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LMIs in Control/pages/Discrete-Time Detectability

Discrete-Time Detectability

A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.

Discrete-Time LTI systems can be made detectable using observer gain L, which can be found using LMI optimization, such that the close loop system is detectable.

The System
Discrete-Time LTI System with state space realization $$(A_d,B_d,C_d,D_d)$$ $$ \begin{align} &A_d \in \bf{R^{n*n}}, &B_d \in \bf{R^{n*m}}, &C_d \in \bf{R^{p*n}}, &D_d \in \bf{R^{p*m}} \;\\ \end{align}$$

The Data
The matrices: System $$ (A_d,B_d,C_d,D_d), P, W $$.

The Optimization Problem
The following feasibility problem should be optimized:

Maximize P while obeying the LMI constraints. Then L is found.

The LMI:
Discrete-Time Detectability

The LMI formulation

$$ \begin{align} P \in {S^{n}}; W \in {R^{m*n}}\;\\ &P>0\\ \begin{bmatrix}P & A_d^TP+C_d^TW\\
 * & P\end{bmatrix}&>0,\\

L = P^{-1}W

\end{align}$$

Conclusion:
The system is detectabe iff there exits a $$P$$, such that $$P>0$$. The matrix $$A_d+LC_d$$ is Schur with $$L = P^{-1}W$$

Implementation
A link to CodeOcean or other online implementation of the LMIMATLAB Code

Related LMIs
- Continuous time Detectability


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LMIs in Control/Stability Analysis/Stability of Systems with Integral Quadratic Constraints

 * Stability of Quadratic Constrained Systems

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


text:
LMIs in Control/pages/L2 gain of systems with multiplicative noise

The System

\begin{align} x(k+1)&=Ax(k)+B_ww(k)+\sum_{i=1}^{L}(A_ix(k)+B_{w,i}w(k))p_i(k),\quad x(0)=0,\\ z(k)&=C_zx(k)+D_{zw}w(k)+\sum_{i=1}^{L}(C_{z,i}x(k)+D_{zw,i}w(k))p_i(k), \end{align}$$ where $$ p(0), p(1),\dots $$, are independent, identically distributed random variables with $$ Ep(k) = 0, Ep(k)p^\top(k) = \Sigma = diag(\sigma_1,\dots,\sigma_L)$$ and $$x(0)$$ is independent of the process $$p$$.

The Data
The matrices $$ A,B_w,\{A_i.B_{w,i}\}_{i=1}^L,C_z,D_{zw},\{C_{z,i},D_{zw,i}\}_{i=1}^L,\{\sigma_i\}_{i=1}^L $$.

The LMI:

\begin{align} &\min_{\{P \succ 0, \gamma^2\}}\gamma^2 \\ &\quad  s.t. \begin{bmatrix} A & B_w \\ C_z &  D_{zw}\end{bmatrix}^\top \begin{bmatrix} P & 0 \\ 0 &  I \end{bmatrix} \begin{bmatrix} A & B_w \\ C_z &  D_{zw}\end{bmatrix}-\begin{bmatrix} P & 0 \\ 0 &  \gamma^2 I \end{bmatrix}+\sum_{i=1}^{L}\sigma^2_i\begin{bmatrix} A_i & B_{w,i} \\ C_{z,i} &  D_{zw,i}\end{bmatrix}^\top \begin{bmatrix} P & 0 \\ 0 &  I \end{bmatrix} \begin{bmatrix} A_i & B_{w,i} \\ C_{z,i} &  D_{zw,i}\end{bmatrix}^\top \preceq 0 \end{align}$$

Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/a34713575cd8ae9831cb5b7eb759d0fd45a8c37f

Conclusion
The optimal $$ \gamma $$ returns an upper bound on the $$ \mathcal{L}_2 $$ gain of the system. .

Remark
It is straightforward to apply scaling method [Boyd, sec.6.3.4] to obtain component-wise results.


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User:Patjbails/sandbox

Coherence theory vs. Correspondence theory
There are two important theories on truth in philosophy. Coherence theory regards truth as following an individual's subjective set of beliefs without validating an objective truth. In this view, both the accounts from the Chinese victims and the Japanese aggressors would be seen as true. The Japanese aggressors may have their own subjective beliefs in one may or may not have happened, as individual accounts create only limited context for the entire situation.

title: User:Patjbails/sandbox


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English-Hanzi/Angola

Angola is a west-coast country of south-central Africa.

安哥拉是非洲中南部的西海岸国家.

title: English-Hanzi/Angola


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LMIs in Control/pages/Stability of Linear Delayed Differential Equations

The System

\begin{align} \dot x(t)&=Ax(t)+\sum_{i=1}^{L}A_ix(t-\tau_i),\\ \end{align}$$ where $$ x(t) \in \mathbb{R}^n $$ and $$ \tau_i >0$$.

The Data
The matrices $$ A,\{A_i.\tau_{i}\}_{i=1}^L $$.

The LMI:
Solve the following LMIP

\begin{align} &\text{Find} \{P \succ 0, P_1 \succ 0, \dots,P_L \succ 0\} :\\ &\quad  s.t. \begin{bmatrix} A^\top P +PA+\sum_{i=1}^L P_i & PA_1 & \dots & PA_L \\ A^\top_1P &  -P_1 & \dots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ A^\top_L P & 0 & \dots & -P_L \end{bmatrix} \prec 0,P_1 \succ 0, \dots, P_L \succ 0. \end{align}$$

Implementation
https://github.com/mkhajenejad/Mohammad-Khajenejad/commit/50fc71737b69f2cf57d15634f2f19d091bf37d02

Conclusion
The stability of the above linear delayed differential equation is proved, using Lyapunov functionals of the form $$ V(x,t)=x(t)^\top P x(t)+\sum_{i=1}^{L}\int_{0}^L x^\top(t-s)P_i x(t-s) \ ds $$, if the provided LMIP is feasible.

Remark
The techniques for proving stability of norm-bound LDIs [Boyd, ch.5] can also be used.


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English-Hanzi/Algeria

Algeria is a country in the northwest of Africa.

Algeria是非洲西北部的一个国家.

title: English-Hanzi/Algeria


text:
User:Qasim Shah dubai wale/sandbox

hello everybody.

title: User:Qasim Shah dubai wale/sandbox


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Lentis/Technology in the 2019 Hong Kong Protests

The 2019 Hong Kong protests began in response to the Fugitive Offenders and Mutual Legal Assistance in Criminal Matters Legislation (Amendment) Bill 2019, also known as the 2019 Hong Kong extradition bill. Hong Kong citizens feared the bill would allow China to arrest critics of the Chinese government which would severely violate Hong Kong’s freedom of speech. Hong Kong protesters have utilized technology that promotes anonymity, especially in response to suspected Hong Kong facial recognition software and internet censorship. Anonymity is crucial to Hong Kong citizens because of distrust of their government’s altruism and China’s tendency to crackdown on dissent.

Background
Hong Kong was a British colony from 1842 to 1997 when it was returned to China, under the agreement that the Chinese government uphold the principle of "one country, two systems" until 2047. The system entails a high level of autonomy for Hong Kong. The Chinese government respected “one country, two systems” at first, but gradually started to influence Hong Kong’s government to return it under China’s control.

In response to the increasing mainland China intervention to Hong Kong politics, Hong Kong residents have resisted in forms of protests, notably the 1st July protests and 2014 Hong Kong protest, or “Umbrella Movement.” The 2019 Hong Kong protest began in response to the 2019 Hong Kong extradition bill, which was proposed because of a murder case in Taiwan in 2018. The bill was not transparent, so protesters feared the bill would allow the Chinese government to arrest critics in Hong Kong. The protests have grown to more issues. Hong Kong protesters have made five demands:

 * Full withdrawal of extradition bill, which has been already accomplished
 * An independent inquiry into alleged police brutality
 * Retracting the classification of protesters as “rioters”
 * Amnesty for arrested people
 * Dual universal suffrage, for both the Legislative Council and the Chief Executive

Use in Mainland China
China has been using facial recognition software to build smart cities. The facial recognition allows Chinese to use ATMs, to check in at reception, and to pay for goods. It is reported the Chinese government employs 170 million CCTV cameras. Chinese police officers are currently using smart glasses that recognize any suspect or criminal registered in the police database. People are concerned that the Chinese government abuses the biometrics to cement totalitarian rule. For example, the Chinese government has used surveillance to suppress and detain Uyghurs, an ethnic minority.

Protesters
Hong Kong protesters believe a similar level of surveillance and facial recognition used in China is implemented in Hong Kong. Fearing being identified by the Hong Kong government, they have sawed down smart lampposts, which are believed to contain facial recognition technology, and destroyed surveillance cameras. Hong Kong protesters believe exposing their identity would put themselves at risk.

In response to police officers removing badge numbers and acting in plainclothes, some protesters have been posting photos of officers to Telegram channels to track and identify them. One protester, Colin Cheung, attempted to develop an app which would match officer’s faces to a database, although it was not fully implemented. Some Hong Kong police have attached reflective tape to their visors to further obscure their identity, particularly to camera flashes.

The dynamic of being identified in a crowd may be interpreted as a form of Panopticism. In such a case, Foucault saw the observer as having power over the observed. The counter-surveillance of officers is an effective form of activism because it flips their power-dynamic, at a much lower technological cost than FCR. When both groups become anonymous behind masks, however, interactions can become hostile due to lower inhibitions.

Hong Kong Government
The Hong Kong Government denies using facial recognition software with any CCTV systems. The government states that any use of FRS would be regulated by the Personal Data Privacy Ordinance (PDPO). The PDPO outlines Data Protection Principles for the handling of personal data. Notably, subjects of data must provide informed consent of collection, data collection must be limited by necessity, and the collection and use of data should be transparent. The PDPO maintains exemptions for these principles, including the prevention of crime, security, and international relations.

The government denies that the smart lampposts have any facial recognition capabilities. Some features are disabled on the lampposts for privacy concerns: bluetooth tracking, license plate recognition, and high quality video to monitor waste-dumping. One expert warns that any camera in the lampposts could be used, or re-purposed, for facial recognition and surveillance. Without accountability for use, and no technical or legal limitation, protesters cannot trust that the government will not employ facial recognition.

Masks
Protesters have used masks and umbrellas to conceal their faces, and lasers to block cameras. Protesters have been taken away by the police officers did not return, and police do not hold an official record disappearances. This makes protesters afraid of exposing their identity since police can arrest them once the crowd breaks. One case of police abduction is that of Causeway Bay Books, who were booksellers in Hong Kong that were detained in mainland China for publications against the government.

Mask Ban
On October 5, 2019, Chief Executive Carrie Lam passed the Prohibition on Face Covering Regulation under the Emergency Regulations Ordinance (ERO), bypassing legislative process for reasons of "public danger". The Regulation prohibits mask use in public assemblies, whether the assembly is lawful or not. It authorizes police officers to remove masks they believe are being used to prevent identification. The mask ban and arrests were perceived as an escalation to the protests, particularly with the Chinese government's support of the ban. In a crowd, the arrests could have strengthened the support from more neutral protesters, and increased resistance. Mask bans are common in western countries, but opponents the Hong Kong’s ban point out that these countries are democratically accountable to the people. Protesters treat the mask ban with similar distrust as towards the extradition bill, and government more broadly.

The ordinance was deemed unconstitutional on November 18, 2019 by the high court of Hong Kong, on the grounds of “delegating legislative power” and disproportionately restricting freedoms. The Hong Kong government stopped enforcing the ordinance in response. The central government has made some indications they disagree not just with the ruling, but with Hong Kong's freedom to interpret their basic law.

Chinese Censorship
The People's Republic of China regulates and censors the internet with the Great Firewall. The Chinese government increased its control over the internet in the 2000s and has blocked Google search, Wikipedia, Facebook, Twitter and other websites. In their place, the Chinese people use government-monitored social media and websites such as Weibo, Baidu, and Tencent (also known as QQ).

China may try to extend its censorship and Great Firewall to Hong Kong. For example, Telegram, a messaging app used by the Hong Kong protesters, was targeted by a distributed denial-of-service (DDOS) attack. In June 2019, Telegram CEO Pavel Durov stated the IP addresses were primarily Chinese, indicating that the attack originated from the Chinese government.

Hong Kong Censorship
Hong Kong’s basic law guarantees freedom of speech, and Hong Kong’s internet sees relatively little censorship. In October 2019, the Hong Kong court passed a temporary injunction against messages inciting or supporting violence on online forums. An administrator of a protestor Telegram group was arrested, although he was not detained further.

Hong Kong could censor the internet using the colonial-era Emergency Regulations Ordinance (ERO), which was used to ban masks; however, Chief Executive Carrie Lam claimed this will not happen. There are risks that are likely to prevent any such action. Hong Kong serves as an internet hub for Asia, so a large-scale firewall would have rippling effects. Companies in Hong Kong are likely to leave should they perceive unreliable connection to the world. The Central government could coopt any censorship employed by Hong Kong, similar to their intervention into the mask ban.

LIHKG
LIHKG is a popular, Reddit-like forum used by Hong Kong citizens. Protesters use LIHKG to organize and strategize despite the protest having no clear leader. Unlike Chinese social media, LIHKG grants protesters anonymity so they can avoid being targeted or arrested by police.

HKmap.live
HKmap.live is an application that tracks the Hong Kong police's location in real-time along with road blockages, safe spaces, and other notable landmarks. The application is used by protesters to strategize and organize and to avoid police. The application is available online and on the Google Play Store, but was removed from the Apple Store.

Apple
Apple removed HKmap.live, an application used by Hong Kong Protesters, from the Apple Store when criticized by the Chinese. The Chinese claimed that Apple, by "providing a gateway for 'toxic apps' is hurting the feelings of the Chinese people, twisting the facts of Hong Kong affairs, and against the views and principles of the Chinese people." Apple claimed the app was removed because it “was being used maliciously to target individual officers for violence and to victimize individuals and property where no police are present.” However, in China, Apple has removed the Taiwan flag emoji and news applications such as the New York Times and Quartz, the latter of which frequently reports on the Hong Kong Protests. Therefore, Apple’s motivations for removing HKmap.live and its relationship with China are suspect.

Twitter
Twitter is banned by China’s Great Firewall. In August 2019, Twitter announced it had banned 936 accounts originating from within the People’s Republic of China. Twitter claims the accounts were “deliberately and specifically attempting to sow political discord in Hong Kong, including undermining the legitimacy and political positions of the protest movement on the ground.” The accounts were banned on the grounds of “Spam, Coordinated activity, Fake accounts, Attributed activity, Ban evasion” and not for voicing a particular political opinion. Twitter is portraying itself as taking a stand against Chinese propaganda and meddling without taking a clear side on the issue.

Facebook
Facebook is banned in China; however, Facebook admitted to having Chinese advertisers. Facebook CEO Mark Zuckerberg claims that Facebook is present in China through the advertising market which hopefully will lead to a “long term solution” in which Facebook is available to Chinese users.

Conclusion
Facial recognition is a double edged-sword. While it can grant convenience to the people in smart cities, it is also used as a surveillance tool to watch and control those criticize authority, threatening individual privacy. Many technologies using facial recognition were not approved in the democratic western world, since it is deemed as a threat to human rights and privacy. In China, where human rights are less of concern, facial recognition technologies have been widely implemented throughout the country in both beneficial and detrimental ways for its citizens.

While there is no proof of facial recognition software being used by Hong Kong police, protesters cannot trust without accountability and transparency. Protesters have attempted to create a sense of accountability through counter-surveillance. People create accountability using cameras and social media in cases of police brutality and political protests. There is an expectation the government must remain accountable to businesses, and will not censor the internet. The future of the protests depends on the Hong Kong government's accountability.

A crucial use of technology in the 2019 Hong Kong Protests was to maintain anonymity. Anonymity matters to Hong Kong citizens because China is known to suppress and violate the rights of opposition. Thus, Hong Kong protesters dismantled lampposts potentially capable of facial recognition, wear masks during conflicts, and strategize on anonymous, online forums. Esteem for anonymity is common for resistance against powerful authority, and parties will fight over technology that either safeguards or removes anonymity.


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LMIs in Control/pages/Discrete Time H2 Optimal Full State Feedback Control

Discrete-Time H2-Optimal Full-State Feedback Control

A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.

A full state feedback controller design for a Discrete Time system, to minimize the H2 norm of the closed loop system with exogenous input $$w_{k}$$ and performance output $$z_{k}$$.

The System
Discrete-Time LTI System with state space realization $$(A_d,B_d,C_d,D_d)$$ $$ \begin{align} x_{k+1}&=A_dx_k + B_{d1}w_k + B_{d2}u_k\\ z_{k}&=C_{d1}x_k + D_{d12}u_k\\ y_k &= x_k\\ \end{align}$$

The Data
The matrices: System $$ (A_d,B_{d1},B_{d2},C_{d1},D_{d12}), P, Z, F_d $$.

The Optimization Problem
The following feasibility problem should be optimized:

$$ \mu $$ is minimized while obeying the LMI constraints.

The LMI:
Discrete-Time H2-Optimal Full-State Feedback Control

The LMI formulation

H2 norm < $$\mu$$

$$ \begin{align} P \in {S^{n_x}}; Z \in {S^{n_z}}; &F_d \in {R^{n_u*n_x}}; \mu \in {R_{>0}} \;\\ &P>0\\ &Z>0\\ \begin{bmatrix}P & A_dP+B_{d2}F_d & B_{d1}\\
 * & P & 0\\
 * & * & I\end{bmatrix}&>0,\\

\begin{bmatrix}Z & C_{d1}P+D_{d12}F_d\\
 * & P\end{bmatrix}&>0,\\

&trZ<\mu ^2

\end{align}$$

Conclusion:
The H2-optimal full-state feedback gain is recovered by $$K_{d}=F_{d}P^{-1}$$

Implementation
A link to CodeOcean or other online implementation of the LMIMATLAB Code

Related LMIs
- Continuous Time H2 Optimal Full State Feedback Control


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User:LBird BASc/sandbox/ATK/Seminar6/Evidence/Art as Evidence

Introduction
Both positivist and interpretivist insight

art - culture, values, sentiments, materials accessible, attitude towards art

Scientific Analysis
Analysis of the chemical compositions used in artworks can firstly

Gas Chromatography–Mass Spectrometry and Fourier Transform Infrared Spectroscopy

polarized light microscopy (PLM), X-ray diffraction (XRD) and fluorescence (XRF), scanning electron microscopy and microanalysis, Fourier transform infrared microspectrometry (FTIR) and gas chromatography–mass spectrometry (GC-MS). In the last decade, Raman microscopy has become a common tool thanks to its ability to non-destructively characterize pigments, minerals, and a variety of polymers

Subject Matter
Many aspects of the period the artwork was created can be derived from the subject matter of the works.

- medieval - religious

industrial revolution - romanticism

realism - french revolution - art becomes accessible to the rising middle class

dada

Stylistic Choices
movement

renaissance

romanticism

dada


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History of wireless telegraphy and broadcasting in Australia/Topical/Biographies/Walter Isaac Monkhouse

Walter Isaac Monkhouse
Walter Isaac Monkhouse was a prominent amateur operator, amateur broadcaster, amateur club administrator in the late 1920s and early 1930s, and ultimately senior state public servant. His station callsign, if any, is not yet known 4?? (4=Queensland, ?=?, ?=?) and he operated from Brisbane, Queensland. A summary biography has not yet been prepared however the following resources have been assembled in preparation:
 * Transcriptions and Notes - Walter Isaac Monkhouse - More than 150 transcriptions and notes
 * Photos, QSL cards and other graphics - Walter Isaac Monkhouse - Nothing uploaded as yet

Early Life and Family
Walter Isaac Monkhouse was born in New Zealand in 1887 to parents Henry Isaac Monkhouse and Jane Edgar Monkhouse nee Anderson. He studied to become an electrician and, after qualification, he engaged in that field for some years around 1910 at Rangataua in central North Island (Manawatu-Wanganui province).

Central Technical College
In May 1916, effective 10 February 1916, Monkhouse was appointed instructor in telephone mechanics at the Central Technical College, Brisbane within the Queensland state public service.