On Monday, February 24, 2020, Prof. Martin Mönnigmann (RUB Bochum, Germany) gave a lecture on "Accelerating MPC with Closed-Loop Optimal Sequences of Affine Feedback Laws". This is joint work with Prof. Gabriele Pannocchia (University of Pisa, Italy).
The talk addresses the classical infinite-horizon constrained linear-quadratic regulator (CLQR) problem and its receding-horizon variant used in model predictive control (MPC). An analysis of the set of all active sets reveals that the open-loop optimal solution is indeed closed-loop optimal, if all terminal constraints are inactive for the current system state. This implies the sequence of all future MPC feedback signals is already determined by the solution to the current single optimal control problem. Consequently, there is no need to solve additional optimization problems in future time steps. However, this result only applies to the nominal system, i.e., under the assumption of a perfect model and in the absence of disturbances. Robustness with respect to plant-model-mismatch and disturbances can be ensured to some degree, because the solution to the CLQR problem not only provides the sequence of nominally optimal input signals, but a sequence of optimal control laws along with their polytopes of validity. The degree of robustness remains to be analyzed analytically. Computational experiments show that the degree of robustness depends on the problem, but is likely to be relevant in practical applications.