Dynamic Event-Triggered Adaptive Tracking Control for Switched Nonlinear System With Vanishing Control Gains

Abstract

The asymptotic tracking control problem is investigated for nonstrict-feedback switched nonlinear systems by developing a dynamic event-triggered adaptive control technology. A key contribution is to design a hysteresis-type switching rule and an event-triggering-based switching controller to realize the asymptotically convergent target. First, by utilizing the Nussbaum-type function technique, the obstacle caused by unknown nonsmooth saturation nonlinearity is circumvented. Second, a novel gain-dependent switching signal is constructed, which ensures a time interval between any adjacent switching. Furthermore, a dynamic event-triggered schema is established, which allows the occurrence of asynchronous switching phenomenon generated by switching and event-triggering. An event-triggering-based switching controller is designed so that the adaptive asymptotic tracking control problem is solvable even when input saturation and vanishing control gains arise. Finally, simulation results with theoretical analysis are presented to validate the feasibility of the control algorithm. Note to Practitioners - With the development of artificial intelligence techniques, the studies of switched nonlinear systems have received widespread attention. This investigation is motivated by the vanishing control gains problem for switched nonlinear systems. We propose a co-design of a hysteresis-type gain-dependent switching rule and an event-triggering-based switching controller for switched nonlinear systems under input saturation and vanishing control gains. In existing results, the designed control signal is required to enter into the systems everywhere, while we relax the restriction. An improved dynamic event-triggered adaptive control framework has been established to obtain less conservative conditions further, where the control gain is allowed to vanish at some points. This study presents the method for practitioners interested in adaptive control design.