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

A differential game-based strategy, L₂/Lα guidance law, is derived for a missile with large lateral acceleration capability intercepting an evading target that has limited lateral acceleration capability. 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 lower and upper values of the game and the saddle point condition. It is shown that the existence of an open-loop saddle point solution depends on the initial conditions of the engagement. 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 and nonlinear 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 advantages and performance of the proposed guidance algorithm in comparison with classical optimal and differential game-based guidance laws.