A mixed L2/L∞ differential game approach to pursuit-evasion guidance

A differential game based strategy, L₂/L_∞ guidance law, is derived for a missile with large lateral acceleration capability intercepting an evading target which has limited lateral acceleration capability. Planar motion, linearized kinematics, arbitrary-order linear adversaries´ dynamics, and perfect information are assumed. The engagement is formulated as a two-person zero-sum pursuit-evasion game with a linear quadratic cost, where only the maneuverability of the evader is assumed bounded. The open loop solution is derived via direct derivation of the game´s lower and upper values and the saddle point condition. It is shown that the existence of an open loop saddle point solution depends on the engagement´s initial conditions. A closed form guidance law is formulated, consisting of the optimal saddle point strategies and three proposed variants when no saddle point solution exists. Linear simulations are performed for the case of a pursuer with first order control dynamics and an evader with zero-lag dynamics, in order to illustrate the L₂/L_∞ guidance law´s implementation benefits and performance in comparison with a classical optimal guidance law.