Prerequest Fundamentals for Robust Control Theory?

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Mohamed-Mourad Lafifi

Dear Mohammad Fahad,

I suggest you to see links in topic.

-Fundamentals of Control Theory - Encyclopedia of Desalination and ...

www.desware.net/sample-chapters/d10/d12-002.pdf

-Electrical Engineering (EE) - Graduate Course Descriptions - Penn State

bulletins.psu.edu/graduate/courses/E/E_E/584/200708SP

-Introduction to Robust Control

https://www.iitk.ac.in/.../system%20and%20control/.../Lecture1_Int...

-2016 | Robust Control - TOKYO TECH OCW

www.ocw.titech.ac.jp/index.php?...2...

-A Course in Robust Control Theory a convex approach - ResearchGate

https://www.researchgate.net/.../266039355_A_Course_in_Robust_...

Best regards

Mohammad Fahad Al-Malki

Dear Murad,

Thanks a lot for taking interest in replying my question. Please note that I know all these stuff you mentioned and have used them intensively. However, my question is a bout a specific topic; i.e. the mathemtical foundation of robust control.

Let me give an example from Kemin Zhou book (Robust and Optimal Control). If you look at Theorem 16.4, how the thorem is constructed and how the assumptions are made and ultimately what are the mathematical background required to understand the proof of such theorem.

Further, how can you develop such thorems and lay down Lemmas to prove a theorem that support some results you obtained from simulation?

Also, where to find historical treatment of the subject to let the reader be aware of the evolvment of the mathematical foundations of Robust Control.

I have included pages of Thorem & Lemma.

Thanks & regards

Sanjoy Roy

Hi Mohammad,

A strong background of the following will be essential:

Advanced functional analysis, particularly using L1 and Linfinity norms. Of course, that itself requires good understanding of suprema, infima, and convergent variable sequences.

Optimal control mathematics (particularly LQR etc.) - please note, I am not talking of OC implementations !

With best wishes.

-Sanjay

Dear Sanjoy,

Thanks for your comments. You're right the book by Kirk on Optimal Control has shown systematically how the theory of optimal control is linked to solution of pair of ARE. I am looking for the same text book that handles the thories & lemmas of H-infinity control. I will check a reference on Advanced functional analysis

Thanks again

All the best

Hazem Demrdash

Good day Mohammad

Here is what you realy need (though not a traditional text book but still can help)and the downoad link, all my best wishes:

Advanced Mathematical Tools for Automatic Control Engineers Volume 1: Deterministic Techniques Alexander S. Poznyak

http://www.abarkouhiau.ac.ir/bookpdf/1.pdf

Good day to you as well. Thanks so much for taking interest in attending this question. My actual interest is to know how the "theorems" and alike are formed in the Robust Control textbooks. For example, if you pick the book by Kemin Zhou (Robust Optimal Control) and look at Theorem 16.4 (page 419) how the theorem is formed and how the conditions i -> iii are stipulated. After that, how to prove it but let's focus on the first part, the formation. I am interested in this topic. Any comment?

Ok, could you please consult nonlinear control systems analysis and design by horacio J. Maquez, pge 63.

He recomendded a list of references ( all are classical references) on mathematical analysis,vector spaces nd theory of diffenrential equations.

Kindly notice that most of the people who are fluent in this approach have had courses in mathematical analysis, topology, differential geometry. From my own experience, It is not pleasant to do a self study on those topics try to google some universities who arrrange courses for thoe with engineering background since the topics are practiced by

Mathematicians and not engineers.

All my best wishes

Dear Hazem,

if you read my earlier comment about LQR optimal control where the book by D. Kirck shows systematically the derivation of optimal control law using ARE, I would assume that there is a good book or technical report/paper shows in the same fashion the construction of theorems leading to Robust H-inf control law. This is what I am looking for. The book by K Zhou needs explanation.

Thanks for your interest to help.

Ibraheem Kasim Ibraheem

Advanced courses on linear algebra will help in this direction. Moreover, a book by Dennis S. Bernstien

https://www.amazon.com/gp/product/0691140391/ref=s9_acsd_simh_bw_c_x_2_w?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=merchandised-search-3&pf_rd_r=KG2QS6MG2J4Y5M396NE8&pf_rd_r=KG2QS6MG2J4Y5M396NE8&pf_rd_t=101&pf_rd_p=fe185ec9-c8f5-44c0-897e-4c0bde93268c&pf_rd_p=fe185ec9-c8f5-44c0-897e-4c0bde93268c&pf_rd_i=283155

is very important.

Dear Ibraheem,

My point is very specific and it's about formation of theorem for Robust Control such as Thorem 16.4 of Kemin Zhou book. The book you mentioned is about Matrix Algebra won't.