Distributed multi-step subgradient projection algorithm with adaptive event-triggering protocols: a framework of multiagent systems

Abstract

This paper discusses a convex optimisation problem with a common set of constraints in the framework of multi-agent systems. Each agent only exchanges information with its neighbours and collaboratively searches for the optimal solution of the global function. To this addressed problem, a distributed multi-step subgradient projection algorithm is developed, where an adaptive event-triggering protocol is designed to govern the information exchange. It is disclosed that the state of each agent representing the estimate of the optimal solution asymptotically converges to one of the optimal solutions under suitably chosen stepsizes and momentum parameters. Simulation results verify that the proposed algorithm has better convergence performance than the standard event-triggered subgradient projection algorithm. In addition, the communication frequency between agents can be effectively reduced to save communication resource consumption.

Keywords:

• Distributed optimisation
• multi-step subgradient projection algorithm
• adaptive event-triggered protocols
• multi-agent systems

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This work was supported part by the Natural Science Foundation of Anhui Province under Grant 2108085MA07, partially by the AHPU Youth Top-Notch Talent Support Program under Grant 2018BJRC009, partially by AHPU High-End equipment Intelligent Control Innovation Team under Grant 2021CXTD005, and partially by Open Project of Anhui Province Center for International Reasearch of Intelligent Control of High-end Equipment under Grant IRICHE-03.

Notes on contributors

Wenjing An

Wenjing An received the B.Sc. degree in Mathematics and Applied Mathematics from Xuchang University, Xuchang, China, in 2019. She is currently pursuing a master's degree in Operations Research and Cybernetics from University of Shanghai for Science and Technology, Shanghai, China. Her current research interests is Distributed Optimization.

Peifeng Zhao

Peifeng Zhao received the B.Eng. degree from Chizhou University, Chizhou, China, in 2018? and received the M.Eng. degree from Anhui Polytechnic University, Wuhu, China, in 2021. He is currently pursuing the Ph.D. degree in Control Science and Engineering from University of Shanghai for Science and Technology, Shanghai, China. His current research interests include networked control systems and power systems state estimation.

Hongjian Liu

Hongjian Liu received his B.Sc. degree in applied mathematics in 2003 from Anhui University, Hefei, China, and the M.Sc. degree in detection technology and automation equipment in 2009 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in control science and engineering in 2018 from Donghua University, Shanghai, China. In 2016, he was a Research Assistant with the Department of Mathematics, Texas A&M University at Qatar, Doha, Qatar, for two months. From March 2017 to March 2018, he was a Visiting Scholar in the Department of Information Systems and Computing, Brunel University London, UK. He is currently a Professor in the School of Mathematics and Physics, Anhui Polytechnic University, Wuhu, China. Dr. Liu's current research interests include filtering theory, memristive neural networks, and network communication systems. He is a very active reviewer for many international journals.

Jun Hu

Jun Hu received the B.Sc. degree in Information and Computation Science and M.Sc. degree in Applied Mathematics from Harbin University of Science and Technology, Harbin, China, in 2006 and 2009, respectively, and the Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology, Harbin, China, in 2013. From September 2010 to September 2012, he was a Visiting Ph.D. Student in the Department of Information Systems and Computing, Brunel University, U.K. From May 2014 to April 2016, he was an Alexander von Humboldt research fellow at the University of Kaiserslautern, Kaiserslautern, Germany. From January 2018 to January 2021, he was a research fellow at the University of South Wales, Cardiff, U.K. He is a Professor and Ph.D. supervisor in the Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China. His research interests include nonlinear control, filtering and fault estimation, time-varying systems and complex networks. He has published more than 80 papers in refereed international journals. Prof. Hu serves as a reviewer for Mathematical Reviews, as an editor for Neurocomputing, Journal of Intelligent and Fuzzy Systems, Neural Processing Letters, Systems Science and Control Engineering, and as a guest editor for International Journal of General Systems and Information Fusion.