Stable Mutual Tracking Block for a Real Dynamical Object and a Virtual Model-Leader

The work is devoted to the problem of stochastic stable mutual tracking of motions of the real dynamical x-object and the somewhat virtual z-model under the dynamical and informational disturbances. The elaborated algorithms are applied to some differential games on minimax and maximin for the positional quality index of the control process. Results of computer simulation of model problems are presented

Nonlinear positional differential game in the class of mixed strategies

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