Joint chance-constrained model predictive control with probabilistic resolvability

Resolvability or recursive feasibility is an essential property for robust model predictive controllers. However, when an unbounded stochastic uncertainty is present, it is generally impossible to guarantee resolvability. We propose a new concept called probabilistic resolvability. A model-predictive control (MPC) algorithm is probabilistically resolvable if it has feasible solutions at future time steps with a certain probability, given a feasible solution at the current time. We propose a novel joint chance-constrained MPC algorithm that guarantees probabilistic resolvability. The proposed algorithm also guarantees the satisfaction of a joint chance-constraint, which specifies a lower bound on the probability of satisfying a set of state constraints over a finite horizon. Furthermore, with moderate conditions, the finite-horizon optimal control problem solved at each time step in the proposed algorithm is a convex optimization problem.