Bounded-Regret MPC via Perturbation Analysis: Prediction Error, Constraints, and Nonlinearity
Authors: Yiheng Lin, Yang Hu, Guannan Qu, Tongxin Li, Adam Wierman
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | 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. |
| Researcher Affiliation | Academia | Yiheng Lin California Institute of Technology Pasadena, CA, USA yihengl@caltech.edu Yang Hu Harvard University Cambridge, MA, USA yanghu@g.harvard.edu Guannan Qu Carnegie Mellon University Pittsburgh, PA, USA gqu@andrew.cmu.edu Tongxin Li The Chinese University of Hong Kong (Shenzhen) Shenzhen, Guangdong, China litongxin@cuhk.edu.cn Adam Wierman California Institute of Technology Pasadena, CA, USA adamw@caltech.edu |
| Pseudocode | Yes | Algorithm 1 Model Predictive Control (MPCk) Require: Specify the terminal costs Ft for k t < T. 1: for t = 0, 1, . . . , T 1 do 2: t0 min{t + k, T} 3: Observe current state xt and obtain predictions t:t0|t. 4: Solve and commit control action ut := t0 t (xt, t:t0|t; Ft0)vt. |
| Open Source Code | No | The paper states under "If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [N/A]". There is no explicit statement about releasing source code for the methodology. |
| Open Datasets | No | This is a theoretical paper that does not involve empirical experiments with datasets. Therefore, there is no mention of training datasets. |
| Dataset Splits | No | This is a theoretical paper that does not involve empirical experiments with datasets. Therefore, there is no mention of training/validation/test splits. |
| Hardware Specification | No | The paper states under "If you ran experiments... (d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [N/A]". As this is a theoretical paper, no hardware specifications are provided. |
| Software Dependencies | No | The paper states under "If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [N/A]". As this is a theoretical paper, no software dependencies with version numbers are provided. |
| Experiment Setup | No | The paper states under "If you ran experiments... (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [N/A]". As this is a theoretical paper, no experimental setup details are provided. |