Stochastic optimal control guidance law with bounded acceleration

A novel stochastic optimal control guidance law is presented for a missile with bounded acceleration. The nonlinear optimal guidance law (NOGL) is obtained by numerically solving the stochastic optimization problem. Since the certainty equivalence principle is not valid in the investigated problem, the resulting NOGL depends on the conditional probability density function of the estimated states. It is shown that the NOGL is also nonlinear in the estimated zero effort miss distance, and that the probability density function of the miss distance is non-Gaussian. The dependence of the new guidance law on the acceleration limit is investigated and it is shown that only for an extremely large acceleration limit does the proposed guidance law degenerate to the classical optimal linear one.