SOLUTION OF A DELAYED INFORMATION LINEAR PURSUIT-EVASION GAME WITH BOUNDED CONTROLS

Abstract

A class of linear pursuit-evasion games with first-order acceleration dynamics and bounded controls is considered, where the evader has perfect information and the pursuer has delayed information on the lateral acceleration of the evader. The other state variables are perfectly known to the pursuer. This game can be transformed to a perfect information delayed control game with a single state variable, the centre of the uncertainty domain created by the information delay. The delayed dynamics of the game is transformed to a linear first-order partial differential equation coupled with an integral-differential equation, both without delay. These equations are approximated by a set of K + 1 ordinary differential equations of first order, creating an auxiliary game. The necessary conditions of optimality derived for the auxiliary game lead to the solution of the delayed control game by a limit process as K → + ∞. The solution has the same structure as the other, already solved, perfect information linear pursuit-evasion games with bounded controls and indicates that the value of the delayed information pursuit-evasion game is never zero. Asymptotic expressions of the value of the game for small and large values of the information delay are derived.