On calculating the value of a differential game in the class of counterstrategies

For a linear dynamic system with control and disturbance, a feedback control problem is considered, in which the Euclidean norm of the 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.