Accelerated convergence of time‐splitting algorithm by relaxation method
Abstract The alternating direction method of multipliers (ADMM) is a widely used model predictive control (MPC) acceleration method. It adopts the time‐splitting technique, splitting the original problem into independent subproblems. Relaxed ADMM (R‐ADMM) is a generalization of ADMM that often achie...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-05-01
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| Series: | IET Control Theory & Applications |
| Online Access: | https://doi.org/10.1049/cth2.12270 |
| _version_ | 1811280314158284800 |
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| author | Jiaxin Gao Shengbo Eben Li Fei Ma Wenyu Li Hao Sun Maierdanjiang Maihemuti Chun Jin |
| author_facet | Jiaxin Gao Shengbo Eben Li Fei Ma Wenyu Li Hao Sun Maierdanjiang Maihemuti Chun Jin |
| author_sort | Jiaxin Gao |
| collection | DOAJ |
| description | Abstract The alternating direction method of multipliers (ADMM) is a widely used model predictive control (MPC) acceleration method. It adopts the time‐splitting technique, splitting the original problem into independent subproblems. Relaxed ADMM (R‐ADMM) is a generalization of ADMM that often achieves faster convergence. However, its parameters must be chosen by an expert user. Besides, the existing convergence proof of R‐ADMM adopts a first‐order Taylor approximation, which makes the range of relaxation factors conservative. We tackle these weaknesses by giving rigorous evidence and finding the optimal relaxation factor. Firstly, we deduce the convergence of the R‐ADMM algorithm, yielding an accurate range of relaxation factors. Then, we analyze the relationship between convergence rate and relaxation factor and conclude that the optimal relaxation factor depends on a recurrence condition. Since splitting introduces the equality constraint, the decoupled states are getting close in the iteration, meeting the recursive requirements and helping find the optimal relaxation factor. Finally, various trajectory tracking tasks are conducted to verify the efficiency of the R‐ADMM algorithm. And the simulation results show that the R‐ADMM algorithm reduces the number of iterations by 63.7% compared with the ADMM algorithm in the double lane change task. |
| first_indexed | 2024-04-13T01:12:28Z |
| format | Article |
| id | doaj.art-b5ca8e384b2d459fb4478391a8585fc8 |
| institution | Directory Open Access Journal |
| issn | 1751-8644 1751-8652 |
| language | English |
| last_indexed | 2024-04-13T01:12:28Z |
| publishDate | 2022-05-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Control Theory & Applications |
| spelling | doaj.art-b5ca8e384b2d459fb4478391a8585fc82022-12-22T03:09:07ZengWileyIET Control Theory & Applications1751-86441751-86522022-05-0116877678810.1049/cth2.12270Accelerated convergence of time‐splitting algorithm by relaxation methodJiaxin Gao0Shengbo Eben Li1Fei Ma2Wenyu Li3Hao Sun4Maierdanjiang Maihemuti5Chun Jin6School of Mechanical Engineering University of Science and Technology Beijing Beijing ChinaSchool of Vehicle and Mobility Tsinghua University Beijing ChinaSchool of Mechanical Engineering University of Science and Technology Beijing Beijing ChinaCollege of Artificial Intelligence Nankai University Tianjin ChinaSchool of Vehicle and Mobility Tsinghua University Beijing ChinaSchool of Vehicle and Mobility Tsinghua University Beijing ChinaSchool of Mechanical Engineering University of Science and Technology Beijing Beijing ChinaAbstract The alternating direction method of multipliers (ADMM) is a widely used model predictive control (MPC) acceleration method. It adopts the time‐splitting technique, splitting the original problem into independent subproblems. Relaxed ADMM (R‐ADMM) is a generalization of ADMM that often achieves faster convergence. However, its parameters must be chosen by an expert user. Besides, the existing convergence proof of R‐ADMM adopts a first‐order Taylor approximation, which makes the range of relaxation factors conservative. We tackle these weaknesses by giving rigorous evidence and finding the optimal relaxation factor. Firstly, we deduce the convergence of the R‐ADMM algorithm, yielding an accurate range of relaxation factors. Then, we analyze the relationship between convergence rate and relaxation factor and conclude that the optimal relaxation factor depends on a recurrence condition. Since splitting introduces the equality constraint, the decoupled states are getting close in the iteration, meeting the recursive requirements and helping find the optimal relaxation factor. Finally, various trajectory tracking tasks are conducted to verify the efficiency of the R‐ADMM algorithm. And the simulation results show that the R‐ADMM algorithm reduces the number of iterations by 63.7% compared with the ADMM algorithm in the double lane change task.https://doi.org/10.1049/cth2.12270 |
| spellingShingle | Jiaxin Gao Shengbo Eben Li Fei Ma Wenyu Li Hao Sun Maierdanjiang Maihemuti Chun Jin Accelerated convergence of time‐splitting algorithm by relaxation method IET Control Theory & Applications |
| title | Accelerated convergence of time‐splitting algorithm by relaxation method |
| title_full | Accelerated convergence of time‐splitting algorithm by relaxation method |
| title_fullStr | Accelerated convergence of time‐splitting algorithm by relaxation method |
| title_full_unstemmed | Accelerated convergence of time‐splitting algorithm by relaxation method |
| title_short | Accelerated convergence of time‐splitting algorithm by relaxation method |
| title_sort | accelerated convergence of time splitting algorithm by relaxation method |
| url | https://doi.org/10.1049/cth2.12270 |
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