Nonlinear positional differential game in the class of mixed strategies

Krasovskii, A.A. ORCID: https://orcid.org/0000-0003-0940-9366 & Krasovskii, A.N. (2012). Nonlinear positional differential game in the class of mixed strategies. Proceedings of the Steklov Institute of Mathematics 277 (1) 137-143. 10.1134/S0081543812040098.

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Abstract

The feedback control problem is considered for a nonlinear dynamic system under lack of information on disturbances. The problem on minmax-maxmin of the guaranteed result for a given positional quality index is formalized as an antagonistic two-player differential game in the framework of the concept developed in the Sverdlovsk (now Yekaterinburg) school on the theory of differential games. The problem is solved in the class of mixed strategies. The existence of the value of the game and a saddle point is established. The solution to the problem is based on the application of appropriate leader models, the method of extremal shift to the accompanying points and the method of upper convex hulls. The results of the study are applied to a realistic control model. The simulation outputs are presented.

Item Type:	Article
Research Programs:	Advanced Systems Analysis (ASA)
Bibliographic Reference:	Proceedings of the Steklov Institute of Mathematics; 277(1):137-143 (July 2012)
Depositing User:	IIASA Import
Date Deposited:	15 Jan 2016 08:46
Last Modified:	27 Aug 2021 17:22
URI:	https://pure.iiasa.ac.at/9885

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