Asymptotic Event-Based Tracking Design for Nonlinear Systems Under Multiple Unknown Control Directions

This article proposes an event-based asymptotic tracking control method for nonlinear strict-feedback systems with multiple unknown control directions. The system is characterized by multiple unknown control directions, which pose challenges to its performance. In contrast to traditional Nussbaum-type methods, we propose a novel Nussbaum-type function to handle multiple Nussbaum-type gains, ensuring robust asymptotic tracking. Additionally, two event-triggered mechanisms are developed to alleviate the computational complexity of adaptive Nussbaum design. The static event-triggered mechanism significantly improves the system’s responsiveness to dynamic changes by employing dynamically decreasing thresholds. Building on this, a dynamic event-triggered mechanism is introduced, incorporating an internal variable that continuously adjusts the triggering conditions over time. Furthermore, the proposed design not only achieves asymptotic tracking control but also ensures that both event-triggered mechanisms avoid the Zeno phenomenon. To validate the proposed design schemes, a simulation example of a marine surface vehicle is presented.