A new technique for closed loop control of discrete stochastic nonlinear systems

A new approach for optimum control of discrete stochastic nonlinear systems is developed from practical engineering assumptions. Systems amenable to this new approach include optimum guidance and navigation systems for space and terrestrial vehicles, optimum closed-loop process controllers, and optimum controllers for systems with unknown parameters. The solution is obtained by expansion of the stochastic cost function in a power series around a deterministic trajectory with the assumption of linear perturbation estimation and control about that trajectory. Optimization of the expanded cost function gives necessary conditions dependent on the covariance matrices and the deterministic portion of the cost. When the necessary conditions are solved, a set of open-loop controls, perturbation controller gains, and perturbation estimator gains are obtained that can be precomputed and implemented into the system.