Distributed Continuous-Time Algorithm for Time-Varying Optimization With Affine Formation Constraints
In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functi...
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| Vydáno v: | IEEE transactions on automatic control Ročník 68; číslo 4; s. 2615 - 2622 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
IEEE
01.04.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9286, 1558-2523 |
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| Abstract | In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functions, each of which is known by only one individual agent. The optimal solution is a time-varying affine transformation of a nominal configuration rather than some constants. To tackle the difficulty caused by the dynamic aspect of the local cost functions and handle affine formation constraints, the fixed-time distributed estimator and distributed gradient tracking technique are developed, respectively, to compensate the time variation of solution trajectory and calculate the weighted sum of local gradients to eliminate the tracking error. The time-varying optimal solution trajectory is thus accurately tracked with the proposed estimator-based gradient tracking algorithm. Using appropriately chosen coefficients, the tracking error is guaranteed to vanish at an exponential rate. The proposed estimator-based gradient tracking algorithm is further validated through numerical simulations. |
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| AbstractList | In this article, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functions, each of which is known by only one individual agent. The optimal solution is a time-varying affine transformation of a nominal configuration rather than some constants. To tackle the difficulty caused by the dynamic aspect of the local cost functions and handle affine formation constraints, the fixed-time distributed estimator and distributed gradient tracking technique are developed, respectively, to compensate the time variation of solution trajectory and calculate the weighted sum of local gradients to eliminate the tracking error. The time-varying optimal solution trajectory is thus accurately tracked with the proposed estimator-based gradient tracking algorithm. Using appropriately chosen coefficients, the tracking error is guaranteed to vanish at an exponential rate. The proposed estimator-based gradient tracking algorithm is further validated through numerical simulations. |
| Author | Fang, Hao Chen, Jie Yang, Qingkai Wu, Chu Wei, Yue Zeng, Xianlin |
| Author_xml | – sequence: 1 givenname: Chu orcidid: 0000-0002-4894-8453 surname: Wu fullname: Wu, Chu email: wuchu9402@outlook.com organization: School of Automation, Beijing Institute of Technology, Beijing, China – sequence: 2 givenname: Hao orcidid: 0000-0002-9627-0325 surname: Fang fullname: Fang, Hao email: fangh@bit.edu.cn organization: School of Automation, Beijing Institute of Technology, Beijing, China – sequence: 3 givenname: Xianlin orcidid: 0000-0002-6224-9974 surname: Zeng fullname: Zeng, Xianlin email: xianlin.zeng@amss.ac.cn organization: School of Automation, Beijing Institute of Technology, Beijing, China – sequence: 4 givenname: Qingkai orcidid: 0000-0001-9247-7786 surname: Yang fullname: Yang, Qingkai email: qingkyang@gmail.com organization: School of Automation, Beijing Institute of Technology, Beijing, China – sequence: 5 givenname: Yue orcidid: 0000-0003-0942-7062 surname: Wei fullname: Wei, Yue email: weiy@pcl.ac.cn organization: Frontier Research Center, Peng Cheng Laboratory, Shenzhen, China – sequence: 6 givenname: Jie orcidid: 0000-0003-2449-9793 surname: Chen fullname: Chen, Jie email: chenjie@bit.edu.cn organization: School of Automation, Beijing Institute of Technology, Beijing, China |
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| SubjectTerms | Affine formation Affine transformations Algorithms Cost function Costs fixed-time estimator gradient tracking Laplace equations Stress time-varying optimization Time-varying systems Tracking errors Trajectory Trajectory optimization |
| Title | Distributed Continuous-Time Algorithm for Time-Varying Optimization With Affine Formation Constraints |
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