Target evasion from a missile performing multiple switches in guidance law

A planar engagement between a maneuvering target and a homing missile is considered. It is assumed that, during the engagement, the missile carries out multiple switches from one linear guidance law to another, choosing from a prescribed set of guidance laws. This leads to a formulation of a hybrid evasion problem for the target. In the case of complete information on the missile's strategies and switch moments, the optimal evasion strategy has a bang-bang form. The direction of a maximal acceleration command depends on the sign of a switching function and the sign of the zero-effort miss distance in the switched system. In the case of unknown switch moments, a matrix game is formulated, yielding the maximin evasion strategy, which implies the same bang-bang structure of evasive maneuver and guarantees a miss distance not smaller than the lower game value. Employing an optimal mixed evasion strategy guarantees better results on average. Examples where both the missile and the target have first-order strictly proper dynamics, and the missile (exploiting the proportional navigation guidance law) changes its gain once or twice during the engagement are elaborated upon. Monte Carlo simulation results support the theoretical analysis. The obtained results show that, even if the target acts optimally, the missile benefits from the switch in its guidance gain because the resulting miss distance is smaller when compared to the case when it uses a constant gain.