PDE-Based Prescribed-Time Deployment of Networked Multi-agent Systems by Switching

This paper addresses the prescribed-time deployment of multi-agents via a partial differential equation (PDE) approach. Based on the output measurements, a switching control law is suggested and the actuated closed-loop system is modeled by the heat model with the Neumann boundary conditions. The proposed switching rule guarantees that only one leader can use the communication network to transmit the measurement, which reduces the workload. Sufficient conditions based on linear matrix inequalities are derived for the exponential stability of the resulting system. Finally, a simulation example is performed to illustrate the effectiveness of the results.