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Adaptive fixed-time TSM for uncertain nonlinear dynamical system under unknown disturbance.

Saim Ahmed1,2, Ahmad Taher Azar1,2,3, Haoping Wang4

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Summary
This summary is machine-generated.

This study introduces an adaptive terminal sliding mode control (TSM) for nonlinear systems facing disturbances. The novel approach ensures fixed-time stability and smooth control, outperforming existing methods.

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Adaptive Control Theory

Background:

  • Nonlinear systems are susceptible to external disturbances and uncertainties.
  • Existing fixed-time terminal sliding mode control (TSM) methods struggle with unknown dynamics.
  • Robust control is crucial for maintaining system stability under adverse conditions.

Purpose of the Study:

  • To develop an adaptive terminal sliding mode control (TSM) strategy for nonlinear systems with fixed-time convergence.
  • To address limitations of current fixed-time TSM schemes in handling uncertainties and disturbances.
  • To ensure system stability and smooth control input within a predetermined finite time.

Main Methods:

  • Introduction of a novel fixed-time TSM with a specific sliding surface.
  • Development of a new Lemma for fixed-time stability analysis.
  • Integration of an adaptive control scheme with fixed-time TSM to manage unknown dynamics and external disturbances.
  • Lyapunov analysis to rigorously prove closed-loop stability within a fixed time.

Main Results:

  • The proposed adaptive TSM approach achieves quick convergence and fixed-time stability.
  • The control input is demonstrated to be smooth and non-singular.
  • Lyapunov analysis confirms the stability of the closed-loop system within a fixed time.
  • Simulation results validate the efficacy and superiority of the proposed method compared to existing strategies.

Conclusions:

  • The adaptive fixed-time TSM offers a robust solution for controlling nonlinear systems with uncertainties and disturbances.
  • The method provides enhanced performance in terms of convergence speed, control smoothness, and guaranteed fixed-time stability.
  • Simulation examples confirm the practical applicability and effectiveness of the proposed control strategy.