Comparison of Optimal Control and Differential Game Intercept Missile Guidance Laws

Air-to-air missile guidance laws are derived using optimal control and differential game theory with final miss distance as the optimization criterion. A perfect target airframe/autopilot response is assumed, while both perfect and first-order missile responses are considered. With a first-order missile response the target is always able to force a nonzero final miss distance in the differential game formulation. For all other formulations considered there are states from which the missile can force zero terminal miss. In these cases, an auxiliary performance index (e.g., control energy) can be used to specify unique controls. Two simulation scenarios were used to evaluate the guidance laws: one with missile launch near the inner launch boundary and the other near the outer launch boundary. The differential game guidance laws are less sensitive to errors in estimates of current target acceleration than the optimal control laws. The laws based on a perfect missile response performed better for the outer launch boundary scenario; whereas for the inner launch boundary scenario the laws based on a first-order missile response achieved smaller miss distances.