Stochastic MPC for Additive and Multiplicative Uncertainty Using Sample Approximations

We introduce an approach for model predictive control (MPC) of systems with additive and multiplicative stochastic uncertainty subject to chance constraints. Predicted states are bounded within a tube and the chance constraint is considered in a "one step ahead" manner, with robust constraints applied over the remainder of the horizon. The online optimization is formulated as a chance-constrained program that is solved approximately using sampling. We prove that if the optimization is initially feasible, it remains feasible and the closed-loop system is stable. Applying the chance-constraint only one step ahead allows us to state a confidence bound for satisfaction of the chance constraint in closed-loop. Finally, we demonstrate by example that the resulting controller is only mildly more conservative than scenario MPC approaches that have no feasibility guarantee.