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Avtomatika i Telemekhanika, 1984, Issue 8, Pages 5–45 (Mi at4792)  

This article is cited in 8 scientific papers (total in 9 papers)

Surveys

Optimization and invariance of linear stationary control systems

V. A. Yakubovich

Leningrad
Abstract: The survey discusses the relationships between optimization of linear stationary systems subjected to stochastic exogenous signals and robustness or consistent inimplementability of optimal controllers. The relationships between the optimization theory and the invariance theory is determined. The difficulties facing the invariance theory (instability or non-robustness when absolute invariance in attempted), are shown to be attributable to the same causes to which the recently discovered similar difficulties in the stochastic control theory are. A functional is introduced which determines the measure of invariance of a specified output with a specified (deterministic) input of the system and the minimization of this functional is shown to be equivalent to some stochastic optimization. In this way problems of system optimization are found to be solvable by using the invariance property. The relationship with analytical controller design is shown and the role of singular problems demonstrated. Methods of obtaining minimizing sequences are considered for cases where an optimal controller is inexistent. Examples are given where statistical optimization problems are solved with a coarse and structurally and consistently realizable stabilizing controller.

Received: 07.06.1983
Bibliographic databases:
Document Type: Article
UDC: 62-505
Language: Russian
Citation: V. A. Yakubovich, “Optimization and invariance of linear stationary control systems”, Avtomat. i Telemekh., 1984, no. 8, 5–45; Autom. Remote Control, 45:8 (1984), 963–999
Citation in format AMSBIB
\Bibitem{Yak84}
\by V.~A.~Yakubovich
\paper Optimization and invariance of linear stationary control systems
\jour Avtomat. i Telemekh.
\yr 1984
\issue 8
\pages 5--45
\mathnet{http://mi.mathnet.ru/at4792}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=798709}
\zmath{https://zbmath.org/?q=an:0564.93026}
\transl
\jour Autom. Remote Control
\yr 1984
\vol 45
\issue 8
\pages 963--999
Linking options:
  • https://www.mathnet.ru/eng/at4792
  • https://www.mathnet.ru/eng/at/y1984/i8/p5
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Avtomatika i Telemekhanika
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    Full-text PDF :153
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