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Optimal control by least squares support vector machines.

J A Suykens1, J Vandewalle, B De Moor

  • 1Department of Electrical Engineering, ESAT-SISTA, Katholieke Universiteit Leuven, Heverlee, Belgium. johan.suykens@esat.kuleuven.ac.be

Neural Networks : the Official Journal of the International Neural Network Society
|February 24, 2001
PubMed
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Least Squares Support Vector Machines (LS-SVM) offer an effective method for optimal control of nonlinear systems. This approach simplifies controller design by avoiding the need to specify hidden units or kernel centers, enhancing stability and performance.

Area of Science:

  • Control Engineering
  • Machine Learning
  • Nonlinear System Dynamics

Background:

  • Support Vector Machines (SVMs) excel in pattern recognition and function estimation.
  • Optimal control of nonlinear systems presents significant challenges in state-space mapping and stability.
  • Existing methods often require extensive parameter tuning and can suffer from the curse of dimensionality.

Purpose of the Study:

  • Introduce Least Squares Support Vector Machines (LS-SVM) for optimal control of nonlinear systems.
  • Develop a control scheme that maps state space to action space efficiently.
  • Address challenges in controller design, stability, and dimensionality.

Main Methods:

  • Formulate the optimal control problem using LS-SVM for state-action mapping.

Related Experiment Videos

  • Incorporate N-stage optimal control principles.
  • Develop a constrained nonlinear optimization approach with local stability imposition.

    • Main Results:

    • LS-SVM control effectively handles nonlinear systems, demonstrated on pendulum and ball-and-beam examples.
    • The method avoids determining hidden units or specifying Gaussian kernel centers.
    • Dimensionality issues common in radial basis function networks are mitigated.

    Conclusions:

    • LS-SVM provides a robust and efficient framework for optimal control of nonlinear systems.
    • The approach offers advantages over traditional neural network methods in terms of design simplicity and computational efficiency.
    • Demonstrated effectiveness in both stabilization and tracking tasks.