Scenario-based Stochastic MPC with guaranteed recursive feasibility

This paper addresses recursive feasibility, asymptotic stability, as well as the reduction of the online computational complexity, in scenario-based Stochastic Model Predictive Control for systems with time-varying parametric uncertainty. We propose a scheme, based on offline uncertainty sampling, which allows to suitably modify the constraints in such a way that recursive feasibility can be guaranteed robustly. The approach significantly speeds up the online computation, because no samples need to be generated online,, furthermore, unnecessary samples, which create redundant constraints, can be removed offline. Under mild additional assumptions, asymptotic stability with probability one can be proved. A numerical example, which provides a comparison with classical online sampling-based Stochastic MPC, demonstrates the efficacy of the proposed approach.