Stochastic Optimal Guidance of Missiles with Nonlinear Dynamics

Abstract

A stochastic optimal control guidance law is derived for a system with nonlinear dynamics having a bounded acceleration command. In the investigated problem of missile guidance, the kinematics are linear and the measurements Gaussian; however, due to the nonlinear dynamics and the bounded controller, the certainty equivalence principle is not valid. Consequently, the optimal guidance law is obtained by numerically solving the Hamilton-Jacobi equation associated with the stochastic optimization problem. The optimal guidance law depends on the conditional probability density function of the estimated states. Moreover, the guidance law is nonlinear in the estimated zero efiort miss distance and in the missile internal states. It is shown that if rate saturation is present or if the acceleration bound is non-symmetric then a non-zero acceleration command is issued even if the zero efiort miss is zero. The aim of this unusual feature of the guidance law is to position the missile as far as possible from saturation limits, thus placing it in as advantageous situation as possible to deal with expected future target maneuvers.