+7 (3412) 91 60 92

## Archive of Issues

Russia Yekaterinburg
Year
2013
Issue
3
Pages
79-87
 Section Mathematics Title Optimal control under $L_p$-compact constraints on the disturbance Author(-s) Serkov D.A.ab Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb Abstract The problem of the optimization of a guaranteed result for the control system, described by an ordinary differential equation, and a continuous payoff functional, is considered. At every moment the values of the control and of the disturbance are in the given compact sets. The disturbances as functions of time are subject to functional constraints belonging to a given family of constraints. The actions of control are formed by the strategies with full memory. It is demonstrated, that optimal guaranteed result in this problem is equal to the value of the lower game. For the effectiveness of implemented control algorithm additional conditions on the system and appropriate ways of constructing an optimal strategy are specified. Keywords optimal guarantee, strategy with full memory, lower game UDC 517.952, 517.977 MSC 93C15, 49N30, 49N35 DOI 10.20537/vm130307 Received 30 August 2013 Language Russian Citation Serkov D.A. Optimal control under $L_p$-compact constraints on the disturbance, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 3, pp. 79-87. References Krasovskii N.N., Subbotin A.I. Game-theoretical control problems, New York: Springer-Verlag, 1988, 517 p. Krasovskii N.N. Upravlenie dinamicheskoi sistemoi (Control of dynamic system), Moscow: Nauka, 1995. Subbotin A.I., Chentsov A.G. Optimizatsiya garantii v zadachakh upravleniya (Optimization of guarantee in control problems), Moscow: Nauka, 1981, 288 p. Kryazhimskii A.V. The problem of optimization of the ensured result: unimprovability of full-memory strategies, Constantin Caratheodory: An International Tribute, T.M. Rassias Ed., World Scientific, 1991. Kryazhimskii A.V., Osipov Yu.S. On the control modeling in dynamic system, Izv. Akad. Nauk SSSR, Tekhn. Kibernet., 1983, no. 2, pp. 51-60. Osipov Yu.S., Kryazhimskii A.V. Inverse problem of ordinary differential equations: dynamical solutions, London: Gordon and Breach, 1995. Warga J. Optimal'noe upravlenie differentsial'nymi i funktsional'nymi uravneniyami (Optimal control of differential and functional equations), Moscow: Nauka, 1977, 624 p. Serkov D.A. On a property of constructive motions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2009, no. 3, pp. 98-103. Serkov D.A. Optimization of guaranteed results under functional restrictions on the dynamic disturbance, Doklady Mathematics, 2013, vol. 87, issue 3, pp. 310-313. Full text