text:
LMIs in Control/pages/systemzeroswithoutfeedthrough

Let's say we have a transfer function defined as a ratio of two polynomials: $$ \begin{align} H(s) = \frac{N(s)}{D(s)} \\ \end{align}$$ Zeros are the roots of N(s) (the numerator of the transfer function) obtained by setting $$ N(s) = 0 $$ and solving for s.The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs. Similarly, the system zeros are either real or appear in complex conjugate pairs. In the case of system zeros without feedthrough, we take the assumption that $$ D=0 $$.

The System
Consider a continuous-time LTI system, $$ G $$, with minimal statespace representation $$ (A,B,C,0) $$

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

The Data
The matrices:

\begin{align} A \in \mathbb{R}^{n \times n} \\ M \in \mathbb{R}^{n \times q} \\ N \in \mathbb{R}^{q \times n} \\ \end{align}$$

The LMI: System Zeros without feedthrough
The transmission zeros of $$ G(s) = C(sI-A)^-1 B $$ are the eigenvalues of $$ NAM $$, where $$ N \in \mathbb{R}^{q \times n}, M \in \mathbb{R}^{n \times q}, CM = 0, NB = 0, NM = 1. $$. Therefore, $$ G(s) $$ is a minimum phase if and only if there exists $$ P \in \mathbb{S}^{q} $$, where $$ P>0 $$ such that

\begin{align} PNAM + M^T A^T N^T P <0 \end{align}$$

Conclusion:
If P exists, it ensures non-minimum phase. Eigenvalues of NAM then gives the zeros of the system.

Implementation
https://github.com/Ricky-10/coding107/blob/master/Systemzeroswithoutfeedthrough


text:
Talk:Issues in Interdisciplinarity 2019-20/Truth in Cults

Discussion page for team members and anonymous contributors
To the intention of all anonymous editors who made or will make a change on this page, If you are editing or deleting something on this Wikibook, such as a reference, sentence or other content, please state why in your log. One of the references we wanted to use got deleted by someone anonymous and we would like to keep all of our references on this sandbox in order to structure correctly our ideas. The least you can do is send a message on this discussion page in order to let us know that you will be deleting something so we can make sure to save it somewhere else. Thanks.

Brainstorming and instructions for writing members STRUCTURE : - Data or facts about cults (showing why it is interesting to work on this) - general definition : Cult is used in reference to a social group defined by its unusual religious, spiritual or philosophical beliefs. Moreover, the people who are part of a cult generally are interested in a common personality, object or goal. The followers live in a community, under the guidance of a charismatic leader worshipping rituals and veneration. To what extent can truth account for the ‘unusual’ aspect of cults in social sciences, law and religion ? - why are the 2 disciplines linked to cults - Outline where the interdisciplinary issue actually is, how does truth create a tension INSTRUCTIONS : - How the issue chosen plays out in 2 disciplines facing a topic - Showing how truth plays a role in 2 disciplines (for ex ; sociology, law, religious) creating a tension in the definition of cults - The tension caused by truth between the disciplines specifically with regarding cults practice
 * In intro, define truth. What is truth? Can truth be found when studying cults, or is there (theoretically) just an 'optimal' definition which most accurately defines cults. Can there be 'truth' in this topic, or are there just a multitude of subjective viewpoints? This could lead to clashes between disciplines upon studying cults.

In Literature Cult Literature -	‘cult’ literature is rarely defined in literary crit. -	Attracting a cult following, attract a particular community of readers ‘independent of their qualifications’ o	JRR Tolkien’s the Lord of the rings, Franz Kafka’s the Castle -	Catcher in the rye as a ‘personal manifesto’ for many in America in the 60’s and 70’s o	Literature embodies the tendencies and beliefs of a group of people -	Deviance from norms to protest- jackkerouac on the road, chuck palahniuk’s fight club o	applies to baby boomers and Generation X

In Psychology
- Psychological effect of terms used, for example, ‘alternative religious movements’, differing definitions of cults relate to individual perceptions on what a cult is. ‘everyone “knows” that cults and satanic cults exist. They have strong negative feelings regarding cults, and even stronger feelings against satanic cults. By contrast, their feelings regarding alternative religious movements, while not being “positive,” are less negative than their feelings towards cults and satanic cults’

Psychological research investigates how cults are formed from the perspective of the individual person and the group dynamics between people in cults. Psychologists have investigated the following questions: What distinguishes a cult from other forms of communities? What distinguishes cults from other What are the psychological characteristics of people who are attracted to cults and of cult leaders? What techniques are used to persuade people to join and stay in cults? What are the long-term psychological effects of being in a cult?

Psychological definitions of cults involve that members (a) have a shared belief system, (b) a high level of social cohesiveness, (c) are strongly influences by the group’s behavioural norms, (d) impute charismatic or divine power to its leaders and (e) are alien and deviant from the values of the culture that the group lives in. Some psychologists have argued that the psychological processes observed in cults are a continuum from those observed in other groups of people. Arthur Deikman compared the thinking patterns relevant for cults to those people use to function in everyday life. He concluded that distortion of perception, biased thinking, and the inoculation of beliefs and values of others, are commonly in everyday life and that these mental processes set people up for behaviours that are typical for cults: dependency on a leader, complying with the group, avoiding dissent and devaluing outsiders. Given that only some people join cults, it is therefore of interest to investigate psychological risk factors. Curtis and Curtis identified a psychological profile of susceptibility including emotional vulnerability, dissociative states, poor family and other support, and periods of high stress. Clark reported that 60% of people who joined cults had a long history of psychological problems beforehand. For the other 40%, aggressive recruitment techniques were identified as a factor.

West highlights that it is difficult to study the psychological techniques used by cults to recruit members and prevent them from leaving as scientists are not allowed into the cult and thus cannot observe the processes directly. Interviews of people who left cults suggest that mind-control techniques, deception and alienation from families and friends are common. Recruitment processes include a mixture of deception and affection. The introduction is gradual and starts with flattery; overpowering techniques such as love-bombing, offering free meals or medicines, flirting. The recruits are then required to unconditionally surrender to the recruiter or cult leader, isolated from other contacts and outside information and subjected to punishment and abusive behaviour modification techniques.

The psychological profile of cult leaders is more difficult to study as these can usually not be interviewed directly. High charisma associated an authoritarian and narcistic personality have been suggested as a common traits. A case study also highlighted an ability to persuade others with pseudo-logic arguments.

People who leave a cult can have long-lasting psychological distress that may require treatment (Clark JG. Cults. JAMA. 1979; 242(3):279-281.). However, the percentages of persons experiencing clinical symptoms vary widely between studies, from 27 to 95%, and depend on the practices of the cult and the duration of involvement.

- Psychological affect of terms used, for example, ‘alternative religious movements’, differing definitions of cults relate to individual perceptions on what a cult is.

-‘Everyone “knows” that cults and satanic cults exist. They have strong negative feelings regarding cults, and even stronger feelings against satanic cults. By contrast, their feelings regarding alternative religious movements, while not being “positive,” are less negative than their feelings towards cults and satanic cults’

- Perception based on whether people have been in contact with cults or asked to join etc. - psychology Studies questions such as why are people attracted to cults? What techniques do cult leaders use to make people stay in a cult? What are the long-term negative psychological effects of being in a cult? -	Easy messages that are not difficult to follow provide people with a conclusive outlook on life: of (one) truth that is definitive to follow in life. -	Affected by low self esteem levels-> those with lower self esteem are more likely to join/ remain in a cult. This is because it is more easy to ‘break down and build back up (those with low self esteem) in an effort to teach them that the cult is the supportive environment they’re looking for’ -	Neurological effect/psychological effect: receiving lots of positive praise -	effect of being in a cult: giving up money, personal possessions, only interacting with other cult members. Achieved through: o	Social isolation – idea that cult members are superior to former friends o	Humiliation/ having to write down evidence of failure and mistakes o	Being fed false experiences and ideas. REPETITION causes these ideas and beliefs to appear more true. o	Making one think that they are not in a cult- > Dr Margaret tala singer argues people don’t understand what a cult is (i.e. it could be something other than a religious group) Who joins cults? Demographic studies - All backgrounds are effected equally (need data for this) -	empirical truth: women 70% of cult members around the globe o	behavioural interpretation/ interpretive truth gives multiple possible social and cultural explanations of behaviour (psychology) David Bromley Virginia university- women attend more social events, so more likely to actively participate in cults. Sociological reason female oppression by man in history- idea of male authority figure, waiting for guidance. - Perception based on whether people have been in contact with cults or asked to join etc. Lukaseelurs (discuss • contribs) 15:16, 7 December 2019 (UTC)

Lukas Ehlers table

Figure 1: Psychological Research on Cults

Lukaseelurs (discuss • contribs) 16:43, 8 December 2019 (UTC)

extra references: Ogloff JRP, Pfeifer JE. Cults and the law: A discussion of the legality of alleged cult activities. Behavioral Sciences & the Law. 1992;10(1):117–40.

https://www.onlinepsychologydegree.info/what-to-know-about-the-psychology-of-cults/

(need to find actual article citation) Author: Ana Sobral. DOI: https://doi.org/10.1163/9789401208512_005.

https://www.researchgate.net/publication/332602954_Opting_out_deviance_and_generational_identities_in_American_post-war_cult_fiction Lukaseelurs (discuss • contribs) 17:10, 6 December 2019 (UTC)

In Anthropology
- Anthropology and archaeology have similar viewpoints, in a descriptive focus on what cults are/ should be: the processes, the material symbolism. Focuses on precise description of the cultural practices of the cult. BUT: archaeology unable to see gestures and actions of individual humans, only material remains. - Colin Renfrew: - anthropology studies ACTIONS in response to religious beliefs, so may disagree with psychology on why the beliefs occur (i.e religious belief and that in the occult or the spiritual). o cults use attention focusing devices, repeated symbols, places with special functions but also : o rituals both public and hidden o gestures and prayer o wealth and resources put into the ritual practice i.e. in sacrificing something - idea of the sacred deeply bound to the cult leaders, e.g. Shaman’s. - debate in anthropology: Levi Strauss argues that there is no such thing as totemism (define)- ‘not a single phenomenon’. The idea that anthropological observation is biased and led in the face of many assumptions and factors. Are our ideas about cults culturally constructed? Types of Cult: - Cargo cult- idea that end of the world is occurring, which you need to prepare for (Captain Cook) - Witchcraft - Shamanism - sacrificial cults - rites of passages in cults - ASPECTS and practices of religion (religious studies intersecting with anthropology) can be deemed as ‘cult-like’ Such features are : o charismatic leaders e.g. David Koresh of the Branch Davidians o 'us versus them' mentality and alienation from others o hierarchy and obedience o violence: Aum Shin Rikyo cult gas attack on Tokyo subway system 1995 - Comparative anthropology or ethnography may help us determine to what extent ‘cult’ is ‘simply used in common parlance or as a controversial term’ for different groups, and to what extent we are really dealing with the cult. o Idea of ‘self and other’ highly debated and studied in social anthropology  These ideas are mirrored in the way outsiders view cults negatively, and the cult members see the cult as ultimate truth or necessity o since we find it hard to determine what exactly are cult is, a comparison of cultures Lukaseelurs (discuss • contribs) 22:45, 7 December 2019 (UTC)

How did we, as a group, contributed to this Wikibook ?
-[14 November 2019 19:08] Created a Messenger group with all team members to coordinate and plan our Wikibook. -[15 November 2019 13:38] First group meeting during the lecture and discussing about studying Power in Global Surveillance, Censorship, and Cults. Billyhf and Lukaseelurs very interested in Cults and Anthropology, Calixta.henrion and Gabrevon on Global Surveillance. -[15 November 2019 14:00] Calixta.henrion created a Google Doc containing our first brainstorming ideas. -[15 November 2019 14:00] Discussing Lukaseelurs reference on Louis Theroux and cults, watching the documentary found by Gabrevon and his case study. -[19 November 2019 12:00 to 14:00] Meeting with Calixta.henrion and Gabrevon in the BASc common room : creating the Wikibook "Power in Public Surveillance, Censorship and cults" -[19 November 2019 13:30 to 14:00] Billyhf added more references on the Google Doc. -[21 November 2019 18:00 to 19:30] Meeting with Billyhf, Calixta.henrion and Gabrevon in the Student Center. Discussing about changing topics after Gabrevon's view on how Power was used as an issue in our topic, and not as an interdisciplinarity issue. We previously did not consider Power at the levels of disciplines, and we were heading in a wrong directions. After agreeing with Lukaseelurs on Messenger and his research on cults through the initial stages we felt it was more relevant to treat truth as an interdisciplinary issue concerning cults. Identifying what different disciplines, such as Sociology, Law, Psychology and Religious Studies consider true or not about cults is a real issue for an interdisciplinary researcher that is more appropriate to the Approaches To Knowledge syllabus than Global/mass surveillance and power. New Wikibook, Truth in Cults is created by Gabrevon. Six tabs are put into place during our meeting "Introduction", "Truth about cults in Sociology", "In law", "In Psychology", "In Religious Studies", "Conclusion" -[21 November 2019 19:30] More content found after borrowing books in the Science Library by Gabrevon -[23 November 2019 14:30] End of the brainstorming -[26 November 2019 16:32] Coordinated and divided works along with the existing tabs ; Calixta.henrion worked on the introduction, the conclusion, and on Sociology. Billyhf worked on Psychology, Law, and on the introduction. Billyhf's contributions were uploaded by other team members. Gabrevon worked on Religious Studies and Law. Lukaseelurs worked on Psychology, definitions, literature, social anthropology, law.. -[1 December 2019 17:09] Lukaseelurs migrated his contributions from the old Wikibook to the new one. New tabs, Psychology, how Anthropology and Literature considers legitimate a cult or not, have been added by Lukaseelurs. Lukaseelurs (discuss • contribs) 16:47, 6 December 2019 (UTC) Notes and paragraphs for distinctions between social anthropology and archaeology, which could combine with sociology, psychology research paragraphs with references, as well as further notes from research on psychology throughout the project was added, all referenced. Work on 'cult' literature, and work on law was also added. Most of this had been on our original wikibooks page that we created, as this new page was not available for Lukaseelurs. See edit history for both. Lukaseelurs (discuss • contribs) 16:47, 6 December 2019 (UTC) -[3 December 2019 15:41] More content, structure and references added by all team members. Started doing the word count. Calixta and Gabrevon will develop the Sociology tab, Gabrevon will reduce Religious Studies and Billyhf and Lukaseelurs reduce Psychology. Law will be edited by all team members during our next meeting. -(6 December 2019 16:57) Looking to cut down the amount of words - introduction has been drastically reduced by Billyhf with help from Gabrevon and Lukaseelurs. Gabrevon (discuss • contribs) 15:41, 5 December 2019 (UTC) - (6 December 2019 17:14) - Discussed individual edits we would make: Calixta.henrion: Sociology refining her work, and adding in Lukaseelurs work on Anthropology and Archaeology as an example of interdisciplinary conflict, Billyhf work on introduction and conclusion. Lukaseelurs shorten and combine his works on psychology and combine with Billyhf paragraph, Gabrevon further working on his religious studies section and combining his and Lukaseelurs contributions on Law. Cutting down wordcount and adding pictures Lukaseelurs (discuss • contribs) 17:21, 6 December 2019 (UTC) Fixed conclusion as it was vague from my point of view. Tried to conclude what made these issues of Interdisciplinarity. Brought my psychology down from 1500 words to around 300 and made table of all major findings/ behaviours and added due to word count contraints. Also added sentences comparing psychology to law and sociology and their impacts on each other. Lukaseelurs (discuss • contribs) 15:03, 7 December 2019 (UTC) - Calixta.henrion : Modified the Sociology paragraph and finalized it. Reviewed the conclusion. (6 December 2019) - Calixta.henrion : Reduced the introduction for the word limit as well as the conclusion and Sociology. (8 December 2019) sent Calixta.henrion my changes to her sociology paragraph, cutting down the word count from 276 to 234 and sending comments. cut down paragraph for psychology from 400 (excluding table) to new goal of 288. Lukaseelurs (discuss • contribs) 15:54, 8 December 2019 (UTC)

made my table creative commons and added this to the Wikibook. Lukaseelurs (discuss • contribs) 16:46, 8 December 2019 (UTC)

Quickly skimmed over various sections to ensure wording, spelling and grammer was correct.

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


text:
LMIs in Control/pages/Discrete-Time Mixed H2 HInf Optimal Observer

In many applications, perhaps even most, the state of the system cannot be directly known. In this case, you will need to strategically to measure key system outputs that will make the system states indirectly observable. Observers need to converge much faster than the system dynamics in order for their estimations to be accurate. Optimal observer synthesis is therefore advantageous. In this LMI, we seek to optimize both H2 and Hinf norms, to minimize both the average and the maximum error of the observer.

The System

\begin{align}

x_{k+1}&=A_{d}x_{k}+B_{d1,1}w_{1,k}+B_{d1,2}w_{2,k},\\

y_{k}&=C_{c2}x_{k} + D_{d21,1}w_{1,k}+ D_{d21,2}w_{2,k}\\ \end{align} $$

where $$ x \in R^{n}$$  and is the state vector,  $$ A \in R^{n * n}$$  and is the state matrix,  $$ B \in R^{n * r}$$  and is the input matrix,  $$ w \in R^{r}$$  and is the exogenous input,  $$ C \in R^{m * n}$$  and is the output matrix,  $$ D \in R^{m * r}$$  and is the feedthrough matrix,  $$ y \in R^{m}$$ and is the output, and it is assumed that $$(A_{d}, C_{d2})$$ is detectable.

$$ A \in R^{n * n}$$

The Data
The matrices $$ A_{d}, B_{d1}, C_{cd2}, C_{cd1}, D_{d21} $$.

The Optimization Problem
An observer of the form:

\begin{align}

\hat x_{k+1}&=A_{d}\hat x_{k}+ L_{d}(y_{k}-\hat y_{k}),\\

\hat y_{k}&=C_{d2} \hat x_{k} \\ \end{align} $$

is to be designed, where $$ L_{d} \in R^{n_{x} * n_{y}}$$ is the observer gain.

Defining the error state $$ e_{k} = x_{k} - \hat x_{k}$$, the error dynamics are found to be

$$e_{k+1} = (A_{d} - L_{d}C_{d2}) e_{k} + (B_{d1,1} - L_{d}D_{d21,1})w_{1,k} + (B_{d1,2} - L_{d}D_{d21,2})w_{2,k}$$,

and the performance output is defined as

$$ \begin{bmatrix} Z_{1,k} \\ Z_{2,k}\end{bmatrix} = \begin{bmatrix} C_{d1,1} \\ C_{d1,2} \end{bmatrix}e_{k} + \begin{bmatrix} 0 & D_{d11,12} \\ D_{d11,21} & D_{d11,22}\end{bmatrix}\begin{bmatrix} w_{1,k} \\ w_{2,k} \end{bmatrix} $$.

The observer gain $$L_{d}$$ is to be designed to minimize the $$H_{2}$$ norm of the closed loop transfer matrix $$T_{11}(z)$$ from the exogenous input $$w_{2,k}$$ to the performance output $$z_{2,k}$$ is less than $$\gamma _ {d}$$, where

$$ \begin{align} T_{11}(z) &= C_{d1,1}(z1 - (A_{d} - L_{d}C_{d2}))^{-1}(B_{d1,1} - L_{d}D_{d21,1}),\\ T_{22}(z) &= C_{d1,2}(z1 - (A_{d} - L_{d}C_{d2}))^{-1}(B_{d1,2} - L_{d}D_{d21,2}) + D_{d11,22} \end{align} $$

The LMI: Discrete-Time Mixed H2-Hinf-Optimal Observer
The discrete-time mixed-$$H_{2}H_{inf}$$-optimal observer gain is synthesized by solving for $$P \in S^{n_{x}}$$, $$Z \in S^{n_{z}}$$, $$G_{d} \in R^{n_{x} * n_{y}}$$, and $$v \in R_{>0}$$ that minimize J$$(v) = v$$ subject to $$P>0, Z>0$$,

\begin{align}

\begin{bmatrix}P & PA_{d}-G_{d}C_{d2} & PB_{d1,1}-G_{d}D_{d21,1}\\
 * & P & 0\\
 * & * & 1\end{bmatrix}&>0,\\

\begin{bmatrix}P & PA_{d}-G_{d}C_{d2} & PB_{d1,2}-G_{d}D_{d21,2} & 0\\
 * & P & 0 & C^{T}_{d1,2}\\
 * & * & \gamma_{d} 1 & D^{T}_{d11,22}\\
 * & * & * & \gamma_{d} 1\end{bmatrix}&>0,\\

\begin{bmatrix} Z & PC_{d1,1}\\
 * & P\end{bmatrix}&>0,\\

trZ<v

\end{align}$$

where $$tr$$ refers to the trace of a matrix.

Conclusion:
The mixed-$$H_{2}H_{inf}$$-optimal observer gain is recovered by $$L_{d} = P^{-1}G_{d}$$, the $$H_{2}$$ norm of $$T_{11}(z)$$ is less than $$\mu = \sqrt{v}$$, and the $$H_{inf}$$ norm of $$T_{22}(z)$$ is less than $$\gamma_{d}$$. This result gives us a matrix of observer gains $$L_{d}$$ that allow us to optimally observe the states of the system indirectly as:

\begin{align}

\hat x_{k+1}&=A_{d}\hat x_{k}+ L_{d}(y_{k}-\hat y_{k}),\\

\hat y_{k}&=C_{d2} \hat x_{k} \\ \end{align} $$

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/rezajamesahmed/LMImatlabcode/blob/master/mixedh2hinfobsdiscretetime.m

Related LMIs
Discrete-Time_Hinfinity-Optimal_Observer

Discrete-Time_H2-Optimal_Observer


text:
LMIs in Control/pages/stabilization of second order systems

Stabilization is a vastly important concept in controls, and is no less important for second order systems. A second order system can be conceptualized most simply by the model of a mass-spring-damper. Velocity and position are of course chosen as the states for this system, and the state space model can be written as it is below. The goal of stabilization in this context is to design a control law that is made up of two controller gain matrices $$ K_{p} \in R^{r*m_{p}} $$, $$ K_{d} \in R^{r*m_{d}}  $$. These allow the construction of a stabilized closed loop controller.

The System
Here, we want to stabilize a second order system of the following form:

\begin{align} M \ddot x + D \dot x + K x&=B u, \end{align}$$ where $$x \in R^{n}$$ and $$u \in R^{r}$$ are the state vector and the control vector, respectively, and M (called the "mass matrix"), D (called the "structural damping matrix"), K (called the "stiffness matrix"), and B are the system coefficient matrices of appropriate dimensions.

To make the system follow standard convention, we reformulate the system as:

\begin{align} A_{2} \ddot x + A_{1} \dot x + A_{0} x&=B u\\ y_{d} &= C_{d}\dot x\\ y_{p} &= C_{p}x, \end{align}$$ where: $$x \in R^{n}$$ and $$u \in R^{r}$$ are the state vector and the control vector, respectively; $$y_{d} \in R^{m_{d}}$$ and $$y_{p} \in R^{m_{p}}$$ are the derivative output vector and the proportional output vector, respectively; and $$A_{2}, A_{1}, A_{0}, B, C_{d},$$ and $$C_{p}$$ are the system coefficient matrices of appropriate dimension. Note that $$A_{2}$$ must be $$ > 0 $$, and $$A_{0}, A_{2}$$ must be $$\in S^{n}$$.

To further define: $$x$$ is$$\in R^{n}$$ and is the state vector, $$A_{0} $$ is $$\in R^{n*n}$$ and is the state matrix on $$ x $$, $$A_{1} $$ is $$\in R^{n*n}$$ and is the state matrix on $$ \dot x $$ , $$A_{2} $$ is $$\in R^{n*n}$$ and is the state matrix on $$ \ddot x $$, $$B$$ is $$\in R^{n*r}$$ and is the input matrix, $$u$$ is $$\in R^{r}$$ and is the input, $$C_{d} $$ and $$C_{p} $$ are $$\in R^{m*n}$$ and are the output matrices, $$y_{d}$$ is $$\in R^{m}$$ and is the output from $$C_{d} $$, and $$y_{p}$$ is $$\in R^{m}$$ and is the output from $$C_{p} $$.

$$\in R^{n}$$

The Data
The matrices $$ A_{2}, A_{1}, A_{0}, B, C_{d}, C_{p}$$.

The Optimization Problem
For the system described, we choose the following control law

\begin{align} u &= K_{p}y_{p} + K_{d}y_{d}\\ &= K_{p}C_{p}\hat x + K_{d}C_{d}x, \end{align} $$ with $$ K_{p} \in R^{r*m_{p}} $$, $$ K_{d} \in R^{r*m_{d}}  $$, we obtain the closed-loop system as follows:

\begin{align} A_{2}\ddot x + (A_{1} - BK_{p}C_{p})\dot x + (A_{0} - BK_{d}C_{d})x &=0.\\ \end{align} $$ We are tasked to design a state feedback control law such that the above system is hurwitz stable.

First, in order to solve this problem, we need to introduce a Lemma. This Lemma comes from Appendix A.6 in "LMI's in Control systems" by Guang-Ren Duan and Hai-Hua Yu. This Lemma states the following:

\begin{align} A_{2}> 0, A_{1} + A^{T}_{1} > 0, A_{0} > 0\\ \end{align} $$

The LMI: Stabilization of Second Order Systems
There is a solution if there exists matrices $$K_{p} \in R^{r*m_{p}}$$ and $$K_{d} \in R^{r*m_{d}}$$ that satisfy the following LMIs:

\begin{align} A_{0} - BK_{d}C_{d} > 0, \end{align}$$ and

\begin{align} (A_{1} - BK_{p}C_{p}) + (A_{1} - BK_{p}C_{p})^{T} > 0. \end{align}$$

Conclusion:
Finally, having solved the LMI the optimization will produce two matrices, $$ K_{p}$$ and $$ K_{d}$$ that can be substituted into the system as

\begin{align} u &= K_{p}C_{p} \dot x + K_{d}C_{d}x \end{align}$$

to obtain a stabilized second order system.

Implementation
This implementation requires Yalmip and Sedumi. https://github.com/rezajamesahmed/LMImatlabcode/blob/master/stab2ndorder.m

Related LMIs
Robust Stabilization of Second-Order Systems


text:
User:Nappellman

Free dictionaries

Programs for learning foreign languages are very popular. A significant part of the programs helps students memorize foreign words. The student needs to remember 2000-3000 words and more. Programmers must not only write program code, correct errors, make improvements, but also spend time writing words into dictionaries. Each programmer makes his own dictionaries. Therefore, it is proposed here to use ready-made free dictionaries of foreign words. Each text file contains words for one letter of the alphabet. Each line of the file contains one word in seven European languages.

dictionary_A.txt dictionary_B.txt dictionary_C.txt dictionary_D.txt dictionary_E.txt

Dictionaries are added as soon as they are developed.

In each line, words are separated by a standard separator - a comma.

PHP Example

title: User:Nappellman


text:
Issues in Interdisciplinarity 2019-20/Truth in the Prison System

Introduction
The concept of prison arose in the 18th century as an institution that aimed to replace the capital punishment system, by punishing individuals who have committed illegal offenses whilst simultaneously aiming to reform them. The United States has the highest incarceration rates globally, with approximately 1,471,200 individuals imprisoned in 2018. While incarceration rates have generally decreased since 2017, the effectiveness of the American penal system in achieving criminal reform and reducing crime is still controversial: a study showed nearly "two-thirds of all prisoners are rearrested within three years of release".

Different disciplines view the effectiveness of rehabilitation differently, thus providing multiple perspectives about the success of prison rehabilitation.

Sociology and Prison Group Behaviour
Stanton Wheeler used the concept of 'prisonization' to illustrate the impact of prison socialisation on rehabilitation. He argues that prisoners undergo “prisonization” when they assimilate into the prison culture, resulting in a difficult rehabilitation process. Prisoners internalise a criminal outlook and are less likely to follow the conventional value and moral system, especially as their time in prison increases, based on empirical research on prisoner conformity levels to ‘good’ values and norms. Since they risk being alienated from other inmates by conforming to staff rules, they would mostly choose non-conformity to rules. However, prior to release, conformity increases.

Additionally, Donald Cressey uses the Theory of Differential Association to argue that the best way to reform criminals is to integrate them into noncriminal groups so they inherit the desired values of a law-abiding citizen. He extends this theory to explain that the behaviour exhibited by a felon is not solely a product of group interactions but an inherent characteristic of the group itself. By this reasoning, the ideal approach to reform criminals requires an attempt to change the entire group behaviour which subsequently alters individual behaviour. Consequently, individual therapy and counselling is not sufficient to alter the group’s culture. A backwards approach is taken whereby the whole group is reformed to alter individual behaviour.

Economics and the Cost of Prison
Rather than evaluating the efficiency of the institution using recidivism rates, economists focus more on economic reintegration as an indicator of the success of prison systems. Earned incomes which are obtained by the successful incorporation of criminals back into the labour market provide financial stability, which economists argue will inherently reduce recidivism by dis-incentivising the desire to commit crime.

Statistics show that "incarceration reduces average lifetime income growth by one-third", highlighting how imprisonment makes economic reintegration harder; the prison system actually prevents future national economic growth by causing a deterioration of human capital. An analysis of work and opportunity before and after incarceration showed that 55% of prisoners have a reported income after release. Even of those with an income, it is often less than that of an individual with a full-time job paid at minimum wage.

Economics also highlights the cost of prisons. The direct cost - equivalent to the amount taxpayers pay - is estimated to be $80 billion a year in the US, whereas indirect cost is between $500 billion to $1 trillion per year. Economics provides a widened understanding of the complete economic cost of prisons which includes opportunity costs such as the "foregone wages of incarcerated persons, increased infant mortality, and increased criminality of children with incarcerated parents, and higher welfare costs associated with families of incarcerated parents".

Psychology and the Effects of Institutionalisation
It can be argued that prisons are effective at preventing crime due to deterrence theory, as individuals weigh the possibility of incarceration versus their desire to pursue criminal activity. However, evidence suggests that once imprisoned, inmates are more likely to reoffend as the prison institution socializes them towards heightened criminality through peer influence or the ‘hardening’ necessary to integrate within the unpredictable prison environment.

The effects of institutionalization present significant obstacles to post-prison adjustment, from the disabling consequences of ‘prisonization’ to exacerbated mental illness from lack of proper treatment that focus on the needs of the individual rather than as a group. According to the Bureau of Justice Statistics, an estimated 56% of state prisoners have a mental health issue, with only 1 in 3 having received treatment since incarceration. Prisoners face a difficult transition after release and have a 13-fold increase in risk of death from cardiovascular disease, homicide, suicide, and drug overdose in the first two weeks after prison release as compared to a similar demographic sample. Prison victimization, nonviolent or violent, also contributed to depressive and post-traumatic stress symptoms, made worse by the inescapability of the prison environment.

Conclusion
The main tension evident between sociology and psychology is the approach in criminal reform that each discipline advocates for. Sociology focuses on reforming the group, while psychology advocates for an individual-based approach. Furthermore, they have different constructions of truth due to different approaches of defining 'efficacy'. Sociology judges the good/bad behaviour of inmates, while psychology looks at well-being - emphasizing the poor mental health consequences of imprisonment. These varying versions of truth create contrasting conclusions about the success of prisons, where sociology seems to support the prison system while psychology does not.

Embedded in sociology’s approach to prisoner rehabilitation is a social constructionist view, which contrasts with psychology’s interpretivist view of addressing prisoners’ psychological well-being. Social constructionism is anti-essentialist, opposing the idea that a person has a discoverable nature which is what traditional psychology understands. Sociology, by proposing group rehabilitation of prisoners, reveals its social constructionist focus on the process of social interaction that creates certain phenomena or forms of knowledge.

Social constructionism also views knowledge as historically and culturally specific, distinct from psychology’s view that human nature can be universalised. This can be problematic if psychology tries to obtain truth by using a methodology that establishes conclusions based on group generalizations that cannot always successfully be extrapolated to all individuals.

In contrast to both psychology and sociology, which advocate for behavioral and mental reform, economics instead emphasizes rehabilitation for the sake of reintegration into the workforce. It takes a more positivist approach as it attempts to establish a conclusion through empirical observation and analysis. This perspective differs from other more qualitative-based disciplines that measure the success of the prison system by evaluating inmate behaviour, rather than the cost and contributions they may have on the economy before and after incarceration.

However, it is often difficult to measure such costs, made evident by the controversial National Institute of Justice report published by Edwin Zedlewski in 1987. His cost-benefit analysis was described as ‘fatally flawed’ by experts who argued that Zedlewski assigned inflated social costs to crimes, producing skewed results. Thus, even in a quantitative-based discipline like economics, it is difficult to obtain conclusive truths because of the inherent bias present in methodological approaches when assigning costs.

Each discipline alone fails to capture the complexity of the discussion surrounding prison efficacy. Variations in how each discipline measures success in prisons leads to clashes surrounding whether the modern-punishment system is successful. Hence, with each discipline highlighting a unique but important perspective, analysing this issue through an interdisciplinary lens is crucial to provide a complete picture.


text:
OpenSCAD Tutorial/Chapter 7

Creating repeating patterns of parts/models - For loops
In the previous chapter you used if statements to control whether some part of your design should be created or not. In this chapter you are going to find out how you can create multiple parts or objects when they form a specific pattern.

Given the following car model as an example you are going to learn how to create such patterns.

After the previous exercise, you have probably realized that creating a pattern of cars in this manner is not very efficient; a new statement has to be written for every car, and this results in a lot of code duplication in your script. Typically, you can use a for loop to achieve the same results a lot easier. The for loop provides a way to repeat the same set of statements a certain number of times, with small, predictable changes applied each time. Take a look at the following example.

There are a few things you should notice about the syntax of the for loop. First the keyword for is typed out followed by a pair of parentheses. Inside the parentheses the variable of the for loop is defined. It’s advisable to give a descriptive name to the for loop variables when applicable. In this case the variable is named dy because it represents the number of units that each car needs to be translated along the Y axis. The definition of the variable indicates that its first value will be 0 units and all following values will be incremented by 50 units each until the value 450 is reached. This means that the variable dy will take ten different values in total throughout the execution of the for loop repetitions. These values are 0, 50, 100, 150, 200, 250, 300, 350, 400 and 450. These values form a vector, which in contrast to a single value is a sequence of values. In the first repetition the variable will take the first value of the vector, which is 0. In the second repetition the second value, which is 50. And so forth. The different consecutive values that the for loop variable takes throughout the repetitions of the for loop is the key concept which makes the for loop suitable for creating patterns of multiple parts or models. Finally, after the closing parenthesis follows a pair of curly brackets. Inside the curly brackets exist the statements that will be executed repeatedly as many times as the number of values of the for loop variable. In this case the single statement inside the curly brackets will be executed 10 times which is the number of values that the dy variable will take. To avoid creating 10 cars that are completely overlapping the amount of translation along the Y axis on each repetition of the for loop is parameterized using the dy variable. The dy variable has a different value on each repetition of the for loop thus creating the desired pattern.

Creating more complex patterns
In the previous examples the for loop variable dy was used directly to modify some aspect of each individual model that composes the pattern. The only aspect that was modified was the translation of each model along the Y or X axis. On each repetition the value of the dy variable was equal to the desired translation on each model.

When more than one aspect of the model needs to be modified it’s a better practice for the for loop variable to take integer values 0, 1, 2, 3 etc. The required values for modifying different aspects of the model (ex. translation along some axis, scaling of some part) are then produced from those integer values that the for loop variable takes. In the following example this concept is used to simultaneously translate each car 50 and 70 units along the positive direction of the Y and X axis.

There are a few things you should notice. The for loop variable is now named i. When the for loop variable is used in this way it’s usually called index and given the name i. Since the for loop variable takes integer values you need to multiply it by a proper number to produce the desired amount of translation along each axis. Specifically, the desired amount of translation along the Y axis is produced by multiplying the for loop variable by 50. Similarly the desired amount of translation along the X axis is produced by multiplying the for loop variable by 70.

The patterns you are creating are already becoming cooler, here is an interesting one.

In the above pattern the cars have been placed at equally spaced points at the circumference of a perfect circle that has a radius of 200 units. There are a few important points you should pay attention to if you wish to create such patterns. The first is that in order to create a circular pattern you need to use polar coordinates. Depending on your background you may have noticed the use of polar coordinates just by glancing at the code or you may have no idea what it is. In the latter case, the only thing that you need to know is that polar coordinates are a way to produce the X and Y coordinates of a given point of a circle when you know the radius of the circle and the angle that corresponds to that point. The angle 0 corresponds to the point of the circle that belongs to the positive direction X axis. The positive counting direction of the angle is from the X to the Y axis. This means the positive Y axis corresponds to 90 degrees, the negative X axis to 180 degrees, the negative Y axis to 270 degrees and if you complete the circle the positive X axis to 360 degrees. According to the polar coordinates the X coordinate can be calculated by multiplying the radius of the circle by the cosine of the angle, while the Y coordinate can be calculated by multiplying the radius of the circle by the sine of the angle. This is how the desired amount of translation along the X and Y axis is produced.

The second thing you should notice is what values the for loop variable i takes. The variable i starts from 0 and is incremented by 36 on each repetition in order to position 10 equally spaced cars on the circle (360/10 = 36). The first car that is created at 0 angle and the car that correspond to 360 degrees would be exactly overlapping. In order to avoid this, you need to instruct the for loop variable to stop incrementing before it reaches 360. If you are lazy calculating 360 - 36 = 324, you can just put the limit at 359. This will work fine because the for loop variable will only take the values 0, 36, 72, 108 144, 180, 216, 252, 288 and 324, since incrementing by another 36 units would result in 360 which exceeds 359.

By using additional variables and naming them properly you can make your scripts more descriptive and usable so that it’s easier for anyone (or even you at a later point in time) to understand what they are doing and how to use them. For example, the previous script can take the following form.

On the above script it is self-explanatory that the for loop variable i corresponds to the angle. It is also clearer what the amount of translation along each axis is. In addition, it is easy to customize this pattern by changing the radius and/or the number of cars.

Challenge

 * facing away from the origin

 * driving counterclockwise

 * driving clockwise

Now that you are getting a hold of using for loops to create patterns it’s time to put you new skills in the development of a more sophisticated wheel design!

Creating patterns of patterns - Nested for loops
The following script creates a row of cars along the Y axis.

If you have been paying close attention to the tutorial so far, you may have noticed that the script above is not very efficient. It has a lot of code duplication and the number of rows can’t be easily modified. You faced a similar situation in the beginning of this chapter when you wanted to create a row of cars. To solve that problem, you wrapped the statement that creates a piece of the pattern (a single car) inside a for loop. This generated the whole pattern (a row of cars) without having to type out a statement for each individual car. The same principle can be applied here. In this case, the repeating pattern will be the row of cars, which itself is a repeating pattern of individual cars. Following the same process as before, the statements that create a row of cars will be placed inside a for loop in order to create the pattern of rows of cars. The result is that a for loop is placed inside of another for loop. For loops that are used in this way are called nested for loops. The following example demonstrates this concept.

You should notice the following concept. During the first repetition of the outer for loop, all iterations of the inner for loop are executed, thus creating the first row of cars. During the second repetition of the outer for loop all repetitions of the inner for loop are executed, thus creating the second row of cars. And so forth. Each row is positioned by the dx variable, which holds the parameterized translation along the X axis. During each iteration of the outer loop, a new value of dx is used. This value then holds steady while the inner loop executes and modifies the dy value. In this way, a row of cars is generated at each value of dx.

title: OpenSCAD Tutorial/Chapter 7


text:
LMIs in Control/pages/systemzeroswithfeedthrough

Let's say we have a transfer function defined as a ratio of two polynomials: $$ \begin{align} H(s) = \frac{N(s)}{D(s)} \\ \end{align}$$ Zeros are the roots of N(s) (the numerator of the transfer function) obtained by setting $$ N(s) = 0 $$ and solving for s.The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs. Similarly, the system zeros are either real or appear in complex conjugate pairs. In the case of system zeros with feedthrough, we take $$ D $$ as full rank.

The System
Consider a continuous-time LTI system, $$ G $$, with minimal statespace representation $$ (A,B,C,D) $$

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

The Data
The matrices needed as inputs are:

\begin{align} A \in \mathbb{R}^{n \times n} \\ B \in \mathbb{R}^{n \times m} \\ N \in \mathbb{R}^{p \times n} \\ \end{align}$$ In this case, $$ m \leq p $$

The LMI: System Zeros with feedthrough
The transmission zeros of $$ G(s) = C(sI-A)^-1 B + D $$ are the eigenvalues of $$ A-B(D^T D)^{-1} D^T C $$. Therefore, $$ G(s) $$ is a minimum phase if and only if there exists $$ P \in \mathbb{S}^{q} $$, where $$ P>0 $$ such that

\begin{align} P(A-B(D^T D)^{-1} D^T C) + (A-B(D^T D)^{-1} D^T C)^T P < 0 \\ \end{align}$$

Conclusion:
If P exists, it ensures non-minimum phase. Eigenvalues of $$ A-B(D^T D)^{-1} D^T C $$ then gives the zeros of the system.

Related LMIs
LMIs_in_Controls/pages/systemzeroswithoutfeedthrough

Implementation
https://github.com/Ricky-10/coding107/blob/master/systemzeroswithfeedthrough


text:
User:Herminewiki17/sandbox

Issues in interdisciplinarity: Evidence and Dreams

Useful sources

title: User:Herminewiki17/sandbox


text:
OpenSCAD Tutorial/Chapter 8

Rotationally extruding 3D objects from 2D objects
So far you have been creating a lot of models and customizing your car designs while developing solid parametric modelling skills and exploring different features of OpenSCAD. It’s quite impressive when you consider that every model you have created so far makes use of just three primitives: the sphere, the cube and the cylinder. By combining these primitives with the transformation commands you can create a plethora of models, but there are still models that can’t be created by using these primitives alone. One such example is the following wheel design.

The above wheel design requires the creation of an object that looks like a donut.

This donut shaped object can’t be created with the use of the sphere, cube and cylinder primitives. Instead it requires the use of 2D primitives and a new command which can create 3D shapes from 2D profiles. Specifically, the donut can be created by first defining a circular 2D profile using the circle primitive and then rotationally extruding this profile using the rotate_extrude command.

There are a few things you should notice about the 2D profile that you have created. In this case, the 2D profile is created using the circle command, and the diameter is set equal to the tyre_diameter variable. This was done because the donut-shaped object will correspond to the tyre of the wheel. Later on, you may discover other 2D primitives like the square command.

Any 2D profiles you plan to extrude should be created on the X-Y plane, and typically in the region where X is positive. Defined mathematically, 2D profiles usually reside where X ≥ 0, and Z = 0. Also, 2D profiles always have zero thickness. This means that 2D profiles are never used directly as a part of the model, but are instead used in conjunction with the rotate_extrude and linear_extrude commands to define 3D objects.

You should notice a few things about the use of the rotate_extrude command as well. The rotate extrude command is used to create 3D objects, and always requires a 2D profile as an input. The commands that create the desired 2D profile need to be placed inside the pair of curly brackets that follows the rotate_extrude command. The 3D object that is created by the rotate_extrude command is the result of rotating the 2D profile around the Y axis. The resulting 3D object is then placed so that its axis of rotation lies along the Z-axis. This quirk can take some getting used to at first, so it may help to review the process one step at a time.

First, the rotate_extrude command takes a 2D profile as an input.

Then it creates a 3D object which is the result of rotating the supplied 2D profile around the Y axis.

Finally, it places the 3D model as if it were rotated by 90 degrees around the X axis. The result is that the Y axis which the model was revolved around has been rotated up to align with the Z axis.

The rotate_extrude command has one input parameter named angle. The angle parameter is used to define how many degrees the 2D profile will be rotated around the Y axis. In this case the angle parameter is set equal to 360 degrees which corresponds to a full circle.

Setting the angle parameter equal to 60 degrees would create the following model.

While setting it equal to 270 degrees would create the following one. And so forth.

You should remember that axisymmetric objects can be completely created out of a rotate_extrude command. The previous wheel design is a concrete example of this. Whether you decide to create an axisymmetric object by supplying the 2D profile of the whole object and by using a single rotate_extrude or by using a rotate_extrude command only for its parts that can’t be created in any other way, depends on each case and is up to you. If you wanted for example to further modularize your wheel designs and separate them into combinable tire and rim modules, you would inevitably need to create the donut-shaped tire using a rotate_extrude command. Since in this case the rim of the wheel would be a separate module without a rotate_extrude command already present in it, the simplest and most straight forward way to create it would be by using a cylinder command.

Challenge
It’s time to put your new knowledge into practice to create a rim for a mini robot car project.

This wheel design looks about right for a mini robot car application, but you could do something to give more traction to your robot. Instead of 3D printing the whole wheel, you could just 3D print the rim and then add an O-ring or rubber band as the tire for more traction. The resulting wheel would look like the following image, where the O-ring or rubber band is represented by the blue color.

The corresponding rim that you would have to 3D print in this case is the following.

 * First approach

 * Second approach

Often, it's helpful to consider the manufacturing process that will be used in an object's creation when designing a new part. Usually, this consideration promotes designs that accommodate the manufacturing method at hand, but it can guide your modeling process as well.

For example, consider a scenario where instead of using additive manufacturing like 3D printing to manufacture this robot wheel, you used subtractive manufacturing like lathe or a mill. In this case you might opt to use the second approach, since it would more closely replicate the manufacturing process at hand, and could give you a better estimate of how many steps the final manufacturing process might take.

Linearly extruding 3D objects from 2D objects
As briefly mentioned, there is another OpenSCAD command that can be used to create 3D objects from supplied 2D profiles. This is the linear_extrude command. In contrast to the rotate_extrude command, linear_extrude creates a 3D object by extending along the Z axis a 2D profile that lies on the XY plane. Similar to the rotate_extrude command, linear_extrude can be used when the 3D object you want to create can’t be directly created by combining available 3D primitives. One such example is the following.

The above object is a tube that has the following profile.

There are a few points you should notice regarding the use of linear_extrude. The syntax of linear_extrude is similar to the syntax of the rotate_extrude command. The commands that create the 2D profile that will be extruded along the Z axis need to be placed inside a pair of curly brackets that follows the linear_extrude command. The parameter height is used to define how many units along the Z axis the 2D profile is going to be extruded. By default, the 2D profile is extruded along the positive direction of the Z axis by an amount of units equal to the value assigned to the height parameter.

By passing an additional parameter named center and setting it equal to true, the 2D profile is extruded along both directions of the Z axis. The total length of the resulting object will still be equal to the height parameter.

An additional parameter named twist can also be used to twist the resulting 3D object around the Z axis by the specified angle.

Finally, another parameter named scale can be used to scale one end of the resulting 3D by the specified scaling factor.

It should be pretty clear by now how the rotate_extrude and linear_extrude commands give you the ability to create objects that wouldn’t be possible by directly combining the available 3D primitives. You can use these commands to create more abstract and artistic designs but let’s see how you could use the linear_extrude command to create a new car body.

As mentioned, the rotate_extrude and linear_extrude commands can also be used to create more abstract objects. When the supplied 2D profile is created using the available circle and square 2D primitives and when the twist and scale parameters of the linear_extrude command are not utilized, then the resulting 3D object could also be directly created using the available 3D primitives. What really makes the use of these commands much more powerful is the ability to create any 2D profile that is not a combination of circles and squares but rather an arbitrary shape. This ability is available through the use of the polygon 2D primitive which you are going to learn about in the next chapter.

title: OpenSCAD Tutorial/Chapter 8


text:
LMIs in Control/H2Optimalobserver

State observer is a system that provides estimates of internal states of a given real system, from measurements of the inputs and outputs of the real system.The goal of $$ H_2$$ -optimal state estimation is to design an observer that minimizes the $$ H_2 $$ norm of the closed-loop transfer matrix from w to z. Kalman filter is a form of Optimal Observer.

The System
Consider the continuous-time generalized plant $$ P $$ with state-space realization

\begin{align} \dot x&=Ax+B_1w(t),\\ y&=C_2x+D_{21}w\\ \end{align}$$

The Data
The matrices needed as input are $$ A,B,C,D $$.

The Optimization Problem
The task is to design an observer of the following form:

\begin{align} \dot{\hat{x}}=A\hat{x} + L(y - \hat{y}),\\ \hat{y} = C_2\hat{x}\\ \end{align}$$

The LMI: $$ H_2 $$ Optimal Observer
LMIs in the variables $$ P, G, Z, \nu $$ are given by:

\begin{align}

\begin{bmatrix} PA+ A^TP-GC_2-{C_2}^TG^T && PB_1-GD_{21}\\ \star && -1 \end{bmatrix} <0\\ trZ < \nu \end{align}$$

Conclusion:
The $$ H_2$$ -optimal observer gain is recovered by $$ L = P^{-1}G $$ and the $$ H_2 $$ norm of T(s) is $$ \mu = \sqrt {\nu} $$

Implementation
https://github.com/Ricky-10/coding107/blob/master/H2%20Optimal%20Observer

= External Links =

A list of references documenting and validating the LMI.

 * LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
 * LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
 * LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
 * https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.1310

title: LMIs in Control/H2Optimalobserver


text:
OpenSCAD Tutorial/Chapter 9

Doing math calculations in OpenSCAD
So far you have learned that OpenSCAD variables can hold only one value throughout the execution of a script, the last value that has been assigned to them. You have also learned that a common use of OpenSCAD variables is to provide parameterization of your models. In this case every parameterized model would have a few independent variables, whose values you can change to tune that model. These variables are usually directly assigned a value as in the following examples.

Another thing that you have seen a few times already, but which has not been mentioned explicitly is the ability to perform mathematical operations using variables and hard-coded values in your script. One example of this is in implementing the car's wheelbase. Recall that the car's axles and wheels were translated along the X axis and away from the origin by half the value of the wheelbase. Since in this case the wheelbase is a variable that has already been defined in your script, you can calculate the amount of units by dividing the wheelbase variable by two. A similar thing was done with the track variable to place the left and right wheels of the car. Recall that the left and right wheels were translated along the Y axis and away from the origin by half the value of the track.

Addition, subtraction, multiplication and division are represented in OpenSCAD with the signs +, -, * and /. Apart from these fundamental operations, there are also a number of additional mathematical operations that can be useful when building more complex models. Two examples of this are the cosine and sine functions that you used to define a circular pattern of cars. Specifically, you used the cosine and sine functions to transform the polar coordinates of each car into Cartesian coordinates in order to translate it in its proper position. You can find all available math functions briefly listed in the cheat sheet.

In the above case you are not only using available mathematical operations in your script, but you are also defining two additional variables dx and dy to store the result of your calculations in order to increase the readability of your script. This is something that could also be done in your car models. Take for example the following car model.

In the above model, mathematical operations are used to calculate the required amount of translation for each wheel and axle along the X and Y axis.

Creating any 2D object with the polygon primitive
Aside from the circle and square 2D primitives, there is another primitive that lets you design practically any 2D object. This is the polygon primitive, which lets you define 2D objects by providing a list that contains the coordinates of their points. Let’s say you want to design the following 2D part.

One way to go about designing this part without using the polygon primitive would be to start from a square that corresponds to the outer dimensions of this part and then subtract a properly rotated and translated square from its top right corner. Calculating the proper angle of rotation and amount of translation would be a time-consuming task. Additionally, following this strategy for a more complex object wouldn’t be possible. Instead, you can create this object using the polygon primitive in the following way.

There are a few things you should notice regarding the use of the polygon primitive. The polygon primitive uses a list of points as inputs. The points, or vertices, are represented using pairs of X and Y coordinates, and are provided in order. When defining the list, you may start with any vertex you like and you can traverse them in either a clockwise or counterclockwise order. In the example above, the first vertex is at the origin (0,0), while the remaining vertices are listed in a clockwise direction. All vertices (pairs of X and Y coordinates) p0, p1, …, p4 are placed inside a list named points. This list is then passed to the polygon command to create the corresponding object.

Whether a variable has only a single value or it’s a list of values, you can print its content on the console using the echo command.

The output in the console is: 0, 0], [0, 30], [15, 30], [35, 20], [35, 0

Naming each point separately (p0, p1, …) is not required but it’s recommended to better keep track of your design. You could also directly define the list of points to be passed to the polygon command.

Moreover, you don’t even have to define a variable to store the list of points. You can directly define the list of points when calling the polygon command.

The above practices are not recommended. Instead the use of additional variables as in the first example is encouraged in order to make your scripts more readable and extendable.

You could also parameterize the definition of the points’ coordinates according to the given dimensions, which will give you the ability to rapidly modify the dimensions of your object. This can be achieved by introducing one variable for each given dimension and by defining the coordinates of the points using appropriate mathematical expressions.

Challenge
It’s time to use your new skills to create the body of a racing car!

Creating more complex object using the polygon primitive and math
From the above examples it should be quite obvious that the polygon primitive opens up possibilities to create objects that would hardly be possible by just using the fundamental 2D or 3D primitives. In these examples you created custom 2D profiles by defining the coordinates of their points according to a given design. To unlock the true power of the polygon command though, and to create even more complex and impressive designs, you have to programmatically define the points of your profiles using math. This is because defining each point separately is not scalable to the hundreds of points that are required to design smooth non-square profiles. One example of this is the following heart. Can you manually define the required points to create it? There is no way.

Instead of manually defining each point, which would be practically impossible, this model was programmatically defined using the following parametric equations.

x = 16⋅sin(t)3 y = 13⋅cos(t) − 5⋅cos(2⋅t) − 2⋅cos(3⋅t) − cos(4⋅t)

When the range of the t variable covers values from 0 to 360 degrees, the above equations give the X and Y coordinates for the outline of the heart, starting from the top middle point and moving in a clockwise direction. Using the above equations, a list that contains each point’s coordinates can be generated in the following way.

There are a few things you should notice about the syntax of list generation. First the name of the variable where the list will be stored is typed out. Then follows the equal sign (as in every variable assignment) and a pair of square brackets. Inside the pair of square brackets, the first thing that is typed out is the keyword for. After the keyword for follows a pair of parentheses inside of which the consecutive values that the corresponding variable is going to take are defined. This variable is similar to the for loop variable encountered in for loops. The number of elements that the generated list is going to have is equal to the number of values that this variable is going to take. For every value that this variable takes, one element of the list is defined. What each element of the list is going to be, is specified after the closing parenthesis. In this case each element of the generated list is itself a list that has two elements, one for each coordinate of the corresponding point. The t variable goes from 0 to 360 which is the required range to produce the whole outline of the heart. Since the polygon shouldn't include duplicate points, 359.999 is used instead of 360. By choosing a smaller or bigger value for the step variable, the amount of points that will be created can be controlled. Specifically, in order to create n points the step variable needs to be defined in the following way.

Putting all these together, the heart can be created with the following script.

You can see that by using 500 points the resolution of the outline is very good.

Using more or less points is up to you. If you want to create an object that closely resembles the underlying mathematical equations, you should increase the number of points. Instead, if you opt for a low poly style you should decrease the number of points.

Solution for exercise i, [1, 2, 3, 4, 5, 6]:

Solution for exercise ii, [10, 8, 6, 4, 2, 0, -2]:

Solution for exercise iii, 3, 30], [4, 40], [5, 50], [6, 60:

Note that when no step is provided, a default of 1 is used.

OpenSCAD also allows you to define your own mathematical functions, which can be useful when a mathematical expression is particularly long, or when you would like to use it multiple times. These functions work similarly to modules, except that instead of defining a design they define a mathematical process. After a function has been defined, you can use it by invoking its name and providing the necessary input parameters. For example, you can define a function that accepts the parameter t, and returns the X and Y coordinates of the corresponding point of the heart's outline.

In this case the script that creates the heart would take the following form.

There are a few things you should notice about the definition of a function. First the word function is typed out. Then follows the name that you want to give to the function. In this case the function is named heart_coordinates. After the name of the function follows a pair of parentheses that contains the input parameters of the function. Like module parameters, the input parameters in a function can have default values. In this case, the only input parameter is the polar angle of the current step t and it’s not given a default value. After the closing parenthesis follows the equal sign and the command that defines the pair of X and Y coordinates of the heart’s outline.

The generation of the list of points can also be turned in a function. This can be done in a similar fashion as follows.

In this case the script that creates the heart would take the following form.

In short you should remember that any command that returns a single value or a list of values can be turned into a function. Like modules, functions should be used to organize your designs and make them reusable.

Another challenge
You are going to put your new skills into practice to create an aerodynamic spoiler for your racing car!

title: OpenSCAD Tutorial/Chapter 9


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LMIs in Control/pages/LMI for Nonrotating Missiles Attitude Control yaw roll channel

LMI for Attitude Control of Nonrotating Missles, Yaw/Roll Channel

Deriving the exact dynamic modeling of a missile is a very complicated procedure. Thus, a simplified model is used to model the missile dynamics. To do so, we consider a simplified attitude system model for the yaw/roll channel of the system. We aim to achieve a non-rotating motion of missiles. Note that the attitude control design for the yaw/roll channel and the pitch channel can be solved exactly in the same way except for different representing matrices of the system.

The System
The state-space representation for the yaw/roll channel can be written as follows:

$$ \begin{align} \dot{x}(t) &= A(t)x(t) + B_{1}(t)u(t) + B_{2}(t)d(t) \\ y(t) &= C(t)x(t) + D_{1}(t)u(t) + D_{2}(t)d(t) \end{align} $$

where $$ x = [\beta \quad w_{y} \quad w_{x} \quad \delta_{x} \quad \delta_{y}]^{\text{T}}$$, $$ u = [\delta_{xc} \quad \delta_{yc} ]^{\text{T}} $$, $$ y = [n_{z} \quad w_{x}]^{\text{T}}$$, and $$ d = \delta_{z}$$ are the state variable, control input, output, and disturbance vectors, respectively. The paprameters $$ \alpha $$, $$ w_{z} $$, $$ \delta_{z} $$, $$ \delta_{zc} $$, $$ n_{y} $$, $$ \beta $$, and $$ w_{y} $$ stand for the attack angle, pitch angular velocity, the elevator deflection, the input actuator deflection, the overload on the side direction, the sideslip angle, and the yaw angular velocity, respectively.

The Data
In the aforementioned yaw/roll channel system, the matrices $$ A(t), B_{1}(t), B_{2}(t), C(t), D_{1}(t),$$ and $$D_{2}(t)$$ are given as:

$$ \begin{align} A(t) = \begin{bmatrix} A_{11}(t) & A_{12}(t)\\ 0    & A_{22}(t) \end{bmatrix} \end{align} $$

where

$$ \begin{align} A_{11}(t) = \begin{bmatrix} -b_{4}(t) & 1 & \frac{\alpha(t)}{57.3} \\ -\acute{b}_{1}(t)b_{4}(t) - b_{2}(t) & -\acute{b}_{1}(t) - \acute{b}_{1}(t) & \frac{J_{y}-J_{z}}{57.3J_{x}}{w}_{z}(t) - \frac{\acute{b}_{1}\alpha(t)}{57.3}\\ c_{2}(t) & \frac{J_{y}-J_{z}}{57.3J_{x}}{w}_{z}(t) & -c_{1}(t) \end{bmatrix} \end{align} $$

$$ \begin{align} A_{12}(t) = \begin{bmatrix} 0 & -b_{5}(t)\\ 0 & -\acute{b}_{1}(t)\acute{b}_{5} - b_{3}(t) \\ -c_{3}(t) & c_{4}(t) \end{bmatrix} \end{align} $$

$$ \begin{align} A_{22}(t) = -\frac{1}{\tau_{x}\tau_{y}} \begin{bmatrix} \tau_{y} & 0\\ 0 & \tau_{x} \end{bmatrix} \end{align} $$

and

$$ \begin{align} B_{1}(t) = \begin{bmatrix} 0 & 0\\ 0 & 0\\ 0 & 0\\ \frac{1}{\tau_{x}} & 0\\ 0 & \frac{1}{\tau_{y}} \end{bmatrix}, \quad B_{2}(t) = \begin{bmatrix} a_{6}(t) \\ -\acute{b}_{1}(t)a_{6}(t) \\ 0\\ 0 \\ 0 \end{bmatrix} \end{align} $$

$$ \begin{align} C(t) = -\frac{1}{57.3g} \begin{bmatrix} V(t)b_{4}(t) & 0 & 0 & 0 & V(t)b_{5}(t)\\ 0 & 0 & -57.3g & 0 & 0 \end{bmatrix} \end{align} $$

$$ \begin{align} D_{1}(t) = 0, \quad D_{2}(t) = -\frac{V(t)}{57.3g} \begin{bmatrix} b_{6}(t) \\ 0 \end{bmatrix} \end{align} $$

where $$ a_{1}(t) \sim a_{6}(t), \quad b_{1}(t) \sim b_{7}(t), \acute{a}_{1}(t), \acute{b}_{1}(t) $$ and $$ c_{1}(t) \sim c_{4}(t) $$ are the system parameters. Moreover, $$ V $$ is the speed of the missle and $$J_{x}$$, $$J_{y}$$, and $$J_{z}$$ are the rotary inertia of the missle corresponding to the body coordinates.

The Optimization Problem
The optimization problem is to find a state feedback control law $$ u= Kx$$ such that:

1. The closed-loop system:

$$ \begin{align} \dot{x} &= (A+B_{1}K)x + B_{2}d \\ z &= (C + D_{1}K)x + D_{2}d \end{align} $$

is stable.

2. The $$ H_{\infty} $$ norm of the transfer function:

$$G_{zd}(s) = (C + D_{1}K)(sI-(A+B_{1}K))^{-1}B_{2} + D_{2}$$

is less than a positive scalar value, $$ \gamma $$. Thus:

$$ ||G_{zd}(s)||_{\infty} < \gamma $$

The LMI: LMI for non-rotating missle attitude control
Using Theorem 8.1 in [1], the problem can be equivalently expressed in the following form:

$$ \begin{align} &\text{min} \quad \gamma \\ &\text{s.t.} \quad X > 0 \\ &\begin{bmatrix} (AX+B_{1}W)^{T} + AX+B_{1}W & B_{2} & (CX+D_{1}W)^{T} \\ B_{2}^{T} & -\gamma I & D_{2}^{T} \\ CX + D_{1}W & D_{2} & -\gamma I \end{bmatrix} < 0 \end{align}$$

Conclusion:
As mentioned, the aim is to attenuate the disturbance on the performance of the missile. The parameter $$ \gamma $$ is the disturbance attenuation level. When the matrices $$ W $$ and $$ X $$ are determined in the optimization problem, the controller gain matrix can be computed by:

$$ K = WX^{-1} $$

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/asalimil/LMI-for-Attitude-Control-Nonrotating-Missle-Yaw-Roll-Channel

Related LMIs
LMI for Attitude Control of Nonrotating Missles, Pitch Channel

Return to Main Page
LMIs in Control/Tools


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User:Feliixs/sandbox

credit card

title: User:Feliixs/sandbox


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User talk:Timed Levels

--Pi zero (discuss • contribs) 00:29, 25 November 2019 (UTC)

title: User talk:Timed Levels


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User:Sylvia Chung Yan Shan

F4 Chapter 7: Acid and Bases

title: User:Sylvia Chung Yan Shan


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User talk:Defence Carlos

English
Hello Wikipedia it is so great to have you Defence Carlos (discuss • contribs) 07:49, 25 November 2019 (UTC)

English
Hello Wikibooks Defence Carlos (discuss • contribs) 07:50, 25 November 2019 (UTC)

title: User talk:Defence Carlos


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User:Defence Carlos

I am Defence Carlos from Los Angeles in California 😍😍

title: User:Defence Carlos


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User:Defence Carlos/sandbox

no way i am not

title: User:Defence Carlos/sandbox


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User talk:Defence Carlos/sandbox

Wikipedia
Haha zia phela zia phela zi mnadi ka khulu Hello wikieverything Defence Carlos (discuss • contribs) 10:43, 25 November 2019 (UTC)

title: User talk:Defence Carlos/sandbox


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World Stamp Catalogue/Hong Kong

Postage Stamps by Year
Note: Please note that the above information is based on the 2015 edition of Yang's Postage Stamp & Postal History Catalogue of Hong Kong.

title: World Stamp Catalogue/Hong Kong


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World Stamp Catalogue/Hong Kong/1860-1869

Definitive Stamp

1862 Queen Victoria 1st Issue

Watermark: Unwatermarked

Perforation: 14

Printer: De La Rue & Co.

1863 Queen Victoria 2nd Issue

Watermark: Crown CC

Perforation: 14

Printer: De La Rue & Co.


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Cookbook:Bua Loi (Rice Balls in Sweet Coconut Milk)

Bua loi is a traditional Thai rice flour dessert. It is often prepared for religious or ritual ceremonies, but it can also be eaten as an everyday dish. Bua loi are often brightly colored with various ingredients (see notes).

Ingredients

 * 2 cups sweet glutinous rice flour
 * 1 cup steamed and mashed taro root
 * ¼ cup water
 * Coconut milk

Procedure

 * 1) Combine rice flour, mashed taro, and water to make a dough.
 * 2) Shape the dough into small balls, using additional rice flour to prevent sticking.
 * 3) Bring a large pot of water to a boil. Add the dough balls to the boiling water. They will initially sink but will gradually float to the surface as they cook.
 * 4) Remove the cooked bua loi from the pot, and drain the water.
 * 5) Transfer the bua loi to a dish, and serve with coconut milk. This dish is best served hot.

Notes, tips, and variations

 * If you want to make your bua loi more colorful, you can add pumpkin (yellow) or pandan (green).


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Issues in Interdisciplinarity 2019-20/Truth in Cambridge Analytica Scandal

This Wikibook chapter explores how the truth about the Facebook–Cambridge Analytica data scandal is portrayed in different disciplines and why these contrasting truths create an interdisciplinary issue.

Case Study: The Facebook-Cambridge Analytica Scandal
The scandal was publicized in 2018 when the political consulting firm Cambridge Analytica (CA) was reported to have been harvesting data from Facebook profiles to sway the 2016 United States presidential campaign in favour of Republican candidate Ted Cruz. Upon further investigation, CA was found to have influenced more than 200 elections worldwide, including Donald Trump's 2016 campaign, where the data of up to 87 million Facebook profiles was compromised.

The acquisition of the data
In 2013, the data scientist Aleksandr Kogan developed a personality quiz app called "thisisyourdigitallife", which paid people to answer 120 questions, but first required the user to provide access to their Facebook activity. Kogan was researching the link between Facebook activity and personality. Later that year, Kogan was contacted by the firm SCL Group, a parent company of CA, with a business proposal: SCL would pay Kogan to get more people to take the survey if he provided them with the gathered data. SCL was interested in the app as it gathered data from its users as well as their friends' data, such as likes, posts, comments, location, and even private messages. An estimated number of 270 000 people took the survey, compromising the private data of 87 million people.

Law
Under 2013 Terms of Service, Facebook's Application Programming Interface (API) allowed developers to access the data of an individual in question and their friends. Kogan's 2013 operations were legal since Facebook users were expected to have agreed to the terms and conditions that put them at such data extraction risk. However, Facebook changed its API version in April 2014, limiting the data scope new app developers could have, but giving existent apps a one-year enforcement delay to redesign their software to match the new API. Kogan had the right to keep harvesting data under the 2013 API for one more year. Consequently, in 2015, "thisismydigitallife" ceased its operations but was allowed to keep all the data it had harvested. Regarding the initial agreement between Kogan and Facebook, Kogan explicitly stated his possible intention to sell, to which Facebook knowingly agreed, although it conflicted with sections of Facebook's Platform Policy. The positive and objective truth from the discipline of law is that the data collected by Kogan was gathered and sold to CA legally.

Human Rights
Article 12 of the Universal Declaration of Human Rights declares the right to privacy. We see a clear violation of this principle as it was unrighteous to gather users' personal data without consent as it took advantage of the users' unawareness and trust. Facebook was therefore fined £500,000 by the Information Commissioner's Office in the UK for the supposed breaching of British Privacy Law section DPP1 (Data Protection Principles), as the data collection was carried out unjustly, although legally.

Psychology
To influence the voters, CA quantified 5 different personality traits in all 87 million profiles following the OCEAN (The Big Five Personality Traits) model: Openness, Conscientiousness, Extroversion, Agreeableness, and Neuroticism.

Once the psychographic information was obtained, CA chose to target some voters on the topic of creation of jobs: a person scoring high in the "openness" category was targeted with an ad on gaining experience through work, whilst a highly neurotic person got another ad on receiving security and emotional stability through work. Micro-targeting voters is much more efficient as it appeals to the individual, rather than being a mass distribution of one advertisement.

Data Science
To convert the raw data into individual OCEAN profiles, CA used a process called data mining, which predicts information based on patterns. CA began by developing a training data set (the initial Facebook activity and answers to the survey), on which they could base the target variable data set on (Facebook data they wanted to make predictions on). Using artificial neural networks, the CA team mathematically linked the initial Facebook data (270000 survey participants) to their self-declared personality attributes by continually optimizing the weight of neural network connections to perfect prediction processes. Once this training data set perfected, they applied it to the target variable set, which resulted in 87 million OCEAN personality predictions of astounding accuracy.

CA used another algorithm that generated custom Facebook ads for each individual, as Facebook's extremely lenient Advertisement Policy allowed such political targeting to take place.

Ethics, Politics, and Media
From the viewpoint of democratic ideals, social platforms being manipulatively used for micro-targeting voters is unethical because it violates the fundamental "fair and free" aspect of democracy. It gives rich campaigners the ability to indirectly suppress freedom of choice. However, this is an example of subjective truth. From a consequentialist and autocratic point of view, manipulating people in order to guide society for the autocratic "greater good" is justified. The media calling out what happened in 2018 puts into light the democratic bias which forms our current definitions of what is right and what is wrong.

Ethics as a discipline and concept is socially constructed. Thus, a constructivist approach to the scandal allows for a better understanding of why, as advocates of democracy, some people believe it was unethical.

Law
From the perspective of the objective and positivist truth gathered from international Law, the exploitation of personal data by CA in 2016 does not have any legal consequences as it was conducted under jurisdiction. The data mining for psychographic profiles was legal as CA owned the raw data, and the micro-targeting of voters through Facebook is legal as their Advertisement Policy allows this. Although CA's influence in the 2014 and 2016 elections possibly violated US election law which forbids foreign involvement in elections, the issue has not been taken to court.

Conclusion
To understand the Cambridge Analytica scandal, it is imperative to take an interdisciplinary approach as the disciplines of law, data science, psychology, and politics come into play. However, we observe that the objective and positive truth provided by law clashes with the constructivist and subjective truth provided by ethics. Legally speaking, nothing illicit took place: the reason personal information was accessed was a loophole in Facebook's API. Using psychology and data science, CA was able to transform the data into information warfare and as a consequence influence over 200 elections worldwide. However, from a modern-day ethical perspective, this was a malicious and predatory act as it undermined the fundamental values of democracy and violated human rights. This scandal exemplifies an interdisciplinary issue related to the concept of truth: the law maintains that nothing wrong happened, while modern-day ethics clearly condemns the scandal.


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Micronations/List of past micronations/Province of Bumbunga

The Province of Bumbunga (-33.915°N, 138.229°W) was an Australian secessionist micronation located on a farm at Bumbunga near Snowtown and Lochiel, South Australia, from 1976 until approximately 2000. Its founder and only ruler was a British monkey trainer, uranium prospector, and postmaster named Alec Brackstone.

Historical Background
In November 1975 the Australian Labor Party government of Prime Minister Gough Whitlam was dismissed under controversial circumstances by Governor-General John Kerr, the official governmental representative of Queen Elizabeth II. Brackstone, an ardent British monarchist, became alarmed by what he saw as a drift away from the Australian system of constitutional monarchy toward outright republicanism. To ensure that at least a portion of the Australian continent would always remain loyal to the British Crown, he declared his four-hectare property northeast of Adelaide to be the independent Province of Bumbunga on 29 March 1976, and appointed himself its "governor-general".

Economy
Brackstone then set about attracting tourism by planting thousands of strawberry plants in the pattern of a huge scale model of Great Britain. He intended to conduct weddings on his property, during which soil from the appropriate British county would be sprinkled on the ground. Implementation was delayed when Australian customs authorities seized the soil Brackstone had imported from the UK, and the entire enterprise was scuttled when the strawberry fields perished during a drought.

In 1980 Bumbunga began issuing cinderella stamps portraying members of the British royal family (except Sarah Ferguson, whom Brackstone disliked). Later issues addressed anti-nuclear sentiments and other social causes while retaining the royal theme. Though worthless as postage, they became popular with philatelists and oddity collectors. Fifteen series of 5000 copies each were eventually produced.

Fall
In 1987 changes to Australian investment laws that reduced the attraction of philatelic investments led Brackstone to abandon his commercial operations, and Bumbunga slid into relative oblivion. In 1999 Brackstone was arrested and charged with possession of illegal firearms. His assertion of diplomatic immunity due to his status as Bumbunga's sovereign was unsuccessful but, according to Brackstone, the charges were ultimately dropped nevertheless. In 2018 Brackstone was interviewed at his residence in Clare, South Australia, still claiming to be Governor of the province.


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text: Shelf:University College London projects/ancestry


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Issues in Interdisciplinarity 2019-20/Evidence in Intermittent Fasting

This chapter discusses the use of evidence concerning biology, sociology, marketing, among others, when analysing intermittent fasting to outline the importance of an interdisciplinary approach and explore issues facing interdisciplinary researchers. To grasp a better understanding of why intermittent fasting is an important topic, a discussion about how our eating choices are impacted everyday through advertisements is necessary.

Introduction
The act of fasting, defined by the Oxford Dictionary as "a period during which you do not eat food", has been a common practice for centuries. In Ancient Greece, it already enjoyed vast popularity and was heavily endorsed by Hippocrates for its benefits.

Ever since, fasting has been used for medical and religious reasoning. It plays a great role in the world's major religions. In Christianity and Judaism, fasting is associated with mourning and atonement for sins. Islam made fasting easy by correlating it with self-purification during Ramadan. Passages from the Quran illustrate how people are encouraged to fast:''"…And fasting is good for you, if you only knew." (Ch.2:v.185) ''

Today, one of the most common types of fasting is intermittent fasting. This emboldens individuals to eat during a certain period of time, for example, six hours, and then, to fast for the remaining time, in this case, 18 hours. Alternative approaches on intermittent fasting exist, namely alternate-day fasting, periodic fasting, and time-restricted feeding, each allowing you to eat for different lengths of time.

In the last decades, the volume of academic research on intermittent fasting has increased, each discipline coming up with its own form of evidence.

Anthropological view on eating patterns
Anthropology concentrates on the behaviour of our ancestors and individuals from primitive and Palaeolithic cultures who lived their lives as hunter-gatherers. Anthropologist showed that these individuals used to hunt for food to ensure their survival. Thus, their next meal was often unpredicted, unscheduled, and could fluctuate depending on the season. Even though they were unaware of their eating patterns, individuals in the primitive society used to fast as a way of life.

Sociological view on eating patterns
Sociology, which studies "the interaction and collective behaviour of organised groups of human beings", focuses on how eating habits were established and became cultural patterns through time. The evidence found, such as field research through observation and scholarly books, have confirmed that eating at regimented times is a cultural pattern people have embraced because there is comfort in predictability .

Sociologist Robin Fox revealed how breakfast times used to depend on social status rather than nutritional needs. The upper-class had later breakfasts than the working class, suggesting they had time for leisure activities.

However, this eating pattern no longer works with today’s modern schedules. Evidence, particularly a survey overseen by the US Department of Agriculture, exposed a deviation from breakfast and lunch being the main meals to lunch and dinner. We can, therefore, deduce that modern itineraries dissonate with the eating patterns we have adopted.

Genetical Perspective
Genetics examines the "heredity and variations of organisms". Researchers question eating habits based on our genome. Undoubtedly, as humans used to live as hunters-gatherers, oscillating between periods of fast and feast, the genes selected were adapted to our originative lifestyle. Looking at our genotypes' evolution we can have a better understanding of our metabolism. Evidence illustrate that the "three meals a day" pattern answers social requirements rather than obliging our bodies' metabolism.

Evidence, from scholarly articles and genetical experiments, shows that a current major health issue, insulin resistance, may be the consequence of the encounter between the genomes selected during the Palaeolithic era and our current lifestyle, characterised by the abundance of food.

One experiment undertook subjected eight men to fasting, following up with laboratory reports of blood flow and insulin rates. The results show that intermittent fasting improves our metabolic status and increases insulin action, reducing the mismatch between our genotypes and eating habits.

Physiological Perspective
Physiology focuses on the impact of Intermittent fasting on our bodies. Scientists entrust on evidence suchlike experiments on rodents and humans to show its benefits. Studies show that intermittent fasting improves metabolism's stress resistance across species, proving that this diet contributes to lifespan extension.

Furthermore, intermittent fasting aids the function and resilience of the cardiovascular system. As evidence, scientists have observed a decrease in heart rate and blood pressure of rats that were undergoing intermittent fasting.

Another study published in The Journal of Nutritional Biochemistry unveiled that intermittent fasting improved left ventricular function and recovery of blood pressure and heart rate.

Neurosciences Perspective
Neurosciences inspect the consequences of intermittent fasting on our brain and our memory by mainly using evidence from brain scans or MRI. Some studies have found that putting mice on intermittent fasting leads to an increase in their memory and improves their reaction to stress.

Consumerism in society
Following the emergence of marketing and consumerism in the food industry, the methods that are used to sell products have changed substantially as time passed. Our eating habits can be explained by the advanced marketing techniques that they use, encouraging us to overeat.

Marketing and overeating
One of the key factors behind overeating is choice. Being exposed to the same stimuli, particularly food, will numb senses leading to "sensory-specific satiety". Therefore, people eat more when they have more food choices. For example, 'Starbucks' claims that there are over 80.000 possible drink combinations available. The powerful marketing techniques behind this array of variety are personalisation and convenience which persuade consumers into a purchase.

The psychology of overeating
Advertising, as defined by Cambridge Dictionary “the business of trying to persuade people to buy products”, is deeply enrooted in the food industry. This industry is always looking to persuade people to overeat “to satisfy stockholders”. They allocate substantial amounts of money on food advertising, therefore insinuating the impactful role it has on consumer purchases.

Evidence, namely the study led by the University of Wollongong, clearly suggests the influence advertisements have on eating behaviours. Participants were required to watch movies segments interspersed with either food or non-food advertisements over six days. The results of the study found participants ate more after being exposed to promotions.

Conclusion
The evidence clearly suggests that Intermittent fasting is beneficial for our health and that the "three meals a day" approach is solely a social construction. Yet, our eating habits remain unchanged.

The lack of cohesion and thorough discussion on evidence between the disciplines led to an underestimation of the importance of fasting. By bringing together evidence on fasting with an interdisciplinary spectrum, it would improve its' analysis and is more likely to impact on society's flawed eating habits.

Nonetheless, even if an interdisciplinary researcher tried to link the evidence, he would still face the issue of recognition. Findings done by more subjective disciplines such as social sciences or marketing are often disregarded by scientifical branches of academia that perceive evidence done through experiments as absolute. Therefore, there is a fundamental disagreement on the actual nature of evidence leading to disharmony of opinions as previously seen.


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Talk:Issues in Interdisciplinarity 2019-20/Evidence in Intermittent Fasting

Meeting with the group. Shared all our new researches and ideas. Decided to change our issue from "Power" to "Evidence" Clarified what our issues, disciplines and case study was Planned what we want to do next Next meeting on Friday at 3pm LouiseUCL (discuss • contribs) 15:16, 25 November 2019 (UTC)

Meeting with the group on Friday, Wiki-book starting to look good, still need few modifications. Mainly need to work on introduction, conclusion, neurosciences... Need to cut the number of words because too long (around 1500). Next meeting on Monday LouiseUCL (discuss • contribs) 22:04, 4 December 2019 (UTC)

Meeting on Monday. Whent trough wikibook lines by lines, making small modifications. Still need to make few changes in introduction and conclusion. Meeting again on Thursday for a last check. LouiseUCL (discuss • contribs) 10:05, 5 December 2019 (UTC)

Meeting Thursday. We made very small changes were we still needed to. Wikibook officially finished! :) LouiseUCL (discuss • contribs) 09:38, 8 December 2019 (UTC)