Complete Solutions to an Automatic Target Recognition (ATR) Differential Game With Singular Surfaces

An automatic target recognition (ATR) differential game between a radar that moves with simple motion and a turn-constrained target is examined in which a radar continuously acquires information about a target until the prescribed information requirement is fulfilled. The radar strives to satisfy the information requirement in minimum time while the target strives to prolong the engagement for as long as possible where the information collection rate is dependent on the relative geometry of the system. We develop the regular equilibrium conditions and the singular solution conditions for the nine singular surfaces within the global solution. We provide illustrative examples of equilibrium state trajectories that are constructed by solving a multipoint boundary value problem where we combine regular and singular solution segments in a piecewise manner. Using the singular surfaces within the global solution of the game, we synthesize the equilibrium feedback controller for the target. The performance of alternative, subequilibrium radar controllers is tested against the synthesized controller to show the Nash equilibrium of the calculated equilibrium control strategies.