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Nonlinear adaptive wavelet control using constructive wavelet networks.

Jian-Xin Xu1, Ying Tan

  • 1Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore. elexujx@nus.edu.sg

IEEE Transactions on Neural Networks
|February 7, 2007
PubMed
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This study introduces an adaptive wavelet-network control method for nonlinear systems. It efficiently adjusts network structure for improved precision without trial-and-error, simplifying controller design.

Area of Science:

  • Control Systems Engineering
  • Artificial Intelligence
  • Dynamical Systems Theory

Background:

  • Highly nonlinear and uncertain dynamical systems present significant control challenges.
  • Traditional neural networks (NNs) and wavelet networks often require pre-defined structures, leading to potential inadequacy or redundancy.
  • Achieving precise approximation in complex systems necessitates adaptive and efficient network design.

Purpose of the Study:

  • To propose an adaptive wavelet-network-based control approach for highly nonlinear uncertain dynamical systems.
  • To leverage the unique properties of wavelet networks for online, constructive controller structure adjustment.
  • To avoid the limitations of trial-and-error in selecting network architectures for control applications.

Main Methods:

Related Experiment Videos

  • Utilizing wavelet networks, which offer orthonormality and multiresolution properties for universal approximation.
  • Implementing an adaptive wavelet controller (AWC) that allows online structural adjustment by increasing network resolution.
  • Applying the AWC to nonlinear dynamical systems, including those with partially known models and affine-in-input structures, as well as nonlinear nonaffine systems.

Main Results:

  • The proposed adaptive wavelet network facilitates constructive online adjustment of the controller's structure.
  • Orthonormality ensures that adding new resolutions does not disrupt the existing network.
  • Multiresolution guarantees improved approximation precision with added resolutions, avoiding suboptimal network sizing.

Conclusions:

  • The adaptive wavelet network provides an effective and efficient method for controlling highly nonlinear uncertain dynamical systems.
  • This approach simplifies the construction and tuning of controllers, moving from coarse to fine levels until performance requirements are met.
  • The method successfully addresses challenges in both affine and nonaffine nonlinear systems, offering a robust control solution.