A game-control problem under lack of information

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.