Stochastic Optimal Control of Single-Input Discrete Bilinear Systems.

Abstract : Optimal control of a class of single-input, discrete, stochastic bilinear systems is discussed. The control is assumed to be unbounded and the cost functional quadratic in state. A closed-form solution has been obtained for the stochastic control problem with perfect state observation, and with additive and multiplicative noise in the state equation. It is demonstrated that the presence of noise considerably simplifies the analysis compared to the deterministic case by virtue of integration over certain sets of measure zero. When the state equation has additive noise and the observation equation is noisy, a perturbation controller is obtained to minimize the instantaneous mean-square departure from the nominal, which is chosen to be the solution to the deterministic optimal control problem.