Analytical Performance Prediction for Robust Constrained Model Predictive Control

This paper presents a new analysis tool for predicting the closed-loop performance of a robust constrained Model Predictive Control (MPC) scheme. Currently, performance is typically evaluated by numerical simulation, leading to extensive computation when investigating the effect of controller parameters, such as horizon length, cost weightings, and constraint settings. The method in this paper avoids this computational burden, enabling a rapid study of the trades between the design parameters and performance. Previous work developed an MPC scheme employing constraint tightening to achieve robust feasibility and constraint satisfaction despite the action of an unknown but bounded disturbance. This paper shows that the expected performance of that scheme can be predicted using a combination of the gains of two linear systems, the optimal control for the unconstrained system, and a candidate policy used in performing the constraint tightening. The method also accounts for possible mismatch between the predicted level of disturbance and the actual level encountered. The predictions are compared with simulation results for several examples.