On Calculating the Value of a Differential Game in the Class of Counter Strategies

Abstract

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