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 | Venue 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 EMAIL Yang Hu Tsinghua University Beijing, China EMAIL Guanya Shi California Institute of Technology Pasadena, CA, USA EMAIL Haoyuan Sun California Institute of Technology Pasadena, CA, USA EMAIL Guannan Qu California Institute of Technology Pasadena, CA, USA EMAIL Adam Wierman California Institute of Technology Pasadena, CA, USA EMAIL |
| 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. |