Dynamic Event-Triggered Adaptive Tracking Control for Switched Nonlinear Systems with Vanishing Control Gains
Application of Dynamic Event-Triggered Adaptive Control in Switched Nonlinear Systems
Academic Background
With the rapid development of artificial intelligence technologies, the study of switched nonlinear systems has gained widespread attention. Switched systems are complex systems composed of multiple subsystems, where the system switches between different subsystems, each described by distinct differential or difference equations. These systems have broad applications in engineering practices, such as power systems, robotic control, and autonomous driving. However, challenges such as uncertainties, input saturation, and vanishing control gains make the control design of switched nonlinear systems particularly difficult.
Input saturation refers to situations where the control input signals are physically constrained, leading to degraded system performance or even instability. Vanishing control gains mean that at certain moments, the system’s control signals cannot effectively enter the subsystem, causing a loss of control. These issues are particularly common in practical applications, making the design of effective control strategies to handle these nonlinearities a critical research focus.
With advancements in network systems, computers, and microelectronics, event-triggered control (ETC) has become an important direction in the study of switched nonlinear systems. The basic idea of ETC is to perform data sampling and transmission only when specific triggering events occur, thereby reducing the system’s communication burden and computational resource consumption. However, in switched systems, asynchronous switching phenomena between the event-triggering mechanism and system switching can degrade control performance. Effectively handling this asynchrony has become a technical challenge.
Research Motivation and Problems
The motivation for this study stems from the vanishing control gain problem in switched nonlinear systems. Most existing research assumes that the system’s control gains are non-zero throughout, meaning control signals can continuously enter the system. However, in many practical systems, control gains vanish at certain moments, preventing the system from receiving control signals. The vanishing of control gains makes existing control methods for switched systems difficult to apply directly. Thus, designing a new switching rule and control strategy to address this issue is a key focus of this research.
Additionally, input saturation further complicates system control. Most existing control methods can only ensure bounded output tracking errors but fail to achieve asymptotic convergence. Therefore, designing an adaptive tracking control strategy that handles input saturation while achieving asymptotic error convergence is an important goal of this study.
Source of the Paper
This paper is co-authored by Dong Yang, Yanrui Sun, and Haibin Sun from the School of Engineering, Qufu Normal University, Guangdeng Zong from the School of Control Science and Engineering, Tiangong University, and Tao Liu from the Department of Electrical and Electronic Engineering, The University of Hong Kong. The paper was published in IEEE Transactions on Automation Science and Engineering and officially released in 2025. The research received support from the National Natural Science Foundation of China, the National Key Research and Development Program of China, and the Natural Science Foundation of Shandong Province.
Research Content and Innovations
The main objective of this study is to design a dynamic event-triggered adaptive control strategy to address input saturation and vanishing control gains in switched nonlinear systems, achieving asymptotic convergence of output tracking errors. Specifically, the research proposes the following innovative methods:
Nussbaum Function-Based Input Saturation Handling: By introducing the Nussbaum function (Nussbaum-Type Function), the research addresses the nonlinear issues caused by input saturation. The Nussbaum function, a special type of even function, adjusts control gains under non-saturated conditions, effectively tackling input saturation.
Gain-Dependent Switching Rule: Unlike existing research, the switching rule designed in this study considers the vanishing of control gains. By proposing a hysteresis-type gain-dependent switching rule (Hysteresis-Type Gain-Dependent Switching Law), the system ensures that when control gains vanish, the system switches to the next subsystem, guaranteeing effective control signal input.
Dynamic Event-Triggered Mechanism (DETM): The study introduces a dynamic event-triggered mechanism (DETM), allowing for asynchronous phenomena between switching and event-triggering. Compared to traditional event-triggered mechanisms, DETM reduces the frequency of data sampling and transmission, further lowering the system’s communication and computational burden.
Event-Triggering-Based Switching Controller Design: To address input saturation and vanishing control gains, the research proposes an event-triggering-based switching controller. This controller allows control gains to vanish at certain moments while achieving asymptotic error convergence through adaptive control strategies.
Research Process and Methods
System Modeling and Analysis: The study first models the switched nonlinear system with input saturation and vanishing control gains, analyzing the system’s dynamic behavior. By introducing the Nussbaum function and dynamic event-triggered mechanism, a new control framework is proposed to effectively handle the system’s nonlinearities.
Switching Rule Design: To address the vanishing control gain problem, a hysteresis-type gain-dependent switching rule is designed. This rule ensures that the system switches to the next subsystem when control gains vanish, guaranteeing effective control signal input.
Dynamic Event-Triggered Mechanism Design: The study introduces a dynamic event-triggered mechanism by incorporating internal dynamic variables into the triggering conditions, reducing the frequency of data sampling and transmission. Compared to previous research, this mechanism effectively avoids the Zeno phenomenon (infinite triggering) under asynchronous switching.
Adaptive Controller Design: By combining the radial basis function neural network (RBFNN) and the Nussbaum function, an adaptive controller is designed to address system uncertainties and input saturation. This controller achieves asymptotic convergence of output tracking errors even when control gains vanish.
Simulation Verification: To validate the effectiveness of the proposed control strategy, simulation experiments are conducted. The results demonstrate that the dynamic event-triggered adaptive control strategy effectively handles input saturation and vanishing control gains, achieving asymptotic convergence of output tracking errors.
Research Results and Conclusions
Through theoretical analysis and simulation experiments, the study draws the following conclusions:
Solving the Vanishing Control Gain Problem: The hysteresis-type gain-dependent switching rule effectively addresses the vanishing control gain problem, ensuring that the system switches to the next subsystem when control gains vanish, guaranteeing effective control signal input.
Handling Input Saturation: By introducing the Nussbaum function and adaptive control strategies, the proposed method effectively handles input saturation and achieves asymptotic convergence of output tracking errors.
Effectiveness of the Dynamic Event-Triggered Mechanism: The proposed dynamic event-triggered mechanism reduces the frequency of data sampling and transmission under asynchronous switching while avoiding the Zeno phenomenon without limiting the maximum asynchronous time.
Research Significance and Value
The proposed dynamic event-triggered adaptive control strategy provides new insights and methods for controlling switched nonlinear systems, offering significant theoretical and practical value. First, by introducing the Nussbaum function and dynamic event-triggered mechanism, the research successfully addresses input saturation and vanishing control gains, expanding the applicability of existing control methods. Second, the hysteresis-type gain-dependent switching rule and event-triggering-based switching controller provide new tools for the control design of switched nonlinear systems, ensuring stability and performance in complex environments.
Research Highlights
Innovative Switching Rule: The hysteresis-type gain-dependent switching rule effectively addresses the vanishing control gain problem, ensuring effective control signal input.
Dynamic Event-Triggered Mechanism: The designed dynamic event-triggered mechanism reduces the frequency of data sampling and transmission under asynchronous switching, avoiding the Zeno phenomenon.
Adaptive Control Strategy: By combining RBFNN and the Nussbaum function, an adaptive controller is designed to achieve asymptotic convergence of output tracking errors under input saturation and vanishing control gains.
Future Research Directions
Although this study has made significant progress in controlling switched nonlinear systems, many issues remain to be explored. For example, extending the proposed dynamic event-triggered adaptive control technology to switched systems under cyberattacks, especially addressing security control problems like denial-of-service (DoS) attacks, is an important future research direction.
Conclusion
This study proposes a dynamic event-triggered adaptive control strategy that successfully addresses input saturation and vanishing control gains in switched nonlinear systems while achieving asymptotic convergence of output tracking errors. Through simulation experiments and theoretical analysis, the effectiveness and feasibility of the proposed control strategy are validated. The research provides new theoretical support and practical guidance for the control design of switched nonlinear systems, offering significant academic and application value.