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Prescribed-time control weak disturbance decoupling problems for strict-feedback-like systems with unknown control

Na Wang1, Xiaoping Liu2, Yajing Zhao3

  • 1School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, 250101, China.

ISA Transactions
|August 29, 2025
PubMed
Summary

This study introduces a novel adaptive prescribed-time controller that ensures task completion and stability, even with disturbances. It overcomes limitations of existing controllers for long-term operation and disturbance attenuation.

Keywords:
BacksteppingPrescribed-time controlStrict-feedback-like systemWeak disturbance decouplingZero dynamics

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Area of Science:

  • Control Engineering
  • Nonlinear Systems Theory
  • Robotics

Background:

  • Existing prescribed-time controllers face challenges with long-term operation due to ill-defined or non-differentiable adjustment functions.
  • Disturbance decoupling has been a significant unaddressed issue in prescribed-time control.

Purpose of the Study:

  • To design an adaptive controller for uncertain nonlinear systems that attenuates disturbances and bounds system output error at a prescribed time.
  • To ensure bounded stability of system states in the absence of disturbances.

Main Methods:

  • Smoothing existing prescribed-time adjustment functions using a linear combination of exponential functions for infinite-time differentiability.
  • Defining a new weighted norm to handle system uncertainties and disturbances.
  • Constructing an adaptive prescribed-time almost disturbance decoupling controller for strict-feedback-like nonlinear systems.

Main Results:

  • The proposed controller effectively overcomes issues related to unbounded derivatives caused by non-differentiable functions in prior methods.
  • Comparative simulations demonstrate superior performance over existing controllers, both before and after the prescribed time.
  • The controller shows significant effectiveness in attenuating the impact of disturbances.

Conclusions:

  • The developed adaptive prescribed-time controller offers improved performance and robustness for nonlinear systems with disturbances.
  • The novel approach enhances the reliability and applicability of prescribed-time control in real-world scenarios like assembly line manipulators.
  • The controller ensures arbitrarily small output error bounds at the prescribed time and bounded stability.