Loading…
A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution
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 th...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Default Article |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/2134/25233655.v1 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1818164974983315456 |
|---|---|
| author | Yuan Tan Jun Yang Wen-Hua Chen Shihua Li |
| author_facet | Yuan Tan Jun Yang Wen-Hua Chen Shihua Li |
| author_sort | Yuan Tan (819132) |
| collection | Figshare |
| description | 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. |
| format | Default Article |
| id | rr-article-25233655 |
| institution | Loughborough University |
| publishDate | 2023 |
| record_format | Figshare |
| spelling | rr-article-252336552023-05-08T00:00:00Z A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution Yuan Tan (819132) Jun Yang (4410343) Wen-Hua Chen (1251597) Shihua Li (737625) Engineering Control engineering, mechatronics and robotics Mechanical engineering Applied mathematics Distributionally robust optimization Second-order cone Stochastic model predictive control (SMPC) Two-sided chance constraints 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.<p></p> 2023-05-08T00:00:00Z Text Journal contribution 2134/25233655.v1 https://figshare.com/articles/journal_contribution/A_distributionally_robust_optimization_approach_to_two-sided_chance-constrained_stochastic_model_predictive_control_with_unknown_noise_distribution/25233655 All Rights Reserved |
| spellingShingle | Engineering Control engineering, mechatronics and robotics Mechanical engineering Applied mathematics Distributionally robust optimization Second-order cone Stochastic model predictive control (SMPC) Two-sided chance constraints Yuan Tan Jun Yang Wen-Hua Chen Shihua Li A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution |
| title | A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution |
| title_full | A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution |
| title_fullStr | A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution |
| title_full_unstemmed | A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution |
| title_short | A distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution |
| title_sort | distributionally robust optimization approach to two-sided chance-constrained stochastic model predictive control with unknown noise distribution |
| topic | Engineering Control engineering, mechatronics and robotics Mechanical engineering Applied mathematics Distributionally robust optimization Second-order cone Stochastic model predictive control (SMPC) Two-sided chance constraints |
| url | https://hdl.handle.net/2134/25233655.v1 |