Periodic event-triggered targeted shape control of Lagrangian systems with discrete-time delays

We study the problem of periodic event-triggered targeted formation control for multi-agent Lagrangian systems. We assume that the equations of motion of each agent are derived from a Lagrangian function. Besides, each agent has information about a predefined convex set as a targeted set. The goal of the agents is to achieve the desired formation in the targeted sets, while the information is asynchronously shared by a periodic event-triggering specification, and there is also a time-delay in their communication. A novel distributed control law is proposed for the agents to reach the goal while their velocities are driven to zero. Applications and simulations are provided to validate the theoretical results.