PDE-Based Leader-Following Coordination Control for Flexible Manipulators With Event-Triggered Communication Over Directed Graphs

In this article, we address the leader-following coordination control issue for flexible manipulators modeled by fourth-order partial differential equations (PDEs) within an event-triggered communication framework. Most of the existing research on the coordination control of multiple PDE systems assumes that the communication topology is undirected and that communication between neighboring agents is continuous, leading to significant consumption of communication resources. However, in this study, the communication topology among the virtual leader and followers is described by a directed graph, where the leader's reference signal is accessible only to a subset of the followers. Moreover, an event-triggering mechanism is proposed to avoid continuous signal transmission among agents, effectively mitigating the communication burden. An adaptive boundary control scheme based on filters is designed for each following flexible manipulator to track the leader's angle and eliminate unexpected vibrations in the presence of unknown external disturbances. All the signals of the closed-loop system are uniformly bounded. Simulation results show that the presented control scheme is effective.