Fixed-Time Cluster Optimization for Multi-Agent Systems Based on Piecewise Power-Law Design

Dear Editor, This letter focuses on the fixed-time (FXT) cluster optimization problem of first-order multi-agent systems (FOMASs) in an undirected network, in which the optimization objective is the sum of the objective functions of all clusters. A novel piecewise power-law control protocol with cooperative-competition relations is proposed. Furthermore, a sufficient condition is obtained to ensure that the FOMASs achieve the cluster consensus within an FXT. Then, on the basis of maintaining the cluster consensus, the agents in each cluster converge to the optimal solution of their objective functions in another FXT.