Event-Triggered Adaptive Control for a Class of Uncertain Nonlinear Systems

TLDR

Event‑triggered adaptive control for uncertain nonlinear systems with non‑globally Lipschitz nonlinearities and unknown parameters is challenging because the usual input‑to‑state stability assumption cannot be verified. The authors aim to design an adaptive controller and a triggering rule jointly so that the ISS requirement is eliminated. They introduce three threshold‑based strategies—fixed, relative, and a novel switching threshold—to construct the controller and event trigger. The resulting schemes guarantee global boundedness of all closed‑loop signals and exponential convergence of the tracking/stabilization error to an adjustable compact set.

Abstract

In this technical note, the problem of event-trigger based adaptive control for a class of uncertain nonlinear systems is considered. The nonlinearities of the system are not required to be globally Lipschitz. Since the system contains unknown parameters, it is a difficult task to check the assumption of the input-to-state stability (ISS) with respect to the measurement errors, which is required in most existing literature. To solve this problem, we design both the adaptive controller and the triggering event at the same time such that the ISS assumption is no longer needed. In addition to presenting new design methodologies based on the fixed threshold strategy and relative threshold strategy, we also propose a new strategy named the switching threshold strategy. It is shown that the proposed control schemes guarantee that all the closed-loop signals are globally bounded and the tracking/stabilization error exponentially converges towards a compact set which is adjustable.