Archive of Issues
Russia Yekaterinburg
Section  Mathematics 
Title  Optimal guarantee under the disturbances of Caratheodory type 
Author(s)  Serkov D.A.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
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 actions of the disturbance are assumed to be generated by an unknown function of the Caratheodory type, i.e. by the function continuous with respect to the spatial variable for every value of time variable and measurable with respect to the time variable for every value of spatial one. The actions of control are formed by the strategies with full memory. It is demonstrated, that for a class of control systems the optimal guaranteed result in this problem is equal to the value of the lower game, i.e. to the value of the optimal guaranteed result in the class of quasistrategies. The optimal strategy with full memory, that allows numerical implementation, is provided. An illustrative nonlinear example is given. 
Keywords  optimal guarantee, disturbance of Caratheodory type, strategy with full memory, lower game 
UDC  517.952, 517.977 
MSC  93C15, 49N30, 49N35 
DOI  10.20537/vm120207 
Received  12 March 2012 
Language  Russian 
Citation  Serkov D.A. Optimal guarantee under the disturbances of Caratheodory type, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 2, pp. 7483. 
References 

Full text 