Consensus of Nonlinear Uncertain Delayed Multiagent Systems Modeled by PDEs via Adaptive Boundary Control

Under the influence of nonlinearity, time-varying delay, and uncertainty, the consensus problem is concerned in this study for multiagent systems modeled by partial differential equations, which means that both the time and space variables are included in the dynamic behavior of each agent. First, with a directed graph, an adaptive boundary controller is developed under boundary measurements, which can effectively reduce the control cost with dynamic control gains and a few actuators and sensors installed at the boundary of the spatial domain. Then, through the designed adaptive boundary controller, the linear matrix inequality (LMI)-based consensus conditions are obtained to ensure the exponential stability of the consensus error systems derived by utilizing the inequality techniques and Lyapunov direct approach. Lastly, two numerical examples demonstrate the effectiveness of the presented adaptive boundary control protocols.