Stochastic optimal control guidance law with bounded acceleration

This paper presents a novel stochastic optimal control guidance law for a missile with bounded acceleration. The optimal law is obtained by numerically solving the stochastic optimization problem. Since the certainty equivalence principle is not valid in the current problem, the resulting optimal law depends on the conditional probability density function of the estimated states. The stochastic optimal control guidance law is compared to the classical optimal, linear, guidance law. It is shown that the new guidance law is nonlinear in the estimated zero effort miss distance and that the probability density function of the miss is non-Gaussian. Only for an extremely large acceleration limit does the stochastic optimal control guidance law degenerate to the classical one. Thus, the research approach of taking into account the acceleration limit is validated.