Event-triggered adaptive prescribed performance tracking for nonlinear time-varying systems with unknown control directions

This article deals with the adaptive prescribed performance tracking for nonlinear time-varying systems. To handle multiple unknown control directions, a novel lemma is established by using a general class of Nussbaum functions. To handle unknown time-varying parameters, the congelation of variables method is employed. Different novel functions are introduced to achieve prescribed performance tracking and finite-time prescribed performance tracking, respectively. Meanwhile, the problem of explosion of complexity is avoided by utilizing the command filter and the compensation mechanism. For reasons of saving network resources and reducing communication burden, a new event-triggered mechanism is proposed, which can circumvent the Zeno behavior. Then, an event-triggered adaptive prescribed performance tracking control scheme is constructed and is extended to event-triggered finite-time adaptive prescribed performance tracking, both of which guarantee that all closed-loop signals are bounded and the trajectory of the tracking error can be limited to the prescribed region. Finally, the availability of the control scheme is demonstrated by two examples.