Bounded-Regret MPC via Perturbation Analysis: Prediction Error, Constraints, and Nonlinearity

TL;DR

This paper introduces a unified analysis framework for Model Predictive Control (MPC) that leverages perturbation analysis to establish regret bounds, accommodating prediction errors, nonlinear dynamics, and constraints.

Contribution

The authors develop a general pipeline linking perturbation bounds to MPC regret analysis, extending existing results to nonlinear systems and systems with prediction errors.

Findings

Bounded the dynamic regret of MPC using perturbation analysis.

Extended regret bounds to nonlinear dynamics and constrained systems.

Demonstrated the pipeline's ability to incorporate prediction errors in various settings.

Abstract

We study Model Predictive Control (MPC) and propose a general analysis pipeline to bound its dynamic regret. The pipeline first requires deriving a perturbation bound for a finite-time optimal control problem. Then, the perturbation bound is used to bound the per-step error of MPC, which leads to a bound on the dynamic regret. Thus, our pipeline reduces the study of MPC to the well-studied problem of perturbation analysis, enabling the derivation of regret bounds of MPC under a variety of settings. To demonstrate the power of our pipeline, we use it to generalize existing regret bounds on MPC in linear time-varying (LTV) systems to incorporate prediction errors on costs, dynamics, and disturbances. Further, our pipeline leads to regret bounds on MPC in systems with nonlinear dynamics and constraints.