Distributed fixed-time cluster optimisation for multi-agent systems

This paper considers the distributed cluster optimisation problem of multi-agent systems (MASs). Different from existing optimisation problems, the MASs are divided into several clusters, and each cluster has its own optimisation objective which is the sum of their local objective functions. Firstly, based on communication topology, the distributed optimisation problem with two clusters is considered and a kind of distributed control protocol is proposed. By using the fixed-time stability theory and the convexity of function, it is proved that the MASs can not only achieve cluster consensus in a fixed-time interval, but also solve the optimisation problem asymptotically. Secondly, the MASs with multiple clusters are further considered. We extend the proposed protocol to a more general case and also prove that MASs can achieve cluster consensus in fixed-time and asymptotically reach the optimal solution of the optimisation objective. Finally, some numerical simulations are presented to show the efficacy of the theoretical results.