Formulation of MPC for Multiplicative Stochastic Uncertainty by Multi-Step Probabilistic Sets

Abstract: This paper designs multi-step probabilistic sets for linear, discrete-time, stochastic systems with unbounded multiplicative noise and probabilistic constraints. Multi-step probabilistic sets strengthen IWPp by bringing more degrees of freedom to optimize the applicable region of finite-step probabilistic constraints, and extending the prediction horizon of IWPp to infinity for infinite-horizon probabilistic constraints. Conditions for multi-step probabilistic sets are then incorporated into a stochastic model predictive control algorithm to satisfy probabilistic constraints. Closed-loop mean-square stability is guaranteed by the algorithm. A numerical example shows the performance of the proposed algorithm.