Distributed rotating consensus of second-order multi-agent systems with nonuniform delays

Significance 

Generally, the study of distributed consensus problems is associated with unavoidable delays, particularly in complex practical applications. Consensus problems with delay have been classified into moving consensus and static consensus. Presently, a static consensus has been effectively explored thus leading to numerous insights. For instance, the consensus stability of a multi-agent system with non-uniform delays have been resolved through frequency domain approaches.

Unfortunately, little has been done concerning the moving consensus problems with the current works majoring only on the flocking-like consensus problems consisting of agents moving along a line. This is attributed to possible decoupling of static consensus with zero eigenvalue which is not possible with the moving consensus points. This has further complicated the analyses of moving consensus points. Therefore, researchers have been looking for alternatives and have identified rotating consensus problems as a promising solution. On the other hand, the flocking-like consensus problems with delays involve line moving modes which do not affect the positions of the agents. However, rotating consensus consists of cyclic moving modes thus results in the time-varying of the agent position before consensus.

Recently, a group of researchers at Central South University: Dr. Yonggang Li, Dr. Yi Huang and Dr. Peng Lin in collaboration with Professor Wei Ren at the University of California investigated a distributed consensus problem of second-order multi-agent systems with nonuniform delays. They chosed rotation to enable all the agents to reach a consensus while moving together around a common point along a circle. They purposed to extend the already existing results of rotating consensus developed in [2], by taking into consideration the nonuniform delays.

A distributed algorithm with nonuniform delays was used after which the original system was transformed into an equivalent one. Eventually, a frequency domain method was used to analyze the conditions for the equivalent system. This enabled determination of the upper bound on the maximum delay for the system consensus stability. The research work is published in the research journal, Systems and Control Letters.

The authors observed that it was possible to obtain the upper bound on the maximum delay for the consensus stability. In addition, the rotating consensus problem despite being more complicated as compared to the flocking-like consensus problems, was suitable for analysis of the distributed consensus thus resulting to much more accurate results as compared to the initially obtained ones. It was necessary to validate the results through numerical simulations which produced similar results.

According to the authors, the distributed rotating consensus problem of second-order multi-agent systems with nonuniform delays has potential applications in numerous fields including spacecraft docking and satellite formation flight. Therefore, the study will advance future research works on distributed consensus problems analysis.

About the author

Yonggang Li received the M.S. degree in control science and engineering and the Ph.D. degree in control science and engineering from Central South University, Changsha, China, in 2000 and 2004, respectively. From 2011 to 2012, he was a visiting scholar at the Curtin University, Perth, Australia. Since 2013, he has been a Full Professor with the School of Information Science and Engineering, Central South University.

His current research interests include modeling and optimal control of complex industrial process, process control and intelligent control system, knowledge driven automation.

About the author

Yi Huang received the M.Eng. degree in Control Engineering from Central South University, Hunan, China, in 2016. He is currently working towards the Ph.D. degree with the Control Science and Engineering, Central South University. His research interests include cooperative control and formation control.

About the author

Peng Lin received his B.S. degree in automation from Xidian University, Xi’an, China, in 2004, and the Ph.D. degree in control theory and applications from Beihang University, Beijing, China, in 2010. He is currently a Professor with the School of Information Science and Engineering, Central South University, Changsha 410083, China. His research interests include cooperative control, optimization theory, switching control and robust control.

About the author

Wei Ren is currently a Professor with the Department of Electrical and Computer Engineering, University of California, Riverside. He received the Ph.D. degree in Electrical Engineering from Brigham Young University, Provo, UT, in 2004. Prior to joining UC Riverside in 2011, he was a faculty member at Utah State University and a postdoc at the University of Maryland.

His research focuses on distributed control of multi-agent systems and autonomous control of unmanned vehicles. Dr. Ren is an author of two books Distributed Coordination of Multi-agent Networks (Springer-Verlag, 2011) and Distributed Consensus in Multi-vehicle Cooperative Control (Springer-Verlag, 2008). He was a recipient of the Antonio Ruberti Young Researcher Prize in 2017 and the National Science Foundation CAREER Award in 2008. He is currently an Associate Editor for Automatica and Systems \& Control Letters.

Reference

[1] Li, Y., Huang, Y., Lin, P., & Ren, W. (2018). Distributed rotating consensus of second-order multi-agent systems with nonuniform delays. Systems & Control Letters, 117, 18-22.

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[2] Lin, P., & Jia, Y. (2010). Distributed rotating formation control of multi-agent systems. Systems & Control Letters, 59, 587-595.

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