Stabilizing Refinement of Low-Complexity MPC Controllers

An input refinement strategy to correct a given model predictive control (MPC) law is proposed such that asymptotic stability of the closed-loop system is rigorously enforced. The motivation for developing this strategy is to allow the implementation of MPC laws based on low-complexity optimization problems that do not have incorporated into them the sufficient conditions well-known in MPC theory that enforce stability. Thus low-complexity MPC strategies that happen to achieve good performance as can be verified a posteriori, but offer no a priori guarantees of realizing even a minimal performance objective, can safely be implemented. Three distinct implementation strategies are presented and their merits discussed. The proposed approaches have a low computational burden and are targeted at fast MPC implementations.