Optimal control and numerical optimization for missile interception guidance

Conventional guidance algorithms for exo-atmospheric missile interception, such as Proportional Navigation, provide guidance laws that are derived from conceptual heuristics where certain simplifications have to be made. Typically, these guidance laws have the disadvantage of not being able to fully take into account system and/or vehicle limitations such as maximum thrust. In this paper, optimal control and numerical optimization methods are used to provide a guidance scheme that may incorporate these critical constraints, while still ensuring a successful hit-to-kill interception of the target. Therein, a direct optimal control approach is deployed, based on multiple shooting and a sequential quadratic programming algorithm for solving the resulting nonlinear optimization problem. Numerical results for three distinctive transcription methods for deriving the nonlinear program are presented that illustrate the overall efficiency of numerical optimization as a guidance scheme.