Hierarchical Non-Singular Terminal Sliding Mode Control for Constrained Under-Actuated Nonlinear Systems Against Sensor Faults

Electrical Engineering Engineering Information Science Automation
under-actuated nonlinear systems sensor faults state constraints dynamic event-triggered hierarchical non-singular terminal sliding mode control

Background Introduction

In modern engineering practices, under-actuated systems are widely used in fields such as overhead cranes, wheeled inverted pendulums, and snake robots due to their simple structure, low energy consumption, and high flexibility. However, the number of control inputs in under-actuated systems is less than the degrees of freedom (DOF), posing significant challenges to controller design and stability analysis. Although various control strategies, such as feedback linearization control, adaptive control, and robust control, have been proposed, these methods often face issues like high complexity and dependence on model accuracy in practical applications. Additionally, sensor faults can lead to the loss of partial state information, affecting system monitoring and performance, and even causing system instability. Therefore, designing an efficient and robust control strategy in the presence of sensor faults has become a hot research topic.

Source of the Paper

This paper is co-authored by Minggang Liu, Ning Xu, Huanqing Wang, Guangdeng Zong, Xudong Zhao, and Lun Li, affiliated with the College of Control Science and Engineering at Bohai University, College of Information Science and Technology at Bohai University, College of Mathematical Science at Bohai University, School of Control Science and Engineering at Tiangong University, Faculty of Electronic Information and Electrical Engineering at Dalian University of Technology, and College of Machinery and Automation at Weifang University, respectively. The paper was accepted on February 13, 2025, and published in the journal Nonlinear Dynamics with the DOI 10.1007/s11071-025-11011-8.

Research Content

Research Problem

This paper investigates the adaptive hierarchical non-singular terminal sliding mode control (HNTSMC) problem for under-actuated nonlinear systems with time-varying asymmetric state constraints in the presence of sensor faults. Due to sensor faults, the real state variables of the system cannot be obtained, necessitating system transformation and controller design based on the state information actually measured by the sensors.

Research Process

  1. System Transformation
    Since the real state variables of the system cannot be directly obtained due to sensor faults, this paper employs the Unified Barrier Function (UBF) to transform the original system into an unconstrained system, addressing the issue of time-varying asymmetric state constraints. Specifically, the measured state variables are transformed into unconstrained state variables using UBF, thereby avoiding the impact of state constraints on controller design.

  2. Hierarchical Non-Singular Terminal Sliding Mode Control Design
    For the transformed unconstrained system, this paper proposes a hierarchical non-singular terminal sliding mode control technique. This technique decomposes the control problem of under-actuated systems into multiple layers, each corresponding to a sliding mode controller, thereby resolving the DOF mismatch between control inputs and controlled variables. Additionally, this method avoids the singularity problem that may occur in traditional terminal sliding mode control and achieves finite-time convergence.

  3. Robust Adaptive Fault Compensation Controller Design
    To compensate for the uncertainties and nonlinear dynamics caused by sensor faults, this paper designs a robust adaptive fault compensation controller based on Radial Basis Function Neural Networks (RBFNNs). This controller does not require prior knowledge of the fault coefficients and can adaptively compensate for the effects of faults.

  4. Dynamic Event-Triggered Mechanism
    To reduce unnecessary communication burden, this paper introduces a dynamic event-triggered mechanism (DETM). This mechanism dynamically adjusts the triggering threshold based on the global state, further saving communication resources.

Experimental Results

The effectiveness of the proposed control scheme is verified through a simulation experiment on an overhead crane system. The results show that despite the sensor faults occurring at 40 seconds, the measured state variables remain stable and within the time-varying asymmetric state constraints through the designed fault compensation mechanism. Furthermore, the hierarchical non-singular terminal sliding mode control technique effectively resolves the DOF mismatch between control inputs and controlled variables and achieves finite-time convergence.

Main Conclusions

This paper proposes a dynamic event-triggered adaptive hierarchical non-singular terminal sliding mode control strategy for constrained under-actuated nonlinear systems with sensor faults. The strategy addresses the state constraint problem using the unified barrier function and achieves finite-time convergence through the hierarchical sliding mode control technique. Additionally, the robust adaptive fault compensation controller based on neural networks effectively compensates for the uncertainties and nonlinear dynamics caused by sensor faults. Simulation experiments validate the effectiveness of the control scheme.

Research Highlights

  1. Application of Unified Barrier Function: For the first time, this paper applies the unified barrier function to nonlinear systems with dynamic constraints, solving the problem of time-varying asymmetric state constraints.
  2. Hierarchical Non-Singular Terminal Sliding Mode Control Technique: This technique not only resolves the DOF mismatch between control inputs and controlled variables in under-actuated systems but also avoids the singularity problem in traditional terminal sliding mode control.
  3. Dynamic Event-Triggered Mechanism: Compared to static event-triggered mechanisms, the dynamic event-triggered mechanism further saves communication resources and reduces communication frequency.

Research Significance

This research provides a new solution for controlling under-actuated nonlinear systems with sensor faults, offering significant theoretical and practical value. The proposed control strategy not only effectively handles state constraints but also ensures system stability and robustness in the presence of sensor faults. Additionally, the introduction of the dynamic event-triggered mechanism provides new insights for reducing communication burdens, with broad application prospects.

Summary

By introducing the unified barrier function, hierarchical non-singular terminal sliding mode control technique, and dynamic event-triggered mechanism, this paper proposes an adaptive control strategy for constrained under-actuated nonlinear systems with sensor faults. The strategy demonstrates excellent performance in both theoretical analysis and simulation experiments, providing an important reference for research and applications in related fields.