Intercept Angle Missile Guidance Under Time Varying Acceleration Bounds

A linear quadratic guidance law for a missile with a time varying acceleration constraint is presented. By introducing the constraint into the running cost, the optimization produces time varying gains that shape the missile's trajectory for avoiding no-capture zones. The guidance law is derived for a missile with high-order autopilot dynamics and a terminal intercept angle constraint against a maneuvering target. The acceleration constraint of aerodynamic steering missiles is usually trajectory dependent rather than time dependent. Transforming the constraint into a time-dependent function by analytical means might not be possible, due to the nonlinear nature of the constraint. The problem is alleviated using a simple iterative calculation. For practical implementation reasons, and in order to improve the guidance performance under model uncertainties and disturbances, the guidance command is decomposed into two separate optimizations: one for the acceleration constraint, for which the guidance gains are calculated by a predicted time to go, and the other for the autopilot dynamics, for which the gains are obtained by a real-time time-to-go calculation, resulting in a suboptimal guidance law. The performance of the proposed law is investigated using nonlinear planar simulation, for a missile with first-order autopilot dynamics.