Dynamic Event-Triggered Adaptive Fixed-Time Practical Tracking Control for Nonlinear Systems Through Funnel Function

The article studies an adaptive practical fixed-time tracking control problem of nonlinear system using the funnel control method and the dynamic event-triggered control mechanism. First, an adaptive practical fixed-time controller is built using radial basis function neural networks and an improved funnel function. On the one hand, it eliminates the impact of unknown nonlinear functions on system performance and forces the tracking error to evolve within the funnel boundary. On the other hand, the transient performance of the system is enhanced by the preassigned funnel boundary. Second, a nonlinear command filter with high-order nonlinear term is constructed to solve the problem of “explosion of complexity” in the backstepping approach. Further, the filter error compensating input is designed to counteract the detrimental impacts of the filter error on the tracking performance. In addition, to achieve the dynamic modification of threshold parameters and minimize communication resources, a dynamic event-triggered mechanism is devised based on auxiliary dynamic variables and dynamic threshold parameters. It is rigorously proved theoretically that the closed-loop system is practical fixed-time stable and Zeno behavior is ruled out. Ultimately, the single-link robotic arm system validates the efficiency of the acquired control approach.
Note to Practitioners
—The application of traditional control algorithms is severely limited in real industrial systems due to typical constraints on input, output, and communication resources, particularly in autonomous surface vehicles and robot fields. Nevertheless, the existing methods only take into account asymptotic tracking control problems based on the time-triggered mechanism, which is impracticable for a large number of systems in reality. Therefore, the paper studies the problem of funnel control and communication resource of the nonlinear system, and an adaptive practical tracking control scheme is proposed through the dynamic event-triggered mechanism and funnel function, which not only ensures that the nonlinear system is practical fixed-time stable but also improves the transient and steady-state performances of the nonlinear system.