Model predictive control for drift counteraction of stochastic constrained linear systems

The paper presents a stochastic MPC (SMPC) formulation suitable for maximizing the average time until a discrete-time linear system with additive random disturbance violates prescribed constraints. The SMPC procedure is based on a scenario tree that encodes the most likely system behavior for a given tree density, where each branch of the tree represents a specific evolution of the system that occurs with a certain probability. A mixed-integer linear program (MILP) is developed that maximizes the average time until constraint violation for a given scenario tree. Feedback is provided by reconstructing the scenario tree and recomputing the MILP solution over a receding time horizon based on the current state of the system. The average time until constraint violation achieved by the SMPC strategy approaches the optimal value as the scenario tree density is increased. Two numerical case studies, including an adaptive cruise control problem, demonstrate the effectiveness of the proposed SMPC strategy compared to dynamic programming solutions.