Multi-Step probabilistic sets in model predictive control for stochastic systems with multiplicative uncertainty

This study designs a model predictive controller for linear, discrete-time, stochastic systems with multiplicative noise and probabilistic constraints. The probabilistic invariance has shown its advantage in characterising the stochastic dynamics of the controlled state. Here multi-step probabilistic sets strengthen probabilistic invariance to further satisfy infinite-horizon probabilistic constraints. In addition, multi-step probabilistic sets offer some degrees of freedom to enlarge the feasible region ensured by probabilistic invariance. The controller satisfies given constraints and guarantees closed-loop mean-square stability. Moreover, a simplified controller with lower on-line computational burden is presented. Numerical examples show the performance of the proposed approach.