Bounded-Regret MPC via Perturbation Analysis: Prediction Error, Constraints, and Nonlinearity
Yiheng Lin, Yang Hu, Guannan Qu, Tongxin Li, Adam Wierman
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.
BibTeX
@inproceedings{
lin2022boundedregret,
title={Bounded-Regret {MPC} via Perturbation Analysis: Prediction Error, Constraints, and Nonlinearity},
author={Yiheng Lin and Yang Hu and Guannan Qu and Tongxin Li and Adam Wierman},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=jFVfKsmKa-}
}