Achieving Cluster Formation of Multi-Agent Systems Under Aperiodic Sampling and Communication Delays

This paper addresses the problem of cluster formation control for a networked multi-agent system (MAS) in the simultaneous presence of aperiodic sampling and communication delays. First, to fulfill multiple formation tasks, a group of agents are decomposed into <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula> distinct and nonoverlapping clusters. The agents in each cluster are then driven to achieve a desired formation, whereas the MAS as a whole accomplishes <inline-formula><tex-math notation="LaTeX">$ M $</tex-math></inline-formula> cluster formations. Second, by a proper modeling of aperiodic sampling and communication delays, an aperiodic sampled-data cluster formation protocol (CFP) is delicately constructed such that the information exchanges among neighboring agents only occur intermittently at discrete instants of time. Third, a detailed theoretical analysis of cluster formability is carried out and a sufficient and necessary condition is provided such that the system is <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>-cluster formable. Furthermore, a discontinuous Lyapunov functional approach is developed to derive a design criterion on the existence of an admissible sampled-data CFP. Finally, numerical simulations on a team of nonholonomic mobile robots are given to illustrate the effectiveness of the obtained theoretical result.