ON CALCULATING THE VALUE OF A DIFFERENTIAL GAME IN THE CLASS OF COUNTER STRATEGIES

Mikhail I. Gomoyunov     (Department of Dynamical Systems, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation)
Dmitry V. Kornev     (Institute of Mathematics and Computer Sciences, Ural Federal University; Department of Dynamical Systems, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation)

Abstract


For a linear dynamic system with control and disturbance, a feedback control problem is considered, in which the Euclidean norm of a set of deviations of the system’s motion from given targets at given times is optimized. The problem is formalized into a differential game in “strategy-counterstrategy” classes. A game value computing procedure, which reduces the problem to a recursive construction of upper convex hulls of auxiliary functions, is justified. Results of numerical simulations are presented. 


Keywords


Differential games, Value of the game, Saddle point, Counterstrategies

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References


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DOI: http://dx.doi.org/10.15826/umj.2016.1.004

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