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

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Yiheng Lin, Yang Hu, Guannan Qu, Tongxin Li, Adam Wierman


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.