Adaptive Neural Control for A Network of Parabolic PDEs with Event-triggered Mechanism

This paper investigates the finite-time consensus problem for nonlinear parabolic networks by designing a new tracking controller. For undirected topology, the newly designed controller allows to optimize the consensus time by adjusting the parameter β (0 < β < 1). Firstly, the neural network approximation property is utilized to counteract the uncertain nonlinear dynamics of agents, and the event-triggered mechanism is designed to save energy and reduce the communication burden. Secondly, a tracking control protocol is proposed based on event-triggered mechanism, which drives the multi-agent system to reach leader-follower consensus in finite time. Then, by considering appropriate Lyapunov generalization functions and using some important inequalities, the sufficient condition for achieving finite-time consensus in the multi-agent system is obtained. Finally, the effectiveness of the presented method is verified by simulation.