Conformal Prediction for Distribution-free Optimal Control of Linear Stochastic Systems

作     者：Vlahakis, Eleftherios E. Lindemann, Lars Sopasakis, Pantelis Dimarogonas, Dimos V. 

作者机构：The Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm10044 Sweden The Thomas Lord Department of Computer Science The Ming Hsieh Department of Electrical and Computer Engineering Viterbi School of Engineering University of Southern California Los AngelesCA90089 United States The School of Electronics Electrical Engineering and Computer Science Queen's University Northern Ireland Belfast United Kingdom 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Optimal control systems 

摘      要：We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system within a prediction region (PR). We define PRs as sublevel sets of a nonconformity score over error trajectories, enabling the handling of joint chance constraints. We propose two methods to design feedback control and PRs: one through direct optimization over error trajectory samples, and the other indirectly using the S-procedure with a disturbance ellipsoid obtained from data. By tightening constraints with PRs, we solve a relaxed problem to synthesize a feedback policy. Our method ensures reliable probabilistic guarantees based on marginal coverage, independent of data size. © 2024, CC BY.