A scenario-based convex formulation for probabilistic linear constraints in MPC

This paper develops a model predictive control strategy for stochastic linear systems with both multiplicative and additive uncertainty. As satisfaction of probabilistic constraints as well as performance optimization relies on description of the random system nature, we derive polyhedrons that contain system evolution matrices with prescribed probability. This is achieved by letting each polyhedron incorporates a number of stochastic scenarios of the corresponding evolution matrix. The process is efficient through a designed convex optimization and subsequent off-line scaling and verification. On the basis of the polyhedrons, probabilistic constraints can be transformed into linear constraints and be solved in reduced computation burden. The proposed MPC algorithm ensures the constraints and closed-loop stability. The results are illustrated by a numerical example.