A Fully Distributed Hybrid Control Framework For Non-Differentiable Multi-Agent Optimization

Xia Jiang; Xianlin Zeng; Jian Sun; Jie Chen; Yue Wei

doi:10.1109/JAS.2022.105872

Volume 9 Issue 10

Oct. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(10): 1792-1800

X. Jiang, X. L. Zeng, J. Sun, J. Chen, and Y. Wei, “A fully distributed hybrid control framework for non-differentiable multi-agent optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1792–1800, Oct. 2022. doi: 10.1109/JAS.2022.105872

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X. Jiang, X. L. Zeng, J. Sun, J. Chen, and Y. Wei, “A fully distributed hybrid control framework for non-differentiable multi-agent optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1792–1800, Oct. 2022. doi: 10.1109/JAS.2022.105872

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A Fully Distributed Hybrid Control Framework For Non-Differentiable Multi-Agent Optimization

doi: 10.1109/JAS.2022.105872

1.
Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, and also with the Beijing Institute of Technology Chongqing Innovation Center, Chongqing 401120, China
2.
Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China
3.
School of Electronic and Information Engineering, Tongji University, Shanghai 200082, and also with the Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081, China
4.
Peng Cheng Laboratory, Shenzhen 518055, China

Funds: This work was supported in part by the National Key Research and Development Program of China (2021YFB1714800), the National Natural Science Foundation of China (61925303, 62088101, 62073035, 62173034) and the Natural Science Foundation of Chongqing (2021ZX4100027)

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Author Bio:
Xia Jiang received the bachelor degree in control science and engineering from Shandong University, in 2017. She is currently pursuing the Ph.D. degree in control science and engineering with the School of Automation, Beijing Institute of Technology. Her current research interests include distributed optimization and distributed computation of semi-definite problems

Xianlin Zeng (Member, IEEE) received the B.S. and M.S. degrees in control science and engineering from the Harbin Institute of Technology, in 2009 and 2011, respectively, and the Ph.D. degree in mechanical engineering from the Texas Tech University in 2015. He is currently an Associate Professor in the Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology. His current research interests include distributed optimization, distributed control, and distributed computation of network systems

Jian Sun received the bachelor degree from the Department of Automation and Electric Engineering, Jilin Institute of Technology, in 2001, the master degree from the Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences (CAS), in 2004, and the Ph.D. degree from the Institute of Automation, CAS, in 2007.He was a Research Fellow with the Faculty of Advanced Technology, University of Glamorgan, Pontypridd, U.K., from 2008 to 2009. He was a Post-Doctoral Research Fellow with the Beijing Institute of Technology, from 2007 to 2010. In 2010, he joined the School of Automation, Beijing Institute of Technology, where he has been a Professor since 2013. His current research interests include networked control systems, time-delay systems, and security of cyber-physical systems. Dr. Sun is an Editorial Board Member of the Journal of Systems Science & Complexity and Acta Automatica Sinica

Jie Chen (Fellow, IEEE) received the B.S., M.S., and Ph.D. degrees in control theory and control engineering from the Beijing Institute of Technology, in 1986, 1996, and 2001, respectively. From 1989 to 1990, he was a Visiting Scholar at the California State University, USA. From 1996 to 1997, he was a Research Fellow in the School of Engineering at the University of Birmingham, UK.He is a Professor with the School of Automation, Beijing Institute of Technology, where he serves as the Director of the Key Laboratory of Intelligent Control and Decision of Complex Systems. He also serves as the President of Tongji University. His research interests include complex systems, multiagent systems, multiobjective optimization and decision, and constrained nonlinear control.Prof. Chen is currently the Editor-in-Chief of Unmanned Systems and the Journal of Systems Science and Complexity. He has served on the editorial boards of several journals, including the IEEE Transactions on Cybernetics, International Journal of Robust and Nonlinear Control, and Science China Information Sciences. He is a Fellow of IEEE, IFAC, and a Member of the Chinese Academy of Engineering

Yue Wei received the Ph.D. degree in control science and engineering from the Beijing Institute of Technology, in 2019. He is currently an Assistant Researcher with Peng Cheng Laboratory. His research interests include distributed control and optimization for multi-agent systems
Corresponding author: Xianlin Zeng, e-mail: xianlin.zeng@bit.edu.cn
Received Date: 2021-09-25
Revised Date: 2021-12-28
Accepted Date: 2022-02-16

Available Online: 2022-04-07

Abstract

Abstract

This paper develops a fully distributed hybrid control framework for distributed constrained optimization problems. The individual cost functions are non-differentiable and convex. Based on hybrid dynamical systems, we present a distributed state-dependent hybrid design to improve the transient performance of distributed primal-dual first-order optimization methods. The proposed framework consists of a distributed constrained continuous-time mapping in the form of a differential inclusion and a distributed discrete-time mapping triggered by the satisfaction of local jump set. With the semistability theory of hybrid dynamical systems, the paper proves that the hybrid control algorithm converges to one optimal solution instead of oscillating among different solutions. Numerical simulations illustrate better transient performance of the proposed hybrid algorithm compared with the results of the existing continuous-time algorithms.
- Distributed algorithm,
- hybrid framework,
- multi-agent network,
- non-differentiable optimization

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References(42)

References

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This paper provides a fully distributed hybrid framework for solving the general large-scale constrained optimization problem, whose objective functions may be non-differentiable and non-strongly-convex. By introducing conflict-avoidance rule in the jump mapping, each agent in the network updates local variables by local information and transmitted information from neighbors. To our best knowledge, this is the first work studying fully distributed state-dependent hybrid methods for non-differentiable optimization problems
We provide complete and rigorous convergence proofs for the proposed distributed hybrid method with the invariance principle for hybrid dynamical systems. Because the objective function is non-strongly convex and non-differentiable, there may be a continuum of solutions to the optimization problem. With semi-stability theory, our proposed algorithm guarantees that the variables of different agents converge to one same optimal solution instead of oscillating among different solutions
This work has extended the existing hybrid works on consensus problems to distributed optimization problems. Compared with recent works for distributed optimization, the proposed fully distributed framework does not need a supervisory resetting and reduces the network communication burden. By numerical simulation, the proposed distributed hybrid algorithm shows an improved convergence performance than primal-dual continuous-time methods

A Fully Distributed Hybrid Control Framework For Non-Differentiable Multi-Agent Optimization

doi: 10.1109/JAS.2022.105872

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