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 which 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, where the guidance gains are calculated by a predicted time-to-go, and the other for the autopilot dynamics, where the gains are obtained by a real-time time-to-go calculation, resulting in a sub-optimal guidance law. The performance of the proposed law is investigated using nonlinear planar simulation, for a missile with 1^st order autopilot dynamics.