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Adaptive prescribed-time control for uncertain nonlinear systems while maintaining the zeroed tracking error.

Zhanpeng Zhang1, Yingmin Yi1, Bojun Liu1

  • 1School of Automation and Information Engineering, Xi'an University of Technology, Xi'an 710048, China.

ISA Transactions
|October 23, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces an adaptive prescribed-time control method for uncertain nonlinear systems. It ensures zero tracking errors within a set time by accurately estimating system parameters.

Keywords:
Adaptive backstepping controlMaintaining zero errorParameter estimationPrescribed-time tracking controlUncertain nonlinear system

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Adaptive Control

Background:

  • Accurate prescribed-time tracking control for uncertain nonlinear systems remains a challenge.
  • Maintaining zero state tracking errors after the prescribed settling time is difficult.

Purpose of the Study:

  • To propose a parameter estimation-based adaptive prescribed-time control approach.
  • To address the challenge of achieving and maintaining zero state tracking errors within a specified time for uncertain nonlinear systems.

Main Methods:

  • Utilized a dynamic regressor extension and mixing method with four-layer filters for parameter estimation.
  • Developed an adaptive backstepping control algorithm incorporating a time-varying scaling function.
  • Ensured parameter estimation under initial excitation conditions and regulated errors to zero within the prescribed time.

Main Results:

  • Successfully estimated uncertain parameters accurately.
  • Achieved regulation of both state tracking errors and parameter estimation errors to zero within the prescribed settling time.
  • Proved the boundedness of all closed-loop system signals and the continuity of the control input signal.

Conclusions:

  • The proposed parameter estimation-based adaptive prescribed-time control approach effectively solves the problem of accurate tracking control for uncertain nonlinear systems.
  • The method ensures zero state tracking errors are maintained after the prescribed settling time.
  • Simulation examples validated the effectiveness of the developed control strategy.