Certainty-Equivalence Model Predictive Control: Stability, Performance, and Beyond

Abstract: Handling model mismatch is a common challenge in model-based controller design, particularly in model predictive control (MPC). While robust MPC is effective in managing uncertainties, its conservatism often makes it less desirable in practice. Certainty-equivalence MPC (CE-MPC), which relies on a nominal model, offers an appealing alternative due to its design simplicity and low computational requirements. Contrary to the existing analyses where MPC has access to the true model, this paper investigates CE-MPC for uncertain nonlinear systems with input constraints and parametric uncertainty. The primary contributions of the paper are two-fold. First, a novel perturbation analysis of the MPC value function is provided, without relying on the common assumption of Lipschitz continuity of the stage cost, better tailoring the popular quadratic cost and having broader applicability to value function approximation, online model learning in MPC, and performance-driven MPC design. Second, the stability and performance analysis of CE-MPC are provided, with a quantification of the suboptimality of CE-MPC compared to the infinite-horizon optimal controller with perfect model knowledge. The results provide valuable insights in how the prediction horizon and model mismatch jointly affect stability and performance. Furthermore, the general results are specialized to linear quadratic control, and a competitive ratio bound is derived, serving as the first competitive-ratio bound for MPC of uncertain linear systems with input constraints and multiplicative uncertainty.