On a minimax control problem for a positional functional under geometric and integral constraints on control actions

Within the game-theoretical approach, we consider a minimax feedback control problem for a linear dynamical system with a positional quality index, which is the norm of the deviation of the motion from given target points at given times. Control actions are subject to both geometric and integral constraints. A procedure for the approximate calculation of the optimal guaranteed result and for the construction of a control law that ensures the result is developed. The procedure is based on the recursive construction of upper convex hulls of auxiliary program functions. Results of numerical simulations are presented.