Adaptive Fuzzy Wavelet Neural Network Event-Triggered Consensus Tracking Control for Networked Hyperbolic PDE-ODE Systems

In this article, the event-triggered consensus tracking control problem is explored for a network of hyperbolic partial differential equations (PDEs) with boundary actuator dynamics described by ordinary differential equations. Control input appears in actuator dynamics rather than in the PDE subsystem, which poses an interesting open problem. Unknown nonlinear actuator dynamics and local interconnection information render existing boundary control algorithms no longer applicable. To handle this, based on the infinite and finite-dimension backstepping techniques, a novel distributed adaptive tracking controller is designed to realize the consensus tracking control, where the unknown nonlinearities are determined by using the fuzzy wavelet neural networks. Moreover, due to the resource constraint of the communication channel and computation burden, this article further develops a new event-triggered mechanism in the sensor-to-controller channel. Based on the proposed event-triggered distributed algorithm, it is amply illustrated that consensus tracking control can be realized. Finally, two examples are provided to demonstrate how effectively the designed tracking algorithm performs.