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A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution

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journal contribution
posted on 2024-02-19, 10:23 authored by Yuan Tan, Jun YangJun Yang, Wen-Hua ChenWen-Hua Chen, Shihua Li
In this work, we propose a distributionally robust stochastic model predictive control (DR-SMPC) algorithm to address the problem of multiple two-sided chance constrained discrete-time linear systems corrupted by additive noise. The prevalent mechanism to cope with two-sided chance constraints is the so-called risk allocation approach, which conservatively approximates the two-sided chance constraints with two single chance constraints by applying Bool's inequality. In this proposed DR-SMPC framework, an exact second-order cone approach is adopted to abstract the multiple two-sided chance constraints by considering the first and second moments of the noise. With the proposed DR-SMPC algorithm, the worst-case probability of violating safety constraints is guaranteed to be within a prespecified maximum value. By flexibly adjusting this prespecified maximum probability, the feasible region of the initial state can be increased for the SMPC problem. The recursive feasibility and convergence of the proposed DR-SMPC are rigorously established by introducing a binary initialization strategy for the nominal state. A simulation study of a single spring and double mass system was conducted to demonstrate the effectiveness of the proposed DR-SMPC algorithm.

Funding

National Natural Science Foundation of China under Grants 62025302, 61973080 and 61973081

History

School

  • Aeronautical, Automotive, Chemical and Materials Engineering

Department

  • Aeronautical and Automotive Engineering

Published in

IEEE Transactions on Automatic Control

Volume

69

Issue

1

Pages

574 - 581

Publisher

Institute of Electrical and Electronics Engineers

Version

  • AM (Accepted Manuscript)

Rights holder

© IEEE

Publisher statement

© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Acceptance date

2023-04-21

Publication date

2023-05-08

Copyright date

2023

ISSN

0018-9286

eISSN

1558-2523

Language

  • en

Depositor

Dr Jun Yang. Deposit date: 16 February 2024