Closed-loop chance-constrained MPC with probabilistic resolvability

When an model predictive controller (MPC) is subject to unbounded uncertainty, it is generally impossible to guarantee resolvability or recursive feasibility. In our previous work we developed an open-loop chance-constrained model predictive control (CCMPC) algorithm that is probabilistically resolvable [1], meaning that, given a feasible solution at the current time, the controller is guaranteed to find feasible solutions at future time steps with a certain probability. However, the controller is known to be overly conservative. In this paper we address this issue by extending this approach to a closed-loop CCMPC. We first develop a general closed-loop CCMPC framework building upon the affine disturbance feedback approach, and prove that the proposed closed-loop CCMPC is probabilistically resolvable. We also present two implementations of the proposed closed-loop CCMPC, whose finite-horizon optimal control problem solved at each time step is a convex optimization problem. We empirically demonstrate that the proposed closed-loop CCMPCs are significantly less conservative than the existing open-loop CCMPC.