Optimal Target Interception with Time-Varying Acceleration Constraints

This paper derives new optimal-control-based guidance laws with a time-varying missileac celeration bound for ground-to-air missiles. Saturation may cause a significant miss distance if it is not considered. Ground-to-air missiles climb in altitude, and their acceleration limits vary as their altitude increases. The guidance laws presented in this paper explicitly in corporate a “hard” acceleration command constraint, which gives them an advantage compared to other guidance laws, which usually have unbounded or softly constrained acceleration command limits. The guidance laws are derived for linear, zero and first-order missile dynamics and arbitrary-order, linear target dynamics. The guidance laws are derived from a linear quadrati coptimal control problem with a bounded missile controller. The proposed guidance laws are evaluated in a nonlinear simulation and compared to the classical unbounded acceleration optimal guidance law. The comparison shows a substantial advantage of the proposed guidance laws when encountering missile saturation. It is concluded that explicitly accounting for the missile’s saturation limits substantially improves its performance and capability to intercept the target in challenging scenarios. The improved capability stems from the missile’s prediction of future saturation and earlier maneuvers when the saturation limits are higher.