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Neural network-based control design: an LMI approach.

S Limanond1, J Si

  • 1Department of Electrical Engineering, SSERC, Arizona State University, Tempe, AZ 85287-7606, USA.

IEEE Transactions on Neural Networks
|February 8, 2008
PubMed
Summary
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This study introduces a novel neural network control design for discrete-time nonlinear systems. The method ensures closed-loop stability using linear matrix inequalities and convex optimization for precise control.

Area of Science:

  • Control Theory
  • Artificial Intelligence
  • Nonlinear Systems

Background:

  • Discrete-time nonlinear systems present significant control challenges.
  • Neural networks offer powerful approximation capabilities for complex systems.
  • Existing control methods may struggle with the inherent nonlinearities.

Purpose of the Study:

  • To develop a neural-network-based control design for discrete-time nonlinear systems.
  • To ensure the stability and convergence of the closed-loop system.
  • To provide a systematic procedure for control design using convex optimization.

Main Methods:

  • Approximating the nonlinear system using a sigmoid-based multilayer perceptron.
  • Establishing a linear difference inclusion representation for the neural network.

Related Experiment Videos

  • Designing a state-feedback control law via the certainty equivalence principle.
  • Formulating control design equations as linear matrix inequalities (LMIs).

    • Main Results:

    • The control design is solvable using convex optimization algorithms.
    • Stability of the closed-loop system is guaranteed.
    • A unique global attraction region ensures trajectory convergence to the origin.

    Conclusions:

    • The proposed neural network control design effectively addresses discrete-time nonlinear systems.
    • The LMI-based approach ensures stability and provides a clear design pathway.
    • The method is validated through a illustrative example.