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Effective Fixed-Time Control for Constrained Nonlinear System

Chenglin Gong, Ziming Wang, Guanxuan Jiang, Xin Wang, Yiding Ji

TL;DR

Addresses state-constrained nonlinear control with non-strict bounds by coupling an adaptive fixed-time controller built on a one-to-one asymmetric nonlinear mapping auxiliary system with a logarithmic state transformation and RBFNN-based uncertainty handling. Introduces four multi-threshold event-triggered strategies and a self-triggered scheme, supported by a unified SPFTS analysis and fixed-time convergence bound $T_{\max}$, to reduce communication without sacrificing tracking accuracy. The approach combines backstepping, adaptive laws, and neural-approximation to enforce state constraints and ensure stability, validated by simulations showing substantial reductions in control updates while maintaining performance. This framework enhances data-efficiency and robustness for constrained nonlinear control in engineering applications.

Abstract

In this paper, we tackle the state transformation problem in non-strict full state-constrained systems by introducing an adaptive fixed-time control method, utilizing a one-to-one asymmetric nonlinear mapping auxiliary system. Additionally, we develop a class of multi-threshold event-triggered control strategies that facilitate autonomous controller updates, substantially reducing communication resource consumption. Notably, the self-triggered strategy distinguishes itself from other strategies by obviating the need for continuous real-time monitoring of the controller's state variables. By accurately forecasting the subsequent activation instance, this strategy significantly optimizes the efficiency of the control system. Moreover, our theoretical analysis demonstrates that the semi-global practical fixed-time stability (SPFTS) criterion guarantees both tracking accuracy and closed-loop stability under state constraints, with convergence time independent of initial conditions. Finally, simulation results reveal that the proposed method significantly decreases the frequency of control command updates while maintaining tracking accuracy.

Effective Fixed-Time Control for Constrained Nonlinear System

TL;DR

Addresses state-constrained nonlinear control with non-strict bounds by coupling an adaptive fixed-time controller built on a one-to-one asymmetric nonlinear mapping auxiliary system with a logarithmic state transformation and RBFNN-based uncertainty handling. Introduces four multi-threshold event-triggered strategies and a self-triggered scheme, supported by a unified SPFTS analysis and fixed-time convergence bound , to reduce communication without sacrificing tracking accuracy. The approach combines backstepping, adaptive laws, and neural-approximation to enforce state constraints and ensure stability, validated by simulations showing substantial reductions in control updates while maintaining performance. This framework enhances data-efficiency and robustness for constrained nonlinear control in engineering applications.

Abstract

In this paper, we tackle the state transformation problem in non-strict full state-constrained systems by introducing an adaptive fixed-time control method, utilizing a one-to-one asymmetric nonlinear mapping auxiliary system. Additionally, we develop a class of multi-threshold event-triggered control strategies that facilitate autonomous controller updates, substantially reducing communication resource consumption. Notably, the self-triggered strategy distinguishes itself from other strategies by obviating the need for continuous real-time monitoring of the controller's state variables. By accurately forecasting the subsequent activation instance, this strategy significantly optimizes the efficiency of the control system. Moreover, our theoretical analysis demonstrates that the semi-global practical fixed-time stability (SPFTS) criterion guarantees both tracking accuracy and closed-loop stability under state constraints, with convergence time independent of initial conditions. Finally, simulation results reveal that the proposed method significantly decreases the frequency of control command updates while maintaining tracking accuracy.

Paper Structure

This paper contains 10 sections, 33 equations, 3 figures, 1 table.

Table of Contents

  1. introduction
  2. problem formulation and preliminaries
  3. System Model
  4. RBFNNs
  5. Controller Trigger Program
  6. Controller Design
  7. Multi-threshold event-triggered strategies
  8. Stability Analysis
  9. Illustrative Example
  10. Conclusion

Figures (3)

  • Figure 1: The consistency tracking performance involving signal $x_{1}$ and restricted signal $w_{1}$, along with their corresponding desired signals $x_{r}$ and $w_{r}$, under different ETC strategies, where (a), (b), (c), and (d) represent the fixed threshold, relative threshold, switched threshold and self-triggered strategies respectively.
  • Figure 2: The change of the actual controller $g$ under different ETC strategies, where (a), (b), (c), and (d) represent the fixed threshold, relative threshold, switched threshold and self-triggered strategies respectively.
  • Figure 3: The trigger interval for event triggering under different ETC strategies, where (a), (b), (c), and (d) represent the fixed threshold, relative threshold, switched threshold and self-triggered strategies respectively.

Theorems & Definitions (1)

  • proof