Stroboscopic Strategy in Dynamic Game Problems with Terminal Payoff Function and Integral Constraints on Controls

Abstract

The paper considers linear differential games with terminal payoff function and integral constraints on controls. Sufficient conditions for game termination in a finite guaranteed time in the class of quasi-strategies are formulated. Two schemes of the method of resolving functions are proposed that ensure game termination in a final guaranteed time in the class of stroboscopic strategies. It is shown that without additional assumptions, this time coincides with the guaranteed time in the class of quasistrategies.