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 Izv. IMI UdGU, 2015, Issue 1(45), Pages 37–105 (Mi iimi294)

Linear-convex guarantee optimization problems with control delay

M. I. Gomoyunov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: A control problem under condition of disturbances is considered for a linear dynamical system with control delay. Optimized quality index is nonterminal and contains the evaluation of the system motion by a set of deviations at given instants of time from given targets. Depending on the structure of the quality index the existence of optimal control strategies in appropriate classes of feedback strategies is established. For calculating the value of the optimal guaranteed result and finding the optimal control laws a procedure of backward construction of upper convex hulls of auxiliary functions is proposed. In the case of the positional quality index a reduction of this procedure is performed. This reduction significantly reduces the dimension of the domains of covexified functions. Results of numerical simulations are given.

Keywords: control theory, differential games, control delay, feedback strategies.

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UDC: 517.977.1/.5
MSC: 49N35, 49N70, 49L20

Citation: M. I. Gomoyunov, “Linear-convex guarantee optimization problems with control delay”, Izv. IMI UdGU, 2015, no. 1(45), 37–105

Citation in format AMSBIB
\Bibitem{Gom15} \by M.~I.~Gomoyunov \paper Linear-convex guarantee optimization problems with control delay \jour Izv. IMI UdGU \yr 2015 \issue 1(45) \pages 37--105 \mathnet{http://mi.mathnet.ru/iimi294} \elib{http://elibrary.ru/item.asp?id=23754965} 

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This publication is cited in the following articles:
1. M. I. Gomoyunov, N. Yu. Lukoyanov, “On the numerical solution of differential games for neutral-type linear systems”, Proc. Steklov Inst. Math. (Suppl.), 301, suppl. 1 (2018), 44–56
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