Optimal Linear Feedback Control for a Class of Nonlinear Nonquadratic Non-Gaussian Problems

An optimal linear feedback controller designed for a class of nonlinear stochastic systems with nonquadratic performance criteria by a non-Gaussian approach is presented. The non-Gaussian method is developed through expressing the unknown stationary output density function as a weighted sum of the Gaussian densities with undetermined parameters. With the aid of a Gaussian-sum density, the optimal feedback gain for a control system with complete state information is derived. By assuming that the separation principle is valid for the class of stochastic systems, a nonlinear precomputed-gain filter is then implemented. The method is illustrated by a Duffing-type control system and the performance of a linear feedback controller designed through both quadratic and nonquadratic performance indices is compared.