The L_2/L_∞ Differential Game Guidance

摘要

A differential game based minimax strategy, L_2=L_∞ guidance law, isderived for a missile with large lateral acceleration capability interceptingan evading target which has limited lateral acceleration capability.Planar motion, linearized kinematics, arbitrary-order linear adversaries’dynamics, and perfect information are assumed. The engagement isformulated as a two-person zero-sum pursuit-evasion game with a linearquadratic cost, where only the evader’s control is assumed bounded.Since the existence of a Nash equilibrium solution is not guaranteed, thesolution is derived via direct derivation of the game’s lower and uppervalues and the saddle point condition. It is shown that the existenceof a Nash equilibrium solution depends on the engagement’s initial conditions.Nonlinear simulations are performed for the case of a pursuerwith first order control dynamics and an evader with zero-lag dynamics,in order to illustrate the L_2=L_∞ guidance law’s implementation benefitsby comparison with classical optimal guidance laws.