Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems

Authors: Yiheng Lin, Yang Hu, Guanya Shi, Haoyuan Sun, Guannan Qu, Adam Wierman

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. 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. We provide the first regret and competitive ratio results for a controller in LTV systems with time-varying costs. Specifically, we show that an MPC-style predictive control algorithm (Algorithm 1) achieves a dynamic regret that decays exponentially with respect to the length of prediction window : in the LTV system (Theorem 4.2): $(_:)), where the decay rate _ is a positive constant less than 1.
Researcher Affiliation Academia Yiheng Lin California Institute of Technology Pasadena, CA, USA yihengl@caltech.edu Yang Hu Tsinghua University Beijing, China huy18@mails.tsinghua.edu.cn Guanya Shi California Institute of Technology Pasadena, CA, USA gshi@caltech.edu Haoyuan Sun California Institute of Technology Pasadena, CA, USA hsun2@caltech.edu Guannan Qu California Institute of Technology Pasadena, CA, USA gqu@caltech.edu Adam Wierman California Institute of Technology Pasadena, CA, USA adamw@caltech.edu
Pseudocode Yes Algorithm 1 Predictive Control (% :), Algorithm 2 Predictive Control with Replan Window (% (:, ))
Open Source Code No No statement providing concrete access to source code was found.
Open Datasets No The paper is theoretical and does not use or provide access to datasets for training or evaluation.
Dataset Splits No The paper is theoretical and does not involve data splits for training, validation, or testing.
Hardware Specification No The paper is theoretical and does not describe empirical experiments, therefore no hardware specifications are provided.
Software Dependencies No The paper is theoretical and does not describe empirical experiments or specific software implementations that would require listing dependencies with version numbers.
Experiment Setup No The paper is theoretical and does not describe empirical experiments or specific setups with hyperparameters.