Cheap Control in a Non-Scalarizable Linear-Quadratic Pursuit-Evasion Game: Asymptotic Analysis

In this work, a finite-horizon zero-sum linear-quadratic differential game, modeling pursuit-evasion problem, was considered. the game’s cost function, of control minimizing player (the minimizer/the pursuer) much smaller than maximizing maximizer/the evader) and state variable. This smallness expressed by positive small multiplier (a parameter) square L2-norm minimizer’s in function. Parameter-free sufficient conditions for existence solution players’ optimal state-feedback controls game value), valid all sufficiently values parameter, were presented. The boundedness (with respect to time realizations along corresponding trajectory established. best achievable value from viewpoint derived. A relation between solutions original cheap that obtained one replacing with zero, An illustrative real-life example is