General Results in Optimal Control of Discrete-Time Nonlinear Stochastic Systems

摘要

This document proposes an approach for the control of a general class of discrete-time nonlinear stochastic systems. The system model incorporates a deterministic linear portion together with a nonlinear function of the state and/or control vectors in combination with a white noise vector, where no Gaussian assumption is made. Under certain conditions imposed on the statistics of the additive nonlinear stochastic term, and assuming perfect state information, the optimal control, which minimizes a quadratic performance index subject to the nonlinear control system constraint, is shown to be a linear function of the state vector. This work also shows that for certain infinite horizon problems, an uncertainty threshold can be found such that the designer can, a priori, put an upper bound on the allowable noise covariance to obtain a bounded optimal constant feedback control. Keywords: Theses; Multivariate analysis. (KR)