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Linear Approximation in Time Domain01:21

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Related Experiment Video

Updated: Jul 7, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Stability and approximator convergence in nonparametric nonlinear adaptive control.

J A Farrell1

  • 1College of Engineering, University of California, Riverside, CA 92521-0425, USA.

IEEE Transactions on Neural Networks
|February 8, 2008
PubMed
Summary
This summary is machine-generated.

This study explores adaptive control with passive learning, focusing on system stability and tracking error bounds. It introduces practical conditions for parameter convergence, crucial for real-world control applications.

Related Experiment Videos

Last Updated: Jul 7, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Control Theory
  • Machine Learning
  • Nonlinear Systems

Background:

  • Adaptive control is essential for systems with uncertainties.
  • Passive learning, where inputs aren't freely chosen, is common in control.
  • Stability analysis is critical for reliable adaptive control systems.

Purpose of the Study:

  • Investigate nonparametric nonlinear adaptive control under passive learning.
  • Analyze the stability of system states and parameter estimates.
  • Develop upper bounds for tracking error and define convergence regions.

Main Methods:

  • Nonlinear adaptive control techniques.
  • Stability analysis for parametric and nonparametric models.
  • Persistence of Excitation (PE) analysis for parameter convergence.

Main Results:

  • Stability results for both parametric and nonparametric adaptive control.
  • Established upper bounds on tracking error.
  • Identified practical PE conditions for parameter convergence using locally supported basis functions.

Conclusions:

  • Achieved specialized exponential convergence under relaxed PE conditions.
  • Defined convergence regions for approximators with locally supported basis elements.
  • Demonstrated practical applicability through examples.