A game-control problem under lack of information

Andrew N. Krasovskii^a, Alexandr N. Ladeyschikov<sup>b

a</sup> Ural State Agricultural Academy
^b Ural Federal University

Abstract: The optimal feedback control problem is considered for the nonlinear dynamical system under lack of information on disturbances. The minimax-maximin problem on the guaranteed result for a given positional quality index is formalized in the framework of concepts of the Sverdlovsk-Ekaterinburg school on the theory of differential games, as the two-person antagonistic differential game. The existence of a saddle point and a value of the game is obtained. The solution of a problem is based on the method of extremal shift to accompanying points. Results are illustrated by the model example and its numerical simulation.

Keywords: nonlinear dynamical system, control, disturbance, quality index, guaranteed result, extremal shift, value of the game, saddle point.

UDC: 517.977.8
BBK: 22.18