Optimal Linear Feedback Control for Non-Linear-Non-Quadratic-Non-Gaussian Problems

An optimal linear feedback controller designed for a general non-linear stochastic system with non-quadratic 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, a non-linear 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 non-quadratic performance indices is compared.