Stochastic Model Predictive Control with Dynamic Chance Constraints

Abstract: This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve two subsequent stochastic optimization problems. The first problem concerns finding the maximal feasible probabilities of the dynamic chance constraints. After obtaining the probabilities, the second problem concerns finding an optimal controller using stochastic model predictive control. We solve both stochastic optimization problems by reformulating them into deterministic ones using probabilistic reachable tubes and constraint tightening. We prove that the developed algorithm is recursively feasible and yields closed-loop satisfaction of the dynamic chance constraints. In addition, we will introduce a novel implementation using zonotopes to describe the tightening analytically. Finally, we will end with an example illustrating the method's benefits.