established by Lyapunov stability theory. Simulations show that the proposed method was effective.


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LMIs in Control/Click here to continue/Robust Controls/Robust Unconstrained Model Predictive Control

Model Predictive Control
Model Predictive Control is an open-loop control design procedure where at each sampling time k, plant measurements are obtained and a model of the process is used to predict future outputs of the system. Using these predictions, $$m$$ control moves $$u(k+i|k), i=0,1,...,m-1.$$ are computed by minimizing a nominal cost $$J_p(k)$$ over a prediction horizon $$p$$. The objective is to minimize the nominal cost function.

We consider the nominal cost function as:

 * $$\min_{u(k+i),i=0,1,...,m-1} J_p(k) $$

where,

 * $$ J_p(k) = \Sigma_{i=0}^p[x(k+i|k)^{T}Q_1x(k+i|k) + u(k+i|k)^{T}Ru(k+i|k)]$$

 * $$ Q_1 > 0$$ and $$ R > 0$$

$$Q_1$$ and $$R$$ are positive definite weighting matrices.

In this case, we take $$ p=\infty $$. This is also called infinite horizon MPC.

Uncertainties
Here, we consider system uncertainties that are modeled as polytopic uncertainties or structured uncertainties.

Polytopic Uncertainty
The set $$ \Omega $$ is the polytope $$ \Omega=Co{[A_1 B_1], [A_2 B_2],....,[A_L B_L]} $$

Where, $$ Co $$ denotes the convex hull.

Structured Uncertainty
The operator $$ \Delta $$ is a block-diagonal:
 * $$\Delta = \begin{bmatrix}\Delta_1 & & & \\ & \Delta_2 & & & \\ & & \ddots & \\ & & & \Delta_r\end{bmatrix}$$

Each $$ \Delta $$ can be a repeated scalar block or a full block.

The System
Consider a linear time-varying(LTV) system:

 * $$ x(k+1)=A(k)x(k)+B(k)u(k), $$

 * $$y(k)=CX(k), $$

 * $$\begin{bmatrix} A(k) & B(k)\end{bmatrix}\in \Delta $$

Here, $$ u(k)\in \R^n$$ is the control input, $$ x(k)\in \R^n$$ is the state of the plant and $$ y(k)\in \R^n$$ is the plant output and $$\Delta$$ is uncertainty set that is either polytopic system or structured uncertainty.

We modify the minimization of the nominal cost function to a minimization of the worst-case objective function.

The modified objective function minimizes the robust performance objective as follows:

 * $$\min_{u(k+i),i=0,1,...,m-1} \max_{[A(k+i) B(k+i]\in \Delta,i\geq 0} J_\infty(k) $$

where,

 * $$ J_\infty(k) = \Sigma_{i=0}^\infty[x(k+i|k)^{T}Q_1x(k+i|k) + u(k+i|k)^{T}Ru(k+i|k)]$$

The LMI:Robust Unconstrained Model Predictive Control with State Feedback for polytopic uncertainty
$$\min_{\gamma,Q,Y} \gamma $$

subject to

 * $$\begin{bmatrix} 1 & x(k|k)^T \\ x(k|k) & Q \end{bmatrix} \geq 0

$$

and

 * $$\begin{bmatrix} Q & QA_{j}^T+Y^TB_{j}^T & QQ_{1}^{1/2} & Y^TR^{1/2} \\ A_j Q+B_j Y & Q & 0 & 0 \\ Q_{q}^{1/2} & 0 & \gamma I & 0 \\ R^{1/2}Y & 0 & 0 & \gamma I\end{bmatrix} \geq 0

$$

The LMI:Robust Unconstrained Model Predictive Control with State Feedback for structured uncertainty
$$\min_{\gamma,Q,Y,\Lambda} \gamma $$

subject to

 * $$\begin{bmatrix} 1 & x(k|k)^T \\ x(k|k) & Q \end{bmatrix} \geq 0

$$

 * $$\begin{bmatrix} Q & Y^TR^{1/2} & QQ_{1}^{1/2} & QC_{q}^T+Y^TD_{qu}^T & QA^T+Y^TB^T \\ R^{1/2}Y & \gamma I & 0 & 0 & 0 \\ Q_{1}^{1/2}Q & 0 & \gamma I & 0 & 0 \\ C_{q}Q+D_{qu}Y & 0 & 0 & \Lambda & 0 \\ AQ+BY & 0 & 0 & 0 & Q-B_p \Lambda B_{p}^T\end{bmatrix} \geq 0

$$

where

 * $$\Lambda = \begin{bmatrix}\lambda_1I_{n1} & & & \\ & \lambda_2I_{n2} & & & \\ & & \ddots & \\ & & & \lambda_rI_{nr}\end{bmatrix}>0$$

Conclusion:
The state feedback matrix F in the control law $$u(k+i|k) = Fx(k+i|k), i \geq 0$$ that minimizes the upper bound $$ V(x(k|k)) $$ on the robust performance objective function at sampling time $$ k $$ is given by :

 * $$ F = YQ^{-1} $$

where $$ Q > 0 $$ and $$ Y $$ are obtained from the solution of the above LMI.


text:
User talk:195.141.61.164

Xania   talk 09:55, 2 December 2022 (UTC)

title: User talk:195.141.61.164


text:
LMIs in Control/Click here to continue/Applications of Linear systems/LMI-Based Sliding Mode Robust Control for a Class of Multi-Agent Linear Systems

LMI-Based Sliding Mode Robust Control for a Class of Multi-Agent Linear Systems

The System
The state-space representation:

 * $$ \dot{x}(t)= Ax_i(t) + Bu_i(t)+ di,$$ i=1,⋯,N  .(1)

where $$x_i(t)$$∈$$R^{n}$$, $$u_i$$ ∈ $$R_n$$ are the state and control input of the $$i^{th}$$ agent, $$d_i$$∈$$R^{ n \times 1 }$$ is disturbance term, A and $$B$$∈ $$R^{n \times n}$$ are constant matrices and the initial state is defined by $$x_i(0)$$. The control targets are $$x_i$$→$$x_i^{y}$$, for i=1,...,N. $$x_i^{y}$$ is an ideal instruction.

Assumption. This study deals with the information exchange among agents is modeled by an undirected graph. We assume that the communication topology is connected.

The Design of Controllers
We define the tracking error as $$z_i(t)= x_i(t)-x_i^{y}(t)$$, then

 * $$\dot{z}_i(t)$$= $$\dot{x}_i(t) - \dot{x}_i^{y}(t)$$ = $$Ax_i(t)+Bu_i(t)+d_i - \dot{x}_i^{y}(t)$$  .(2)

Design the tracking error as a sliding mode function, we give the design of control law as

 * $$u_i(t)=F_i(t)x_i(t)+u_i^{y}(t)+u_i^{s}(t)$$   .(3)

Where $$F_i(t)$$ is a state feedback gain matrix which can be obtained by designing LMI.
 * Take forward-feedback control term:
 * $$u_i^{y}(t)=-F_i(t)x_i^{y}(t)-B^{-1}(t)A_i(t)x_i^{y}(t)+B^{-1}(t)\dot{x}_i^{y}(t)$$,

 * Sliding mode robust term:
 * $$u_i^{s}=-B^{-1}$$[$$\eta_isgn(z_i)], \eta_i$$∈$$R^{n x 1}$$,$$d_i^{j}-\eta_i^{j}<0$$ or$$ d_i{j}+\eta_i^{j}>0$$ ,
 * and $$\eta_isgn(zi)=[\eta_i^{1}sgnz_i^{1},...,\eta_i^{n}sgnz_i^{n}]^{T}$$.

The LMI
Theorem 1. Assume that
 * $$A^{T}P_i+M_i^{T}+P_iA+M_i<0$$ is true for any i=1,...,N,   .(4)
 * where $$F_i=(P_iB)^{-1}M_i$$,

then the closed-loop system consisting of (1) and (3) is asymptotic stability.

Implementation
We focus on the multi-agent linear system, without loss of generality, we assume that the system has three agents and B is the unit matrix.

According to (1),
 * B=$$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$$, $$A=\begin{bmatrix}-2.4 & 9.2 & 0 \\ 1 & -1 & 1 \\0 & -16.3 & 3\end{bmatrix}$$

the ideal matrix is [ sin(t)  cos(t)  sin(t) ], the interference matrix is
 * $$d_1=\begin{bmatrix}50 sin(t) \\ 50 cos(t) \\ 50sin(t) \end{bmatrix}$$, $$d_2=\begin{bmatrix}40 sin(t) \\ 40 cos(t) \\ 40sin(t) \end{bmatrix}$$,$$d_3=\begin{bmatrix}50 sin(t) \\ 50 cos(t) \\ 50sin(t) \end{bmatrix}$$,

corresponding to the ideal matrix. Solving LMI (4), let
 * $$P_1=\begin{bmatrix}10000 & 0 & 0 \\ 0 & 10000 & 0 \\0 & 0 & 10000\end{bmatrix}$$,
 * $$P_2=\begin{bmatrix}100000 & 0 & 0 \\ 0 & 100000 & 0 \\0 & 0 & 100000\end{bmatrix}$$,
 * $$P_3=\begin{bmatrix}5000000 & 0 & 0 \\ 0 & 5000000 & 0 \\0 & 0 & 5000000\end{bmatrix}$$,

respectively. Due to (3), let

 * $$\eta1=\begin{bmatrix}50 \\ 50  \\ 50) \end{bmatrix}$$,$$\eta2=\begin{bmatrix}40  \\ 40  \\ 40) \end{bmatrix}$$,$$\eta3=\begin{bmatrix}50  \\ 50  \\ 50) \end{bmatrix}$$

replacing switching function with saturation function and choosing the boundary layer as Δ=0.05. We give simulations are in the following (Figures 1-3).

 * It is clear that from three figures the closed-loop system with disturbance is asymptotic stability, hence, the proposed method is effective.

Conclusion
The multi-agent linear system was studied in this paper. Based on linear matrix inequality technology and sliding mode control, the forward-feedback control term was given. Sufficient conditions for the closed-loop system were established by Lyapunov stability theory. Simulations show that the proposed method was effective.


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LMIs in Control/Click here to continue/Robust Controls/Robust Model Predictive Control with input and output constraints

Model Predictive Control
Model Predictive Control is an open-loop control design procedure where at each sampling time k, plant measurements are obtained and a model of the process is used to predict future outputs of the system. Using these predictions, $$m$$ control moves $$u(k+i|k), i=0,1,...,m-1.$$ are computed by minimizing a nominal cost $$J_p(k)$$ over a prediction horizon $$p$$. The objective is to minimize the nominal cost function.

We consider the nominal cost function as:

 * $$\min_{u(k+i),i=0,1,...,m-1} J_p(k) $$

where,

 * $$ J_p(k) = \Sigma_{i=0}^p[x(k+i|k)^{T}Q_1x(k+i|k) + u(k+i|k)^{T}Ru(k+i|k)]$$

 * $$ Q_1 > 0$$ and $$ R > 0$$

$$Q_1$$ and $$R$$ are positive definite weighting matrices.

In this case, we take $$ p=\infty $$. This is also called infinite horizon MPC.

Uncertainties
Here, we consider system uncertainties that are modeled as polytopic uncertainties or structured uncertainties.

Polytopic Uncertainty
The set $$ \Omega $$ is the polytope $$ \Omega=Co{[A_1 B_1], [A_2 B_2],....,[A_L B_L]} $$

Where, $$ Co $$ denotes the convex hull.

Structured Uncertainty
The operator $$ \Delta $$ is a block-diagonal:
 * $$\Delta = \begin{bmatrix}\Delta_1 & & & \\ & \Delta_2 & & & \\ & & \ddots & \\ & & & \Delta_r\end{bmatrix}$$

Each $$ \Delta $$ can be a repeated scalar block or a full block.

The System
Consider a linear time-varying(LTV) system:

 * $$ x(k+1)=A(k)x(k)+B(k)u(k), $$

 * $$y(k)=CX(k), $$

 * $$\begin{bmatrix} A(k) & B(k)\end{bmatrix}\in \Delta $$

Here, $$ u(k)\in \R^n$$ is the control input, $$ x(k)\in \R^n$$ is the state of the plant and $$ y(k)\in \R^n$$ is the plant output and $$\Delta$$ is uncertainty set that is either polytopic system or structured uncertainty.

We modify the minimization of the nominal cost function to a minimization of the worst-case objective function.

The modified objective function minimizes the robust performance objective as follows:

 * $$\min_{u(k+i),i=0,1,...,m-1} \max_{[A(k+i) B(k+i]\in \Delta,i\geq 0} J_\infty(k) $$

where,

 * $$ J_\infty(k) = \Sigma_{i=0}^\infty[x(k+i|k)^{T}Q_1x(k+i|k) + u(k+i|k)^{T}Ru(k+i|k)]$$

The LMI:Robust Model Predictive Control with State Feedback and input and output constraints for polytopic uncertainty
$$\min_{\gamma,Q,Y} \gamma $$

subject to

 * $$\begin{bmatrix} 1 & x(k|k)^T \\ x(k|k) & Q \end{bmatrix} \geq 0

$$

and

 * $$\begin{bmatrix} Q & QA_{j}^T+Y^TB_{j}^T & QQ_{1}^{1/2} & Y^TR^{1/2} \\ A_j Q+B_j Y & Q & 0 & 0 \\ Q_{q}^{1/2} & 0 & \gamma I & 0 \\ R^{1/2}Y & 0 & 0 & \gamma I\end{bmatrix} \geq 0

$$

Input constraint is given by the following LMI:

 * $$\begin{bmatrix} u_{max}^{2}I & Y \\ Y^T & Q \end{bmatrix} \geq 0 $$

Output constraint is given by the following LMI:

 * $$\begin{bmatrix} Q & (A_{j}Q+B_{j}Y)^T C^T \\ C(A_{j}Q+B_{j}Y) & y_{max}^2 I \end{bmatrix} \geq 0 $$

The LMI:Robust Model Predictive Control with input and output constraints with State Feedback for structured uncertainty
$$\min_{\gamma,Q,Y,\Lambda} \gamma $$

subject to

 * $$\begin{bmatrix} 1 & x(k|k)^T \\ x(k|k) & Q \end{bmatrix} \geq 0

$$

 * $$\begin{bmatrix} Q & Y^TR^{1/2} & QQ_{1}^{1/2} & QC_{q}^T+Y^TD_{qu}^T & QA^T+Y^TB^T \\ R^{1/2}Y & \gamma I & 0 & 0 & 0 \\ Q_{1}^{1/2}Q & 0 & \gamma I & 0 & 0 \\ C_{q}Q+D_{qu}Y & 0 & 0 & \Lambda & 0 \\ AQ+BY & 0 & 0 & 0 & Q-B_p \Lambda B_{p}^T\end{bmatrix} \geq 0

$$

where

 * $$\Lambda = \begin{bmatrix}\lambda_1I_{n1} & & & \\ & \lambda_2I_{n2} & & & \\ & & \ddots & \\ & & & \lambda_{r}I_{nr} \end{bmatrix}>0$$

Input constraint is given by the following LMI:

 * $$\begin{bmatrix} u_{max}^{2}I & Y \\ Y^T & Q \end{bmatrix} \geq 0 $$

Output constraint is given by the following LMI:

 * $$\begin{bmatrix} y_{max}^2 Q & (C_{q}Q+D_{qu}Y)^T & (AQ+BY)^T C^T \\ C_{q}Q+D_{qu}Y & T^{-1} & 0 \\ C(AQ+BY) & 0 & I-CB_{p}T^{-1}B_{p}^T C^T \end{bmatrix} \geq 0 $$

where,

 * T = $$\begin{bmatrix} t_{1}I_{n_1} & & & \\ & t_{2}I_{n_2} & & \\ & & \ddots & \\ & & & t_{r}I_{n_r} \end{bmatrix} \geq 0 $$

Conclusion:
The state feedback matrix F in the control law $$u(k+i|k) = Fx(k+i|k), i \geq 0$$ that minimizes the upper bound $$ V(x(k|k)) $$ on the robust performance objective function at sampling time $$ k $$ is given by :

 * $$ F = YQ^{-1} $$

where $$ Q > 0 $$ and $$ Y $$ are obtained from the solution of the above LMI.


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Lombard/Adverbs and adverbial locutions

Adverb and adverbial locution of manner
Under the influence of Italian language, a class of adverbs of manner has established itself, formed from the root of the adjective followed by the ending -ament: In other cases, there are some periphrases: However, there are also cases of adverbs typical only of Lombard: Adverb locutions are also widespread:
 * giustament = rightly, justly
 * a la svelta = quickly
 * inevid: reluctantly, unwillingly
 * adasi: slowly
 * a bellasi: slowly
 * in genoggion: kneeling, on one's knees
 * a tomborlon: tumbling down
 * de balosset: cunningly
 * de cativ: badly
 * adasi adasi = very slowly

Interrogative adverbs of place
Used for the construction of the interrogative sentences about the site/location/place.

 * Note

Adverbial locutions of place

 * Note

Interrogative adverbial locutions of place
Used for the construction of interrogative sentences and dubitative sentences

Adverbial particle "ghe"
►►► see ►►► Adverbial particles

Adverbial locutions of time
Usage for interrogative sentences

Adverbs of addition
These words, within the sentence, depending on how they are used, can also play the role of copulative conjunctions

Adverbs of evaluation
Other expressions: sigura de sì= yes of course
 * Note

Negating adverbs
Also nananmò - and its dialectal variants - (not yet) and mai (never) are negating adverbs.

* the use of negative adverbs is explained here and here.

 * Note

Interrogative adverbs
►see►►► Direct interrogative sentences

title: Lombard/Adverbs and adverbial locutions


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User talk:2402:3A80:1640:F868:791F:7575:745:AA6A

Dec 2022
Xeverything11 (discuss • contribs) 11:42, 2 December 2022 (UTC)


text:
User talk:120.29.98.232

Dec 2022
Xeverything11 (discuss • contribs) 12:54, 2 December 2022 (UTC)

title: User talk:120.29.98.232


text:
User:Pagers

I joined Wikipedia in September 2022, and the Wikibooks in October 2022.

title: User:Pagers


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LMIs in Control/Click here to continue/Applications of Non-Linear Systems/LMI-based State Feedback Design for Quadcopter Optimal path control and Tracking

Introduction
An LMI-based  state  feedback  approach  that  ensures optimum  path  tracking  and  improved  steady  state performance  of  a  quadrotor  in  both  translational  and rotational movements.

Quadcopter Dynamics
The motion of Quad Copter in 6DOF is controlled by varying the rpm of four rotors individually, thereby changing the vertical, horizontal and rotational forces.

 * ASSUMPTIONS:
 * 1) The structure is symmetric, thus the inertia matrices are diagonal.
 * 2) The center of mass corresponds to the origin of the physical coordinate system.
 * 3) A quadcopter is a rigid body.

State Space Representation

\begin{align} \dot x(t)&=Ax(t)+Bu(t)\\ y(t)&=Cx(t)+Du(t)\\ \end{align}$$

where x(t) is state vector, y(t) is output vector and u(t) is Input or control vector.

$$ \dot x(t)=\frac{d}{dt} x(t) $$
 * A is the system matrix
 * B is the input matrix
 * C is the output matrix
 * D is the feed forward matrix

Quadcopter modelling with 6 degree of freedom

 * REQUIRED 12 STATES:

The state vector x is $$ x^T= $$ $$ \begin{bmatrix} x & y  & z  & x' & y' & z' & \phi & \theta & \psi & \phi' & \theta' & \psi' \end{bmatrix} $$

The Input matrix u is, $$ u^T=$$$$ \begin{bmatrix} U1 & U2 & U3  & U4 \end{bmatrix} $$, where

 * U1 is the Total Upward Force on the quadrotor along z-axis ( T-mg)
 * U2 is the Pitch Torque (about x-axis)
 * U3 is the Roll Torque (about y-axis)
 * U4 is the Yaw Torque (about z-axis)

The Output matrix y is $$ y^T=$$$$ \begin{bmatrix} x & y & z & \phi & \theta & \psi \end{bmatrix} $$

The State differential equations written in matrix form as,

$$ \begin{bmatrix} x'\\ y'\\ z' \\ x''\\ y''\\ z''\\ \phi'\\ \theta'\\ \psi'\\ \phi''\\ \theta''\\ \psi''\\

\end{bmatrix}$$     = $$ \begin{bmatrix} 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & -g & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & g & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \end{bmatrix} $$ $$ \begin{bmatrix} x\\ y\\ z \\ x'\\ y'\\ z'\\ \phi\\ \theta\\ \psi\\ \phi'\\ \theta'\\ \psi'\\

\end{bmatrix}$$ + $$ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \frac{1}{m} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & \frac{1}{l_{x}} & 0 & 0 \\ 0 & 0 & \frac{1}{l_{y}} & 0 \\ 0 & 0 & 0 & \frac{1}{l_{z}} \\ \end{bmatrix} $$$$ \begin{bmatrix} U1\\ U2 \\ U3 \\ U4 \end{bmatrix} $$

The above martices represents the equation $$ x'=Ax+Bu$$

$$ \begin{bmatrix} x\\ y\\ z \\ \phi\\ \theta\\ \psi\\\end{bmatrix} $$=$$ \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ \end{bmatrix} $$$$ \begin{bmatrix} x\\ y\\ z \\ x'\\ y'\\ z'\\ \phi\\ \theta\\ \psi\\ \phi'\\ \theta'\\ \psi'\\

\end{bmatrix}$$+$$ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{bmatrix}$$$$ \begin{bmatrix} U1\\ U2 \\ U3 \\ U4 \end{bmatrix} $$

The above martices represents the equation $$ y=Cx+Du$$

LMI
$$ \begin{bmatrix} PA^T-W^TB^T+AP-BW+\mu^2\delta & -PA^T+W^TB^T-DP & I \\ PD^T-AP+BW & D^TP+PD & -P \\ I & -P & -\delta I \\ \end{bmatrix} <0 $$

 * $$K=WP^-1$$

Solving the above LMI yields the unknown coefficients of the feedback control. The system will be then asymptotically stable and path track will be achieved.

Conclusion
This LMI can be used to analyze the state feedback control and path tracking of a quadcopter.

Implementation
This LMI can be used in a problem and can be solved using the solvers like Yalmip,sedumi,gurobi etc,.


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Using Chrome/Extensions

Extensions are small add-ons that add new functionality to Chrome. Extensions can be downloaded from Chrome Web Store.

What can extensions do
Extensions can add anything from a toolbar button to a completely new feature. They allow the browser to be customized to fit the personal needs of each user, if they need additional features, while Chrome proper remains relatively unadorned.

Many links herein will not necessarily point to a specific extension, but rather to general links at the Chrome Web Store.

title: Using Chrome/Extensions


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Talk:Lombard/Prepositions and prepositional locutions

Translated from
This page was translated from https://it.wikibooks.org/wiki/Lombardo/Preposizioni_e_locuzioni_preposizionali on 2 December 2022 Gat lombard (discuss • contribs) 15:58, 2 December 2022 (UTC)


text:
Basics of fine-art photography/Creating works in abstract photography

Abstract photography is a genre that is the art of displaying a visual image that has no direct connection with objective world.

General information
Abstract photography, also known as non-objective photography, replaces the usual dogma of image recognizability by offering a kind of unreal image instead. A fragment of the natural scene is isolated in order to hide the original context from the viewer. Works in this genre are deliberately staged, demonstrating a seemingly fantastic combination of objects. The effect is achieved with the help of lighting solutions, shades, shadows, and textures; the goal pursued is to convey a feeling, sensation, or other impression.

This genre is based on the perception of form, color and lines (rather than the details and objects characteristic of a conventional image). Proponents of creative direction, abstracting from patterns and stereotypes, moving away from the standard representation, visually transfer the viewer to the world of strange, mysterious images.

Ways of implementation
You can create an abstract image using a standard set of photographic equipment — camera, darkroom, computer; or by direct manipulation of film, paper and other media, including digital ones.

The ability to think outside the box is important, combining an artist and a surrealist; to see a hidden mean in object that is featureless at first glance.

The photographs presented on this page were created by the author in 2022 (based on available material) specifically for Wikibooks and have not been previously published.


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A Latin Reader

This is a collection of Latin dialogues, histories, stories, and readings on the natural sciences composed to aid learners in acquiring an easy facility in reading Latin both classical and post-classical. It is strongly advised that these readings not be used for translation exercises, but for sight-reading.

Dialogues

 * 1) Greetings
 * 2) De Familia Sophiae

Stories

 * 1) De Rege Gilgamesh
 * 2) De Bellis Magorum

title: A Latin Reader


text:
User:Michael A Champagne/sandbox

Haec est pyxis arenae.

title: User:Michael A Champagne/sandbox


text:
User:Michael A Champagne

I write in Latin.

title: User:Michael A Champagne


text:
A Latin Reader/Dialogues/Greetings

Colloquium Primum
Personae: Aurelia, Sophia

Aur: Salve, Sophia!

Sop: Salve similiter, Aurelia!

Aur: Ut vales, amica?

Sop: Bene valeo, ut vales tu?

Aur: Bene valeo!

Colloquium Secundum
Personae: Paulus, Petrus

Pau: Salve, Petre!

Pet: Salve similiter, Paule!

Pau: Ut vales, amice?

Pet: Male valeo, ut vales tu?

Pau: Bene valeo. Spero te melius valiturum.

Pet: Gratias, et ego hoc spero.

Colloquium Tertium
Personae: Maria, Johannes

Mar: Salvus sis, mi care Johannes!

Joh: Et tu salva sis, carissima! Usque valuisti?

Mar: Sic valeo ut nunquam melius!

Joh: Gaudeo tua causa.

Mar: Quid tu? Valesne?

Joh: Quam optime mihi est!

title: A Latin Reader/Dialogues/Greetings


text:
Talk:A Latin Reader

The Purpose of this Reader
The purpose of this reader is to collect a large amount of easy reading material for learners who have already completed their introduction to Latin. The readings here assume the reader is familiar with all the basic structures and grammar of the language, but do not seek to imitate the complex style of genuine Latin authors.

It is meant to be, in other words, a library of readings Roman children might have found accessible, and which will be useful to adult learners. Michael A Champagne (discuss • contribs) 19:29, 2 December 2022 (UTC)

A Note on Style
This book is written using Ramist orthography for the sake of clarity.

 * 1) The vowel U is distinguished from the consonant V. This prevents confusion in words such as volvi and volui, conserui and conservi, and salui and salvi.
 * 2) The vowel I is distinguished from the consonant J. This makes clear the phonological difference between et jam and etiam, between iens and jentaculum, between Januarius and iambus.

Michael A Champagne (discuss • contribs) 23:49, 2 December 2022 (UTC)

title: Talk:A Latin Reader


text:
User:Naric12/sandbox

Kindred
Dehumanization, although a concrete historical fact, is not a given destiny but the result of an unjust order that engenders violence in the oppressors, which in turn dehumanizes the oppressed -Paulo Reglus Neves Freire Pedagogia do oprimido (Pedagogy of the Oppressed) 1968

Text
Octavia E. Butler's Kindred is a science fiction novel published in June of 1979 about an African American woman named Dana in the year of 1976 who time travels to the year 1800 to the time of her great great great grandfather Rufus Weylin. Rufus is the son of plantation owner Tom Weylin. By necessity, Dana lives in that time as a slave and so meets a variety of other slaves such as Alice Greenwood (who was born a freewoman and lost her freedom helping a slave escape), Sarah the cook, Nigel, Rufus’ personal slave and Carrie, Nigels wife. All of whom are trying to make the best of their situations under slavery.

Analysis
The novel depicts slavery as a separation between oppressor and the oppressed showing its use to thwart and discourage any attempt on that of those who are oppressed from ever being truly free from their oppression. And while it does that. it also dehumanizes the oppressors to the point of making it so that they can't ever see or understand humanity in those that they oppress. This dehumanization is shown in the book as something that cannot be surpassed. While separating the oppressor and the oppressed, slavery also serves to bind those who are oppressed into a union, where they all support and relate to one another and create a community in order to survive their troubles as they live lives as slaves. This community is one that while created under the horrid conditions of slavery is a one that is strong and worthy of commendation.

Separation of the oppressor and oppressed
To begin, the book deals with the subject of slavery as a method to keep the classes of slave and master separate. This can be shown when Dana reports on how Tom Weylin, the slavemaster and owner of the Weylin plantation, whips a slave for–as Tom perceives it–having talked back to him:

Weylin ordered the man stripped naked and tied to the trunk of a dead tree. As this was being done—by other slaves—Weylin stood whirling his whip and biting his thin lips. Suddenly, he brought the whip down across the slave’s back. The slave’s body jerked and strained against its ropes…It drew blood and screams at every blow. I watched and listened and longed to be away. But Weylin was making an example of the man. He had ordered all of us to watch the beating—all the slaves. (Butler 41)

The example set forth by Tom’s whipping was that the slaves were not above being made a spectacle for any (perceived) reason, that they are not people protected by rights, that they only live by the will of their master. By making other slaves undress and tie this man to a tree and then making those slaves witness this man being beaten so viciously and severely, so plainly and easily without remorse, Tom Weylin asserts his power, over not just the man being whipped but over all the slaves. Making them watch forces them to learn they are helpless, and, most importantly, they learn their place in the hierarchy. They learn that they are beneath Tom. Forcing other slaves to become shameful cohorts compliant in the abuse of one of their own also makes the slaves feel even more helpless and worthless.

Tom also uses violent force to thwart any progress made by any slave that could inch them closer to him. When he catches Dana with an old spelling book, he drags her outside and whips her sick, to the point of her convulsing in her own vomit as he screams at her, “didn't I tell you I didn't want you reading!” (Butler 106). Tom cannot read well and the idea of a slave being able to read well compared to him would put him beneath a lowly slave in his mind. Should one best him in such an important aspect as being educated, then who knows what else they could best him in?

In other attempts to keep the relationship of slave and master unbreakable, Tom and his son catch Dana during her attempted escape from the plantation, knock her out cold and then strip her, tie her up so she cannot defend herself, and then beat her into a stupor so strong she was unaware of the events that happened after and only able to focus on the pain of being beaten and battered. All of this was done to discourage any further escape attempts. In punishing Dana, Tom directly enforces his will over her so that she may never escape from his grasp. He wants the beating to be something she fears if she were to ever think of escaping again.

Through the characterization of Tom’s son, Rufus Weylin, Kindred makes clear that this white supremacist oppression dehumanizes both the slave and the slave owner. Rufus sometimes seems desperate to escape his inevitable role in oppressing the people he loves, which makes him a monster in their eyes. For example, he laments and excuses his rape of Alice by blaming her for his behavior: “I wouldn't have to hurt [Alice] if she hadn't just kept saying no” (Butler 123). Rufus is utterly unfamiliar with the idea that he could love a woman without needing to have her, that he would have to respect her feelings about the idea of loving him. He is incapable of loving her without thinking she has to be his, making him devoid of empathy towards Alice. He wants to love her but he can’t do it without making her his own. Tom understands this inescapable divide between slave and slave master when he tells Rufus that he is “going to have to whip [Alice] sick again to get what you want from her” (Butler 161) after Alice has recuperated from the traumatic wounds inflicted by hunting dogs as she escaped Rufus after the rape.

Rufus doesn't protest at all about what his father is telling him because there's no other choice to make a woman who doesn't love you obey you. Rufus understands that he can't love Alice as a wife and she won’t love him as a husband, not unless under the immediate threat of being whipped or sold. Still, Rufus is unrelenting in his chase to make Alice his, and doesn't have any level that's too low to stoop to in order to get what he wants, as he tells Dana after she is reluctant to help him convince Alice to have sex with him willingly: ”I'll have her whether you help or not. All I want you to do is fix it so I don't have to beat her, you're no friend of hers if you won't do that much!” (Butler 164). Not only is he forcing Alice under the threat of violence but he is guilt tripping Dana to help. Here he is thinking he's offering her the most amicable solution to the situation but Dana and Alice are both being hurt here. He wants Alice to love him and he won't tolerate Alice being anything else but his lover. Doing this only causes Alice to suffer and Dana is bound to live with her guilt, further dehumanizing himself in their eyes.

Slavery, albeit a horrid institution, does result in some form of community, though at first that community seems to be merely an introjection of the roles imposed by the slave master.

Community from slavery
Butler shows this community created by slavery by using some slave children playing pretending to be slaves at a slave sale with one another. When one child says that another slave child is worth 200 dollars, they reply that they’re worth more than 200 dollars to which the first child leads with: “You ain’t supposed to say nothing. When Marse Tom bought Mama and me, we didn’t say nothing”(Butler 99). The child speaking here has accepted his life as a slave and is even trying to find fun in being someone who buys slaves. They’ve integrated being slaves in their games and playing with the other slave children this way shows a common ground they all share with each other. Within the novel Butler often shows examples of slaves trying to make the most out of their lives and fostering a community. Many try to lessen the indignity of living as a slave. Sarah, for instance, has lost many of her children to the slave trade and as a consequence has accepted her situation out of fear. As the Weylin’s cook, she is considered the “mammy” of the Weylin plantation, and as such she is resented by some of the slaves. even though she tries to keep them out of trouble by giving them chores that need to be done. Unfortunately, her orders sometimes get ignored by those who would rather not do any labor, so Sarah fears that “[i]t'll get them the cowhide if they don't” (Butler 144). It is clear she is not doing this for the owners of the plantation but for the slaves’ own sake. She’s protecting her community here with no real gain or consequence happening to her if she did not keep each slave working.

The community that is fostered under slavery’s oppression is so strong that anyone that goes against the freedom of a fellow slave is punished. Alice, Carrie and Tess (who is also a slave) severely beat down a slave for thwarting Dana’s attempt to escape the plantation.

We let her know what would happen to her if she didn’t. Now she’s more scared of us than of Mister Tom”(Butler 179). Both Alice and the other slaves have nothing to gain by protecting Dana, but they understand, just like all the other slaves, that the desire to escape is one that they all share. They believe that if any of them were to run that the rest of the slaves would want them to make it to the North to be free. It's a sentiment shared by the community and because of that anyone who inhibits someone's attempt to be free is an enemy. A community who wants nothing more than the safety and even freedom of other members of said community regardless of what they gain is a true community.

The novel Kindred shows that slavery is a institution that separates slave and slave owner into two distinct experiences so that one can never really relate to the other dehumanizing both the slave and the slave owner and serves as a barrier from either class breaking free from their roles. In 1852, American social reformer, abolitionist and writer Frederick Douglass, spoke of slavery’s existence in the newly independent colonies as turning the humanity of those who benefit from it into a lie. Its grip was strong upon even those who tried their damnedest to escape. But although the separation between slave and master existed, it resulted in a community that is unified and  hardened by its far-reaching influence.

Further reading/ Further learning

 * Frederick Douglass, “What to the Slave is the Fourth of July?”
 * Ta-Nehisi Coates (2015)--We were eight years in power
 * The Origins of Modern Day Policing
 * The New York Times Magazine The1619 Project:
 * Yale University’s Legacies of American Slavery

title: User:Naric12/sandbox


text:
Basics of fine-art photography/Self-portrait

Self-portrait is an image by the author of himself, in this case with the help of a camera. Can be considered as a separate genre, or (more precisely) a subgenre of portrait photography.

General information
The term self-portrait was originally conceived, refer to an artist's own portrait.

In relation to capturing oneself with a photographic apparatus, the word "selfie" has been relatively recently introduced, formed by the abbreviation of the term "self portrait" for a simplified pronunciation in colloquial speech.

However, if regarding to the work of artist, the concept of "self-portrait" indicates that the result belongs to art; “selfie” does not mean a work created as an art object (or with a claim to something creative), but is only an image of the owner of a camera or smartphone (tourist, vacationer, beachgoer, etc.) made by him with outstretched hand or using a special stick. Such photographs are created for commemorative (family) albums; publications in social networks; memories of tourist trips, vacations abroad and are not related to concept, the basics of which are covered in this textbook.

Ways of implementation
In order to make an exposure-quality, artistically portrait of yourself, preparatory steps will be required. Initially, you need to decide on the idea: what your portrait will mean, for what purpose it is conceived. Take a look at some examples:
 * Self-portrait made for the textbook "Hobo Tourism Journalism", where the author is depicted with a notebook, pen and backpack, and it's symbolic;
 * A variant created in the genre of photoart to illustrate a literary miniature is a staged work corresponding to the text content.
 * The sample of stylized self-portrait for the book "Afghan Prisoner": it is forbidden to take a pictures in places of detention, a self-portrait was made upon returning from the expedition and placed on the inside cover page

Equipment
You can create a self-portrait using a tripod (if the camera is voluminous and heavy) or a clamp (if using a compact camera). It is easy to do without these accessories, following the example of the author, who is a supporter of hobo tourism (where lightweight equipment is used), for this you need to find a level support for the camera — a stump (in the forest), a parapet (in the city), a large stone or boulder (on sea or ocean coast), then set the built-in timer to the maximum time and move away, taking the required position. Modern digital technology, unlike analog (film) cameras, allows you to make an unlimited number of takes, removing unsuccessful options.


text:
A Latin Reader/Stories/De Rege Gilgamesh

The following is a version of "The Epic of Gilgamesh." This ancient story comes to us from Mesopotamia, where it was transmitted orally in both Sumerian and Akkadian cultures prior to being recorded in writing. The influence of this story is felt not only in the later Homeric texts, but also in the Hebrew Bible.

Capitulum Primum
Olim fuit rex cui nomen erat Gilgamesh. Hic autem rex nequaquam bonus fuit. Gilgamesh enim oderunt omnes cives qui urbem Uruk incoluerunt. Gilgamesh filias cepit ante nuptias earum ut eas vi comprimeret. Filios autem et occidit Gilgamesh, et coegit eos strenue laborare.

His rebus turbati, quidam cives deos oraverunt ut aliquid facerent aut auxilium ferrent. Di has orationes exaudiverunt, et novam creaturam creaverunt: Enkidus. Hic fuit homo quasi monstrum, nudus, fortis, ferox, cui nulla virtus nisi saevitia. In omnibus autem rebus fuit par atque aequalis Gilgamesh.

Enkidus per silvas et campos errabat cum eum intuitus est venator. Hic venator deum oravit: Shamash, qui fuit deus solis. Hoc dixit venator Shamash: "O magne Shamash, deus solis, oro ut me adjuves. Monstrum per silvas errat, nudus, pilosus, ferox. Hoc monstrum laqueos meos evertit, neque possum bestias capere. Fac, mi domine, ut hoc monstrum obtruncetur."

His orationibus auditis, nolens destruere Enkidum quem modo creaverant di, Shamash meretricem conduxit ut cum Enkidu coiret, et eo modo eum ad humanitatem vocaret. Haec meretrix cum Enkidu coiit, et factus est Enkidus sicut vir. A muliere in castra ductus, Enkidus mores humanos discere coepit.

Capitulum Secundum
Ubi ductus est Enkidus in castra, coepit discere mores humanos. Vestes gessit, cibum coctum edit, collocutus est cum sociis suis. Cum circum flammam ederent Enkidus et socii sui, quidam vir questus est de Gilgamesh. "Pessimus est omnium regum, immo omnium hominum. Nos aedes et templa aedificare cogit, morimur laboribus, atque uxores nostras ante nuptias vi compremit. Quis pejor rex in mundo inveni potest?"

Cum Enkidus audivisset hanc famam, iratus est valde. "Hujus scelesti hominis facinora non patiar! Gilgamesh ego occidam. Nunquam posthac compremet uxores vestras, neque coget vos frustra laborare." Progressus est ergo ad Uruk.


text:
A Latin Reader/Dialogues/De Familia Sophiae

Personae: Sophia, Petrus

Pet: Salva sis, Sophia.

Sop: Salve similiter, mi Petre. Suntne omnia prospera tibi?

Pet: Bene mihi est. Quid tu?

Sop: Valeo quidem, sed frater meus valde aegrotat. Timeo ne ipsa aegrotare incipiam.

Pet: Curandum est ergo ne visas eum.

Sop: Recte mones, sed quam difficile est cognatos nostros non visere.

Pet: Quot habes fratres et sorores?

Sop: Haha, bene rogas. Mihi sunt tres sorores et duo fratres.

Pet: Quam magnam familiam! Beati sunt parentes vestri.

Sop: Beati quidem sunt. Cum puella essem, nunquam tacita fuit domus nostra. Sed cognatos meos diligo magno amore.

Pet: Inde fit ut difficule sit fratrem aegrotantem non visere.

Sop: Recte dicis. Sed mox ad valetudinem revocabitur. Deinde, eum visam. Bene valeas, Petre!

Pet: Et tu cura ut quam optime valeas!


text:
A Latin Reader/Stories/De Bellis Magorum

This story comes from Finland, and describes the northern lights, as well as two traditional characters in Finnish myth: Nischergurgje and Schlipme.

De Bellis Magorum
TAX TAX TUX TAX! Audite Niscergurgium!

Longe procul in Lapponia, quae terra plena est magis, longe ultra circulum arcticum, sub bruma est semper, et semper est nox. Sed qualem noctem!

Tranquillum est. Micant stellae in caelo sereno et splendet operiens campos et silvas et valles nix. Lacos et rivos tenet frigor.

Ecce! Lucent in caelo aurorae clarae! Rubrae, flavae, roseae, errant sub stellis huc et illuc, virides, violaceae, caeruleae trans caelum saliunt luces!

Et pueruli Lapponiae ubi plurimi magi, quae mysteriis plena est mysteriis capti sunt. Auroram intuentes aures intendunt ut tympana audiant magica, dicentes:

"Ecce! Pugnant bellatores!"

Olim e paludibus glacialibus egressus est Niscergurgius tympana pulsans carminaque canens magica, cum consedit sub pino ut animum relaxaret, et cenam suam carnem cervi coqueret.

Cum autem cenam coqueret, crepitum de arbore audita est. Sursum intendit oculos, et faciem vidit Sclipmi illius scelesti magi Scelestioris Lunae Filiae filii.

Cito cecinit carmen Niscergurgius, ceciditque ad terram Sclipmus.

"Impie Sclipme!" clamavit magus magnus, "Serve scelestae Lunae Filiae! Cui os curvatum! Cui labra semper mala dicentia! Ecce! Carmen meum omnem potestatem tuam arripuit abs te!"

"Niscergurgi!" inquit sceleratus magus, "Adhuc potestatem retineo, vocare queo manes Lunae qui te interficiant!"

Dein stetit Sclipmus et cecinit carmen, et carminis potestate crevit in immensum, et manu sua tenuit clavam ingentem.

"Molam te in tam subtilem quam nix farinam!"

Respondit autem Niscergurgius, "Ecce! Audi carmina mea!"

Cecinit et Niscergurgius, et ipse etiam crevit in immensum, et celsior fuit Sclipmo. Altissima cacumina umbrosorum pinorum vix ad genua ejus tetenderunt, cacumina montium vix ad medium corpus. Inter nubes fuit pectus, tetigit lunam frons, oculi solem intuiti sunt.

"Furatus es meam potestatem!" clamavit scelestus Sclipmus.

Mutati sunt inde ambo in nubes atrae, et in invicem ruerunt. Acris fuit pugna. Strepitus auditus est. Caelum obscurum fuit.

"Iterum potestatem furatus es meam!" clamavit Sclipmus.

Iterum mutati sunt ambo in cervos ingentes, quibus cornua ferrea. Pugna acris fuit. Silvae sonabant fremitu eorum. Terrae motus fecerunt ungulae eorum.

Tandem defatigatus est malus magus, et se mutavit in colubrum grandem, sed Niscergurgius quoque serpens factus est, et amplexi sunt invicem, et conati sunt invicem veneno occidere.

Subito factus est Sclipmus avis ingens, et Niscergurgium adhuc serpentem despexit de alto. Sed et Niscergurgius se mutavit in aquilam, et consecutus est Sclipmum, et ungulis cepit eum, et traxit eum ad terram.

"Nunc omnem furatus es meam potestatem!"

Cruentus mortuus est Sclipmus, corpusque ejus in terram mersus est.

Ad pinum reversus est Niscergurgius ut tympana sua pulsaret et cenam suam coqueret.

Super caput suum luxerunt in caelo aurorae clarae. Rubrae, flavae, roseae, erraverunt sub stellis huc et illuc, virides, violaceae, caeruleae trans caelum saluerunt luces.


text:
Talk:A Latin Reader/Stories/De Bellis Magorum

Not out of scope
This is a Finnish myth on the origins of the northern lights. As a story in Latin, it is inside the scope of the project, which is to give reading material in Latin. Michael A Champagne (discuss • contribs) 01:33, 3 December 2022 (UTC)


text:
Saluto, Jonathan! (Ido)/Chapitro 8

Iniciala pagino – Chapitro 7 – Chapitro 8 – Chapitro 9

Okesma chapitro
Nun Jonathan sidas en la granda veturo kun la duktisto. La duktisto parolas ecelente per la Germana: “La nokto esas kolda, mea Herr (siorulo). Yen brandio, drinkajo facita ex pruni. Voluntez drinkar ol, se vu volas drinkar.”

Jonathan ne drinkas. Ma lu pensas ke esas bona, ke lu havas brandio por drinkar. Jonathan vartas e pensas pri la voyajo.

La veturo iras rapide. Pose, la duktisto turnas la veturo (lu turnas ol un foyo). E lu turnas la veturo – du foyi. Quo? Lu turnas la veturo… tre foyi! Lu turnas lo ankorfoye, ed ankorfoye. Jonathan pensas: “Ka ni ne pasas la sama voyo, unfoye ed ankorfoye? Quante stranja!” Ma Jonathan ne questionas la duktisto, qua esas tre granda, e tre forta.

Jonathan questionas su qua tempo esas. Lu vidas sua horlojo. La horlojo montras la tempo: esas dek-e-du kloki. Ah… dek-e-du kloki, esas noktomezo. Jonathan savas ke la personi en Rumania parolis a lu pri noktomezo, pri dek-e-du kloki, e li dicis ke dek-e-du kloki es mala tempo.

Nun Jonathan audas sono, la sono di multa hundi. La sono esas tre granda! La hundi dicas: “Ulu! Ulu!” Yes, la hundi ululas. La kavali ne prizas ke la hundi ululas. Pose Jonathan audas la ululado di volfi. La ululado dil volfi es mem plu granda kam la ululado dil hundi. La kavali vere ne prizas ke la volfi ululas.

La duktisto dicas al kavali: “Esez kalma.” E la kavali kalmeskas. La kavali esas kalmita, e riiras.

Nun Jonathan vidas foresto: lu vidas multa arbori, e savas ke li esas foresto. E lu audas la vento. Anke la vento dicas: “Ulu! Ulu!” Hike en la foresto, mem la vento ululas. Jonathan ne prizas la ululado dil vento.

Nun Jonathan vidas altra kozo: la nivo. Esas vere kolda! On vidas la nivo nur kande esas kolda.

Quon facas la duktisto? Lu duktas la veturo. Lu ne parolas pri la volfi, lu ne parolas pri la monto, lu nur duktas la veturo. Ma ulatempe Jonathan vidas blua flamo, e la duktisto haltigas la veturo ed iras por vidar ol. Plu tarde Jonathan vidas la flami, un foyo, du foyi, multa foyi. Jonathan ne savas quo es la blua flami.

Ulatempe la duktisto haltigas la veturo e iras fore. Nun Jonathan esas sola kun la kavali. Lu vidas la volfi itere. La volfi ne ululas; li esas tacanta. Jonathan vidas la luno, e pensas: “Ube esas la duktisto? Pro quo lu ne venas?” La kavali ne prizas la tacanta volfi.

Vidante la luno, la volfi komencas movar. Jonathan frapas la veturo. Frapante la veturo, lu dicas: “Ube esas vu, duktisto? Adube vu iris?”

Jonathan audas voco; esas la duktisto. La duktisto dicas: “Forirez, volfi!” E la volfi foriras; nun la volfi esas fore e Jonathan ne vidas la volfi. Vidante la movanta veturo, lu pensas: “La duktisto es vere, vere forta.”

La veturo iradas. Nun on ne povas vidar la luno, pro ke esas nubi. Jonathan sidas en la movanta veturo. La veturo iras plu alte, e plu alte. Vidante la nubi, e pensante pri la voyajo, Jonathan nun volas dormar.

Nun Jonathan savas nulo plus. Lu komencas dormar, e ne savas quon facas la duktisto. La dormanta Jonathan ne vidas ke la veturo arivas al kastelo di Dracula.

Verbi kun -nta
Verbi kun -nta esas adjektivi.

 * Jonathan skribas. Me vidas la skribanta Jonathan.
 * Jonathan interesas lu. Lu pensas ke Jonathan es interesanta.
 * La du libri diferas. Li esas diferanta.

Verbi kun -nte
Verbi kun -nte esas adverbi.

 * Vidante la urbo, me pensis ke ol esis tre bela. (= Me vidis la urbo e pensis ke ol esis tre bela.)

Verbi kun -nta e verbi kun -nte
-nta e -nte esas diferanta. Videz:

 * -nta
 * La dormanta Jonathan ne vidis la kastelo. (Jonathan, qua dormis, ne vidis la kastelo.)
 * -nte
 * Dormante, Jonathan ne vidis la kastelo. (Jonathan dormis e ne vidis la kastelo.)
 * -nta
 * La du manjanta viri vidis lu. (La du viri, qui manjis, vidis lu.)
 * -nte
 * Manjante, la du viri vidis lu. (La du viri manjis e vidis lu.)

foyo

 * Me skribis, e pose me skribis, e pose me skribis. Me skribis tre foyi.
 * Lu drinkis la drinkajo. Pose lu drinkis altra drinkajo. Lu drinkis du foyi.

Ankorfoye = un foyo plus

 * Lu drinkis du foyi. Pose lu drinkis ankorfoye. Lu drinkis tre foyi.

on
on = persono, multa personi, me, tu, li, edc.

 * On parolas la Germana en Germania. = La personi parolas la Germana en Germania.
 * On devas ne drinkar en la veturo. = Tu devas ne drinkar en la veturo, personi devas ne drinkar en la veturo.

-ig-
Komparez:

 * La veturo haltas.
 * La duktisto haltigas la veturo.
 * La kavali kalmeskas. (kalmeskar = komencar esar kalma)
 * La duktisto kalmigas la kavali.

Anke esas verbo, igar. On povas dicar, “La duktisto igas la kavali kalma.”

ri-
ri- + verbo = (verbo) itere

 * ridicar = dicar itere
 * rifacar = facar itere
 * riuzar = uzar itere

-ajo
verbo + -ajo = la kozo quan on (verbo)

 * drink·ar → drink·aj·o
 * manj·ar → manj·aj·o

Vortaro

 * adube = ad + ube
 * arivar
 * brandio
 * blua
 * drinkajo
 * duktar
 * ecelanta
 * facita ex
 * flamo 🔥
 * forirar = irar fore
 * foyo
 * frapar
 * haltigar
 * horlojo
 * luno
 * montrar
 * nivo 🌨❄
 * noktomezo
 * nubo ☁
 * nulo = 0 kozi
 * nur
 * pasar
 * riirar = irar itere
 * sama ↔ diferanta
 * sono
 * tacanta
 * turnar
 * ulatempe
 * ulular
 * ululado
 * vento 💨
 * vere
 * volfo 🐺

Iniciala pagino – Chapitro 7 – Chapitro 8 – Chapitro 9

title: Saluto, Jonathan! (Ido)/Chapitro 8


text:
Basics of fine-art photography/Creating works in archaeological photography

Archaeological photography is a genre of photographic art that specializes in displaying the material sources of the stages of human evolution.

General information
This genre has points of contact with scientific, reportage and travel photography. In the first case, shooting is carried out to fix the results of research; in the second — for illustrations of journalistic articles published in the media; in the third - in order to preserve the memories of the visited objects (archaeological areas, the ruins of disappeared civilizations, museum objects, etc.)

Ways of implementation
The presence of a press card, in particular, a document of freelance correspondent of a print edition (which is feasible in the absence of specialized education in this field), opens up the possibility of getting to archaeological sites, allowing you shoot artifacts extracted by specialists from the cultural layer, as well as the process itself. In other cases, you can visit places open to the public. Historical and archaeological objects, as a rule, are protected by the state on whose territory they are located, a fee may be charged for inspection.

Some examples from the textbook author's practice (in ru):
 * The Great Wall of China, unrestored section (China)
 * Uyu Uyu, ruins of an ancient city (Peru)
 * Tia Seu Ancient Mound, the largest and most ancient structure in Oceania (Samoa).


text:
User:Dr. Van's Labyrinth/sandbox

Link to front page of your volume: Themes in Literature/Belonging and Exile

Dr Van's Labyrinth

'''

Welcome to the labyrinth for our post-colonial literature class at LaGuardia Community College, Fall 2022.'''

'''We are calling this volume: Post-Colonial Investigations: J.M. Coetzee and Others. In this course we read and discussed the works of ten different post-colonial writers.'''

'''We began in Australia with an important film about the treatment of Aborigine half-caste children in the early years of the twentieth century. Then we traveled to Haiti to discuss the work of Edwidge Danticat and we learned a great deal about Haitian history (and its current situation) from a series of New York Times articles published in 2022. South Africa was our next destination, for a deep dive into the experience of apartheid (1947-1994). To understand the racial divide, we read a selection from Trevor Noah's Born a Crime.  in-depth study of J.M. Coetzee’s powerful novel, Waiting for the Barbarians, in which ethical dilemmas of individuals in positions of power are exposed and dissected. Coetzee tells us that the novel is about “the impact of the torture chamber on the life of a man of conscience” (“Into the Dark Chamber”). For our final unit, we reflected on ways a kind of “apartheid” persists in the context of gender and social class. We focused on female short story writers including Chimamanda Ngozi Adichie, Bessie Head, Jumpha Lahiri, and Alice Munro. These selections offered intriguing examples of the ways gender codes are their own form of “colonialism.” The noted Coetzee scholar, David Attwell, explains this connection: “The desired, female colonized is well known as a trope of colonial discourse, whether she represents the interior and its material riches, the landscape, or the purely psychic abundance of the unknown.”'''

'''The essays in this Wikibook are the results of student research on these authors. Welcome to our page and feel free to intereact:)'''

Our readings:

"Children of the Sea" and "1937" by Edwidge Danticat

Born a Crime by Trevor Noah

Waiting for the Barbarians by J.M. Coetzee

"Life" by Bessie Head

"The Thing Around Your Neck" by Chimamanda Ngozi Adichie

"Interpreter of Maladies" by Jhumpa Lahiri

"Boys and Girls" by Alice Munro

"Everyday Use" by Alice Walker

title: User:Dr. Van's Labyrinth/sandbox


text:
Cookbook:Breakfast Cereal

Breakfast cereal, sometimes simply called cereal or cold cereal, is a processed and typically ready-to-eat food derived from cereal grains.

Characteristics
Cereal products are typically based on grains like oats, rice, corn, barley, wheat, and more. They are typically supplemented with additional vitamins and minerals, and they may incorporate additional flavorings and sweeteners. The final product is typically dried and crunchy.

Varieties
Modern breakfast cereals tend to fall into one of the following categories. They may also consist of a blend thereof:

 * Flaked: cereal grains that are broken down, cooked, and shaped into flakes
 * Puffed: cooked cereal grains that are expanded using a pressurized chamber
 * Shredded: cereal grains that are cooked, extruded into strands, and dried
 * Granular: formed from cereal grain flour made into a dough, baked, and ground
 * Extruded dough: made from grains cooked into a dough, extruded into shapes, and dried
 * Granola: Usually rolled oats, sweetened and mixed with nuts and dried fruits

Use
Breakfast cereal is usually eaten for breakfast, often with milk or yogurt, and sometimes sweetened or supplemented with fruit and nuts. It may also be eaten for convenience or as a snack. Additionally, many recipes have emerged that use breakfast cereals as an ingredient, such as cookies and bars, breadings, and various snack mixes.

title: Cookbook:Breakfast Cereal


text:
Themes in Literature/Belonging and Exile

 In loving memory of Veronica A. Cover • For Contributors • For Readers • Volume I: Isolation and Community • Volume II: Belonging and Exile • Volume III: Xenophobia and Xenophilia • Contributors • Print version of introductory material

Post-Colonial Investigations: J.M. Coetzee and Others

 * Preface

 * About the authors whose works are discussed in this volume

 * Keys to the Labyrinth

 * Sights for Sore Eyes

 * The Barbarian in a Civilized Society

 * Loss Grants Freedom

 * Waiting for the Barbarians A Guide to Understanding Barbarians

 * Edwidge Danticat’s “1937”


text:
Consociety/Mythology

Mythology and religion can greatly affect a Consociety. For example, a religion which resides in a Theocratic state that believes in a Monotheistic religion's absolute power granting a single person or family line the right to rule will work much differently than a Theocratic state that believes in a polytheistic religion, where each god gives one person or family line their favor might work much more similarly to a Parliamentary Republic, similar to Great Britain's House of Lords. However, this is far the only way that mythology affects a place. For example, some giant pieces of basalt that jut out into the ocean might be considered the stepping stones of the giants, and aren't built on, though perhaps they go to the furthest out stone to pray to the sea god.

title: Consociety/Mythology


text:
User talk:Michael A Champagne

Welcome
Welcome, Michael A Champagne!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. - 🇺🇦 Слава🇺🇦Україні 🇺🇦 Героям🇺🇦Слава🇺🇦 (talk)🇺🇦 20:24, 3 December 2022 (UTC)

title: User talk:Michael A Champagne


text:
Template:Wt/lmo/tut

All dialects

title: Template:Wt/lmo/tut


text:
LMIs in Control/Stability Analysis/Continuous Time/Transient Output Bound for Non-Autonomous LTI Systems

The System
Consider a continuous-time LTI system with a state-space representation of:

$$\dot{x} = Ax + Bu,$$

$$y = Cx,$$

where $$A \in \mathbb{R}^{n \times n}$$, $$B \in \mathbb{R}^{n \times m}$$, $$C \in \mathbb{R}^{p \times n}                               $$ and $$x(0) = x_0$$,

the transient bound on the output can be evaluated with the following LMI.

The Data
$$A \in \mathbb{R}^{n \times n}$$, $$B \in \mathbb{R}^{n \times m}$$, $$C \in \mathbb{R}^{p \times n}                               $$ and $$x(0) = x_0$$.

The LMI:
The Euclidean norm of the output satisfies

$$\lVert y(T) \rVert _2^{2} \leq \gamma^{2} (\lVert x_0 \rVert _2^{2} + \lVert u \rVert _2T^{2}), \forall T \in \mathbb{R}_{+},$$

if there exists $$P \in \mathbb{S}^{p} $$ and $$\gamma \in \mathbb{R}_{++}$$, where $$P > 0$$, such that

 * $$P - \gamma I \leq 0, $$
 * $$\begin{bmatrix} P & C^T \\ * & \gamma I \end{bmatrix} \geq 0, $$
 * $$\begin{bmatrix} PA + A^TP & PB \\ * & - \gamma I \end{bmatrix} \leq 0 . $$

Conclusion
By using these LMIs, the transient output bound can be found for a given non-autonomous LTI system such that if $$x_0 = 0$$ and $$u$$ is a unit-energy input (i.e., $$\lVert u \rVert _2T^{2} \leq 1, \forall T \in \mathbb{R}_+$$), then the preceding conditions ensure that $$\lVert y(T) \rVert _2 \leq \gamma, \forall T \in \mathbb{R}_+$$.

Implementation
The LMI given above can be implemented and solved using a parser such as YALMIP, along with an LMI solver such as SeDuMi, or MOSEK. (For a detailed list of solvers, please visit this page on Relevant Solvers).


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Basics of fine-art photography/Taking pictures of homeless people

Photographing homeless peopleis a sub-genre of portrait photography, where the author depicts people who dont have permanent housing, in their own particular environment.

General information
Officially, such a style, direction, subgenre does not exist - there is no mention of it in photography textbooks and encyclopedic articles, but since there are works related to this topic (see examples below, in the gallery), it can be considered as subgenre of photography, belonging to the "Portrait".

In addition to homeless people, the shoot may include the depiction of down-and-out people who have housing (in ru: бич), as there is often no visual distinction between the former and the latter. In addition to images of homeless people, the shoot may include the depiction of down-and-out people who have housing (in ru: бич), as there is often no visual distinction between the former and the latter.

A photographer who specializes in this sub-genre may be shooting homeless people in the area of his residence (city, region, country), or around the world (like the author of this textbook, combining photography and non-standard travel).

Photography of the homeless is in close contact with straight photography, intersects with street, genre and documentary photography; is often an candid photography.

Ways of implementation
To create a realistic photograph of homeless person, you must use the shooting techniques described in the "Realism" chapter of this textbook.

Combining work in this creative direction with traveling around the planet — in addition to all the genres and styles listed above, you will learn the intricacies of travel photography, and if objects (i.e. homeless people) are captured in situations that suggest reflection, then you will master one more genre — narrative photography.

It's interesting that...

 * In Cuba, India, Bolivia and some other developing countries, it is sometimes difficult to distinguish between person who has a dwelling and a homeless.
 * The author of this textbook, wandering around the globe, himself often looked like a homeless (image). You can get acquainted with the adventures of a hobo tourist in Wikisource by clicking on the link below.

Wikisource

 * Viktor Pinchuk "Notes of an international tramp"


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LMIs in Control/Click here to continue/LMIs in system and stability Theory/General LMI Region D-Admissibility

The System
Consider $$A, E \in \mathbb{R}^{n \times n}$$. The pair ($$E$$,$$A$$) is D-admissible if it is regular and causal, and the eigenvalues of ($$E$$,$$A$$) lie within the LMI region D of the complex plane, which is defined as

$$D = \{z \in \mathbb{C}: f_D(z) < 0}\$$, where

                                                               $$f_D(z) := \Lambda+z\Phi + \bar z\Phi^T = [\lambda_{kl}+\Phi_{kl}z+\Phi_{lk} \bar z]_{1 \leq k, l\leq m},$$

$$\Lambda \in \mathbb{S}^m, \Phi \in \mathbb{R}^{m\times m}$$, and $$\bar z$$ is the complex complex conjugate of $$z$$.

Conditions
The pair ($$E$$,$$A$$) is D-admissible if and only if any of the following equivalent conditions are satisfied.

 * 1) There exist $$P \in \mathbb S^n, S \in \mathbb R^{(n-n_e)\times (n-n_e)},$$ $$U, V \in \mathbb R^{n \times (n-n_e)},$$ where $$n_e = $$  rank$$(E), \mathcal R(U)=\mathcal N(E^T), \mathcal R(V)=\mathcal N(E),$$and $$P>0,$$ satisfying   $$[\lambda_{kl}EPE^T+\phi_{kl}E^TPA^T+AVSU^T+US^TV^TA^T]_{1 \leq k,l \leq m}<0,$$
 * 2) There exist $$P,Q \in \mathbb S^n,$$ where $$P>0,$$ satisfying $$E^TQE \geq 0$$ and  $$[\lambda_{kl}EPE^T+\phi_{kl}APE+\phi_{lk}E^TPA^T+A^TQA]_{1\leq k,l\leq m}<0,$$
 * 3) There exist $$P \in \mathbb S^n, S \in \mathbb R^{(n-n_e)\times (n-n_e)},U \in \mathbb R^{n \times (n-n_e)},$$ where $$n_e=$$ rank$$(E),UE=0,$$ and $$P>0,$$ satisfying $$[\lambda_{kl}EPE^T+\phi_{kl}APE+\phi_{lk}E^TPA^T+A^TU^TSUA]_{1\leq k,l\leq m}<0,$$
 * 4) There exist $$P \in \mathbb S^n, S \in \mathbb R^{(n-n_e)\times (n-n_e)},$$$$U, V \in \mathbb R^{n \times (n-n_e)},$$ where $$n_e=$$  rank$$(E), \mathcal R(U)=\mathcal N(E^T), \mathcal R(V)=\mathcal N(E),$$ and $$P>0,$$ satisfying   $$\Lambda \otimes EPE^T+\Phi \otimes (APE)+\Phi^T\otimes (EPA^T)+1_{mm} \otimes (AVSU^T+US^TV^TA^T)<0,$$ where $$\otimes $$ is the Kroenecker product and $$1_{mm}$$ is an $$m \times m$$ matrix filled with ones.
 * 5) There exist $$P,Q \in \mathbb S^n,$$ where $$P>0,$$ satisfying $$E^TQE \geq 0$$ and $$\Lambda \otimes EPE^T+\Phi \otimes (APE)+\Phi^T\otimes (EPA^T)+1_{mm} \otimes (A^TQA)<0,$$ where $$\otimes $$ is the Kroenecker product and $$1_{mm}$$ is an $$m \times m$$ matrix filled with ones.
 * 6) There exist $$P \in \mathbb S^n, S \in \mathbb R^{(n-n_e)\times (n-n_e)},U \in \mathbb R^{n \times (n-n_e)},$$ where $$n_e=$$ rank$$(E),UE=0,$$ and $$P>0,$$ satisfying $$\Lambda \otimes EPE^T+\Phi \otimes (APE)+\Phi^T\otimes (EPA^T)+1_{mm} \otimes (A^TU^TSUA)<0,$$ where $$\otimes $$ is the Kroenecker product and $$1_{mm}$$ is an $$m \times m$$ matrix filled with ones.

Reference
Caverly, Ryan; Forbes, James (2021). LMI Properties and Applications in Systems, Stability, and Control Theory.


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LMIs in Control/Click here to continue/LMIs in system and stability Theory/Circular Region D-Admissibility

The System
Consider $$A, E \in \mathbb R^{n \times n},a,b \in \mathbb R$$ and $$d \in \mathbb R_{>0},$$ where $$b \neq 0.$$ The pair $$(E,A) $$ is D-admissible with $$D={z\in \mathbb C : a+2bRe(z)+d \vert z \vert ^2 <0}$$ if and only if there exist $$X \in \mathbb R^{n \times n}$$ and $$\alpha \in \mathbb R$$ such that $$E^TX=X^TE \geq 0$$ and

The LMI (Constraint)
$$\begin{bmatrix} -aE^TX-b(X^TA+A^TX) & A^TX \\ * & d^{-1}E^TX+\alpha(1-E^\dagger E) \end{bmatrix} >0,$$ where $$E^\dagger$$ is the pseudoinverse of $$E$$. The region D describes a circular region of the complex plane with radius $$r=\sqrt {-a/d+b^2/d^2}$$ centered at $$(c,0),$$ where $$c=-b/d.$$

Reference
Caverly, Ryan; Forbes, James (2021). LMI Properties and Applications in Systems, Stability, and Control Theory.


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Talk:Themes in Literature/Belonging and Exile

Links to texts mentioned in the preface
Dr. X (discuss • contribs) 14:26, 4 December 2022 (UTC)
 * Krik? Krak! https://archive.org/details/krikkrak0000dant_y9v4/mode/2up
 * https://archive.org/details/2019-born-a-crime_201908
 * https://archive.org/details/waitingforbarbar00coet
 * https://archive.org/details/danceofhappysha00munr/mode/2up
 * https://archive.org/details/interpreterofmal00jhum_0
 * https://archive.org/details/thingaroundyourn0000adic
 * The Collector of Treasures https://archive.org/details/collectoroftreas0000head_l2z2/mode/2up
 * https://harpers.org/archive/1973/04/everyday-use/


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Themes in Literature/Belonging and Exile/Preface

Welcome to the labyrinth for our post-colonial literature class at LaGuardia Community College, Fall 2022.

We are calling this volume: Post-Colonial Investigations: J.M. Coetzee and Others. In this course we read and discussed the works of ten different post-colonial writers.

 * "I wanted to live outside the history that Empire imposes on its subjects, even its lost subjects. I never wished it for the barbarians that they should have the history of Empire laid upon them. How can I believe that this is cause for shame?"

We began in Australia with an important film about the treatment of Aborigine half-caste children in the early years of the twentieth century, Rabbit-Proof Fence. Then we traveled to Haiti to discuss the work of Edwidge Danticat and we learned a great deal about Haitian history (and its current situation) from a series of New York Times articles published in 2022. South Africa was our next destination, for a deep dive into the experience of apartheid (1947-1994). To understand the racial divide, we read a selection from Trevor Noah's Born a Crime. Then we began an in-depth study of J.M. Coetzee’s powerful novel, Waiting for the Barbarians, in which ethical dilemmas of individuals in positions of power are exposed and dissected. Coetzee tells us that the novel is about “the impact of the torture chamber on the life of a man of conscience” (“Into the Dark Chamber”). For our final unit, we reflected on ways a kind of “apartheid” persists in the context of gender and social class. We focused on female short story writers including Chimamanda Ngozi Adichie, Bessie Head, Jhumpa Lahiri, Alice Munro and Alice Walker. These selections offered intriguing examples of the ways gender codes are their own form of “colonization.” The noted Coetzee scholar, David Attwell, explains this connection: “The desired, female colonized is well known as a trope of colonial discourse, whether she represents the interior and its material riches, the landscape, or the purely psychic abundance of the unknown.”

The essays in this Wikibook are the results of student research on these authors. Welcome to our page and feel free to interact with us.

Phyllis van Slyck, Professor, Department of English, La Guardia Community College (City University of New York)

Our readings:

 * "Children of the Sea" and "1937" by Edwidge Danticat from her short-story collection Krik? Krak!
 * Born a Crime by Trevor Noah
 * Waiting for the Barbarians by J.M. Coetzee
 * "Life" by Bessie Head from her short-story collection The Collector of Treasures
 * "The Thing Around Your Neck" by Chimamanda Ngozi Adichie from her short-story collection The Thing Around Your Neck
 * "Interpreter of Maladies" by Jhumpa Lahiri from her short story collection Interpreter of Maladies
 * "Boys and Girls" by Alice Munro from her short story collection Dance of the Happy Shades and Other Stories
 * "Everyday Use" by Alice Walker


text:
JavaScript/Closures/Exercises

Topic: Closure

1. Write a script that creates a parameterizable function. It accepts a string that 'decorates' logging information with the given parameter. E.g.:. The script shall internally use a closure.

title: JavaScript/Closures/Exercises


text:
JavaScript/Functions/Exercises

Topic: Functions

1. Define a function with one parameter. The function returns a string starting with "The given argument was: " and ends with ". Ok?". Insert the argument between those two strings.

2. Extend the previous function to handle different data types, e.g., Numbers, Objects, ... . Show the data type into the returned string.

3. Define a function that takes two parameters. The function returns the average of both.

4. Define the function of the first exercise with an arrow function.

5. Define a function that takes an array of numbers as its parameter. The function returns the array's length, the smallest element, the largest element, and the average of all elements.

Because a function can return only a single element, all those computed values must be packed into an array (or an object). This array is the return value.

6. Define a function for describing a car. It takes four parameters: producer, model, horsepower, and color. The first two are mandatory; the last two are optional. Define default values for the last two parameters, e.g., "unknown".

{What is the result?

+ Hello world - Runtime error - None of the above
 * type=""}

{What is the result?

- xxx, xxx, xxx - xxx, ppp, ppp + xxx, ppp, xxx - None of the above
 * type=""}

title: JavaScript/Functions/Exercises


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Basics of fine-art photography/Creating works in humanistic photography

Humanistic photography is a genre that focuses on depicting everyday life of ordinary people, where the author's work directly or indirectly contains optimism, sometimes shades of romance.

General information
The origins of the creative direction is usually associated with France of the 30-ies of the XX century; the peak of popularity, during which the genre spread in Europe and beyond — with the postwar period (1945 - 60s).

Intersects with street, genre and, in part, reportage photography (difference: the latter is aimed at depicting specific events, while humanistic photography is not tied to events and dates). Preference is given to black and white tones. Supporters of this genre can be called "poets of the lens".

Ways of implementation
How to create works in this genre? There is nothing easier! Take a small backpack with essentials, purchase a ticket to any overseas country (preferably from among the poor), which will be the starting point of your route. Attach an inexpensive compact camera to your belt with a spare set of batteries…

The plots are already waiting for you, just need to be in one or another point of the globe in time, deftly get the camera out of the case, point the lens and press the shutter release button. After return a few months later, go through the footage. In the meantime, carefully review works of textbook author, made in different parts of the world.


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Basics of fine-art photography/Creating works in conceptual photography

Conceptual photography is a genre (type, style) of photographic art, where the author develops original (peculiar, unusual) ideas for subsequent implementation in his own works.

General information
The genre has points of contact with staged photography; conceptual works are distinguished by extravagance and unusuality; sometimes there are present elements of surrealism and minimalism.

At the origins of this genre lies conceptualism, a creative movement that emerged in the 1960s, whose proponents argued that an object becomes a work of art not because it has aesthetic values, but primarily due to the desire of the author  (that is, at the artist, in a generalized sense of the word). Probably the first experimental works with a conceptual bent were made much earlier than the period mentioned above.

Conceptual photography is usually staged, but, theoretically, it can be random — when author, seeing a “scene” worth capturing, instantly directs the lens and presses the button.

Step-by-step instruction

 * 1) Mentally create a sketch.
 * 2) Prepare everything that is required to implement the idea: paraphernalia, decoration elements, participants (if any will be involved in the plot), not forgetting the correct location of the light source (s).
 * 3) Make sure that composition corresponds to the set theme and looks aesthetically pleasing.
 * 4) Need a previsualization of the scene, that is, a preview before shooting, rough animation sketches, allowing you to experiment with the arrangement of objects and participants, lighting, camera positioning — to be able to choose the best option.
 * 5) Post-processing also plays a role: elements of different images can be combined into one.
 * 6) The name of a photographic work (also like the title of a book or a movie) should smoothly “glide” along the plot, not revealing the meaning directly.
 * 7) It is important that your work makes the viewer think. The purpose of conceptual art is not to display an idea, but to encourage reflection through photography.

The photographs by the author of this textbook, presented in the gallery, will help you become visually familiar with the topic you are studying.


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LMIs in Control/Click here to continue/Applications of Linear systems/Hinf Optimal Stabilization of a Class of Uncertain Impulsive Systems

H$$\infty$$ Optimal Stabilization of a Class of Uncertain Impulsive Systems

Impulsive Systems are a special class of hybrid dynamical system which contains many abrupt changes of states at some certain time instances. Many examples can be found in finance, engineering, and other disciplines. This LMI addressed the problem of designing a feedback control law such that the uncertain closed-loop system is asymptotically stable, and the H$$\infty$$ norm bound constrains on disturbance attentuation for all admissible uncertainties are satisfied.

The System
The following system is assumed:

$$ \begin{align} \dot{x}(t) &= A x(t) + C u(t) \,\,(1)\\ \end{align} $$

When the system (1) is time-invariant and involves uncertain disturbances and proportional impulsive effects is can be rewritten as seen below in (2).

The Data
The system can then be described as:

$$

\begin{align} \dot{x}(t)   &= A x(t) + B w(t) + C u(t) \,\,\, &t\ne t_{k}\\ \ \Delta x(t) &= d_{k} x(t) &t=t_{k} \\ \ z(t) &= E x(t)\\ \ x(t) &= 0 &t=t_{0}=0 \\ \end{align}

$$

Where

$$x(t) \in R^{n} $$ is the state.

$$u(t) \in R^{m} $$ is the control input.

$$w(t) \in R^{p} $$ is the disturbance input with limited energy.

$$z(t) \in R^{n} $$ is the controlled output.

The LMI
Using the Lyapunov function, Schur Complement, the time-domain expression of the L2-norm, and Parseval's Theorem.

$$ \begin{align} &\quad \varepsilon > 0 \,\,\, \& \,\,\, P>0 \in R^{nxn} \\

&\begin{bmatrix} A^{T}P + PA + P(\gamma^{-2}BB^{T}-\varepsilon^{-2}CC^{T})P & E^{T} \\ E & -I \\ \end{bmatrix} < 0 \end{align}$$

Conclusion:
The goal of this LMI is to provide a state feedback robust H$$\infty$$ optimal control technique for impulsive dynamical systems with time varying uncertainty. Based on a positive definite solution of a linear matrix inequality, the proposed robust H$$\infty$$ static state feedback control law guarantees both internally asymptotical stability and robust H$$\infty$$ optimal performance.