Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems
Yiheng Lin, Yang Hu, Guanya Shi, Haoyuan Sun, Guannan Qu, Adam Wierman
Abstract
We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for the future $k$ time steps. We show that when the prediction window $k$ is sufficiently large, predictive control is input-to-state stable and achieves a dynamic regret of $O(\lambda^k T)$, where $\lambda < 1$ is a positive constant. This is the first dynamic regret bound on the predictive control of linear time-varying systems. We also show a variation of predictive control obtains the first competitive bound for the control of linear time-varying systems: $1 + O(\lambda^k)$. Our results are derived using a novel proof framework based on a perturbation bound that characterizes how a small change to the system parameters impacts the optimal trajectory.
BibTeX
@inproceedings{
lin2021perturbationbased,
title={Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems},
author={Yiheng Lin and Yang Hu and Guanya Shi and Haoyuan Sun and Guannan Qu and Adam Wierman},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=xwGeq7I4Opv}
}