Trajectory optimization for closed-loop nonlinear stochastic systems

An improved approximate solution to the nonlinear closed-loop stochastic control problem is presented. The method involves optimizing simultaneously a nominal trajectory, nominal control, and specific form of perturbation controller. It is demonstrated that improved performance is realized over the performance obtained by the widely used method of linearizing the nonlinear system about the deterministic optimal trajectory and employing a Riccati perturbation controller.