Fully distributed observer-based tracking control for Lur'e systems with event-triggered communication

This paper investigates the problem of cooperative tracking for Lur'e systems under directed spanning tree topology. First, a control protocol is proposed to achieve cooperative tracking consensus by a distributed observer, which utilizes only the states of neighboring agents based on the event-triggering conditions with mixed node and edge. Then, an improved tracking protocol is developed by considering the case that only the outputs of neighbors can be obtained. With the aid of adaptive updating parameters, the two protocols do not utilize the minimum eigenvalue of Laplacian matrix, and can deal with the nonlinear dynamics of Lur'e systems in a fully distributed manner. Moreover, with the Lyapunov analysis framework, the tracking errors can be proved to converge to zero in both cases. Zeno behavior is excluded from the event-triggering conditions containing states and outputs of neighbors. Finally, the effectiveness of the proposed protocols is verified by two numerical simulations.