Abstract:
A linear problem of optimal guaranteed control of a delay system is considered in which geometric constraints on control actions and terminal constraints on states are present. A new concept of a state of the problem that represents a finite-dimensional vector is introduced. Three kinds of optimal feedback are defined. We describe methods for implementing open-loop and closable optimal feedbacks. They are based on a fast dual method for the correction of optimal programs. The results are illustrated by examples.
Citation:
R. Gabasov, N. M. Dmitruk, F. M. Kirillova, “Optimal guaranteed control of delay systems”, Control, stability, and inverse problems of dynamics, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 2, 2006, 27–46; Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S26–S46
\Bibitem{GabDmiKir06}
\by R.~Gabasov, N.~M.~Dmitruk, F.~M.~Kirillova
\paper Optimal guaranteed control of delay systems
\inbook Control, stability, and inverse problems of dynamics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 2
\pages 27--46
\mathnet{http://mi.mathnet.ru/timm149}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2338473}
\zmath{https://zbmath.org/?q=an:1134.49016}
\elib{https://elibrary.ru/item.asp?id=12040734}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 255
\issue , suppl. 2
\pages S26--S46
\crossref{https://doi.org/10.1134/S0081543806060034}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33847005453}
Linking options:
https://www.mathnet.ru/eng/timm149
https://www.mathnet.ru/eng/timm/v12/i2/p27
This publication is cited in the following 3 articles:
Natalia M. Dmitruk, “Optimal Control Strategies for Constrained Linear Time-Delay Systems with Disturbances”, J Math Sci, 2024
N. M. Dmitruk, “Optimal strategy with one closing instant for a linear optimal guaranteed control problem”, Comput. Math. Math. Phys., 58:5 (2018), 642–658
R. Gabasov, N. M. Dmitruk, F. M. Kirillova, “Decentralized optimal control of dynamical systems under uncertainty”, Comput. Math. Math. Phys., 51:7 (2011), 1128–1145
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