Two-Stage Differential Game Guidance Law with Terminal Angle and Hard Acceleration Constraints

Addressing interception issues under multiple constraints such as miss distance and terminal angle constraints; limited maneuverability poses significant challenges to guidance law design. Conventional differential game guidance laws with multi-constraints almost encounter overload overshoot issues at end stage for small region. To tackle this problem, we propose a two-stage differential game guidance law with multi-constraints and acceleration hard constraints. First, the flight time of end stage is specified, and the initial conditions of the end stage, which do not exceed the overload capacity, are obtained, and they are used as terminal conditions for the initial stage in differential game solution. Based on establishing guidance and segmented game models, different performance functions are designed for different stages, and Nash solutions to terminal constraint problems and analytical expressions for the initial stage are derived using optimal control and minimax principles. The game space of the end stage is divided based on the overload capabilities of both sides, and switching guidance law design is performed. From simulate results, two-stage guidance law reduces overload requirements 30% while ensuring the same guidance effect and avoiding overshoot, validating the effectiveness of this guidance law.