Game optimal guidance law synthesis for short range missiles

Abstract

A horizontal pursuit-evasion game of kind in the atmosphere between a coasting pursuer with a final velocity constraint and a maneuvering evader of constant speed is considered. For this model, which is suitable to describe short range missile engagements, the adjoint equations can be integrated analytically. This allows us to determine the optimal strategies of the players on the boundary of the capture set, called the barrier, as a function of the current and final values of the state variables. The main effect of the pursuer's final velocity constraint, an important realistic parameter, neglected in previous studies, is a substantial reduction of the capture zone. However, based on this game solution, a feedback guidance law, suitable for real-time implementation, can be synthesized and compared to other guidance laws. The results show that the corresponding capture set is much larger than the firing envelope of a similar missile guided by proportional navigation with the same final velocity constraint.