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. |