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

TL;DR

This paper analyzes certainty-equivalence MPC for uncertain nonlinear systems, providing new stability and performance guarantees, a novel perturbation analysis of the value function, and a competitive ratio bound for linear quadratic control.

Contribution

It introduces a perturbation analysis of the MPC value function without Lipschitz assumptions and offers stability, performance, and competitive ratio bounds for CE-MPC under uncertainty.

Findings

Perturbation analysis applicable to broader cost functions.

Quantified suboptimality of CE-MPC relative to the optimal controller.

Derived a competitive ratio bound for uncertain linear systems.

Abstract

Handling model mismatch is a common challenge in model predictive control (MPC). While robust MPC is effective, its conservatism often makes it less desirable. Certainty-equivalence MPC (CE-MPC), which uses a nominal model, offers an appealing alternative due to its design simplicity and low computational costs. This paper investigates CE-MPC for uncertain nonlinear systems with multiplicative parametric uncertainty and input constraints that are inactive at the steady state. The primary contributions are two-fold. First, a novel perturbation analysis of the MPC value function is provided, without assuming the Lipschitz continuity of the stage cost, better tailoring the widely used quadratic cost and having broader applicability in value function approximation, learning-based MPC, and performance-driven MPC design. Second, the stability and performance analysis of CE-MPC are provided, quantifying the suboptimality of CE-MPC compared to the infinite-horizon optimal controller with perfect model knowledge. The results provide insights in how the prediction horizon and model mismatch jointly affect stability and the worst-case 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.