Predefined-Time Event-Triggered Adaptive Tracking Control for Uncertain Time Delay Nonlinear Systems

This paper raises a predefined-time event-triggered adaptive tracking controller for nonlinear systems with time delays. To mitigate the effects of time-varying delays, a Lyapunov-Krasovskii function is initially introduced. A set of adaptive laws and virtual controllers with switching functions are designed to avoid singularity phenomena. In addition, the event-triggered mechanism with the switching threshold can effectively conserve communication resources while avoiding the occurrence of Zeno behavior. It is theoretically demonstrated that, under the devised control strategy, the system output successfully tracks the reference signal with negligible tracking error within a specified time. Lastly, the validity of the raised control strategy is demonstrated through examples. Note to Practitioners—This paper explores a predefined-time adaptive tracking controller for nonlinear systems with time delays. For instance, in engineering applications such as robotics, completing tasks within a predefined time frame is critical. Failure to account for time delays may cause the control strategy to fall short of achieving the desired performance or even lead to instability. In this context, the development and investigation of event-triggered control are essential in modern control theory, as they effectively address the challenges posed by resource constraints. Considering the aforementioned factors, this paper addresses time delays and proposes a predefined-time event-triggered adaptive tracking control strategy based on backstepping and the Lyapunov-Krasovskii function. The theoretical analysis and simulation results demonstrate that the proposed scheme achieves the expected control objectives.