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

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.