Stochastic MPC with Online-optimized Policies and Closed-loop Guarantees

This paper proposes a stochastic model predictive control method for linear systems affected by additive Gaussian disturbances that optimizes over disturbance feedback matrices online. Closed-loop satisfaction of probabilistic constraints and recursive feasibility of the underlying convex optimization problem is guaranteed. Optimization over feedback policies online increases performance and reduces conservatism compared to fixed-feedback approaches. The central mechanism is a finitely determined maximal admissible set for probabilistic constraints, together with the reconditioning of the predicted probabilistic constraints on the current knowledge at every time step. The proposed method's applicability is demonstrated on a building temperature control example.