Global Event-Triggered Adaptive Stabilization of Nonlinear Time-Delay Systems With Unknown Measurement Sensitivity

Abstract

This paper addresses the problem of global stabilization in nonlinear time-delay systems with unknown measurement sensitivity. Notably, our system allows for the unknown measurement sensitivity to be non-differentiable, coupled with unmeasurable states, which necessitates the development of observers and control input strategies based on dynamic gain. To optimize resource usage and mitigate network congestion, we introduce an event-triggering mechanism based on two events. This mechanism evaluates dynamic gain and control signals, ensuring a guaranteed positive lower bound on execution time. Moreover, the dynamic gain is designed to compensate for the impact of execution errors. The introduction of a relational sensitivity error allows the unknown measurement sensitivity to converge to a small range. By selecting appropriate Lyapunov-Krasovskii functionals, we eliminate the influence of time-delay, ultimately proving global stability of the closed-loop system. Consequently, comparative simulation results validate the effectiveness of the proposed scheme. Note to Practitioners—This paper explores event-triggered control of nonlinear systems with applications in intelligent transportation, robotics, and aerospace. Notably, we address three critical issues. Firstly, we propose methods to manage unmeasurable states, which is essential for systems like autonomous vehicles and drones where full state measurement is often not feasible. Secondly, we improve existing event-triggering mechanisms to optimize network resource usage, significantly reducing communication frequency, which is particularly beneficial in networked control systems, such as smart grids and industrial automation. Thirdly, we tackle the challenge of unknown measurement sensitivity, relevant for systems operating in uncertain environments like industrial robots and aerospace applications where sensor accuracy can vary. Comparative simulations show that our dynamic event-triggered control method effectively reduces network burden, proving its practical value in real-world applications where network bandwidth and reliability are crucial. In future research, we will also consider reducing the transmission frequency from sensor to controller to further improve system performance. Additionally, we aim to explore adaptive mechanisms to better manage uncertainties in measurement sensitivity, thereby expanding the practical applicability of our approach.