Stochastic Receding Horizon Control of Constrained Linear Systems with State and Control Multiplicative Noise

In this paper we develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain linear and quadratic expectation constraints. Our receding horizon formulation is based upon an online optimization that utilizes open-loop plus linear feedback and is solved as a semi-definite programming problem. We also provide a result characterizing stochastic stability for the receding horizon controlled system under a specific choice of terminal weight and terminal constraint. A numerical example is used to illustrate the approach.