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Mixture Basis Function Approximation and Neural Network Embedding Control for Nonlinear Uncertain Systems with Disturbances

Author

Listed:
  • Le Ma

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132000, China)

  • Qiaoyu Zhang

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132000, China)

  • Tianmiao Wang

    (School of Information and Control Engineering, Jilin Institute of Chemical Technology, Jilin 132000, China)

  • Xiaofeng Wu

    (School of Information and Control Engineering, Jilin Institute of Chemical Technology, Jilin 132000, China)

  • Jie Liu

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132000, China)

  • Wenjuan Jiang

    (School of Automation Engineering, Northeast Electric Power University, Jilin 132000, China)

Abstract

A neural network embedding learning control scheme is proposed in this paper, which addresses the performance optimization problem of a class of nonlinear system with unknown dynamics and disturbance by combining with a novel nonlinear function approximator and an improved disturbance observer (DOB). We investigated a mixture basic function (MBF) to approximate the unknown nonlinear dynamics of the system, which allows an approximation in a global scope, replacing the traditional radial basis function (RBF) neural networks technique that only works locally and could be invalid beyond some scope. The classical disturbance observer is improved, and some constraint conditions thus are no longer needed. A neural network embedding learning control scheme is exploited. An arbitrary type of neural network can be embedded into a base controller, and the new controller is capable of optimizing the control performance by tuning the parameters of neural network and satisfying the Lyapunov stability simultaneously. Simulation results verify the effectiveness and advantage of our proposed methods.

Suggested Citation

  • Le Ma & Qiaoyu Zhang & Tianmiao Wang & Xiaofeng Wu & Jie Liu & Wenjuan Jiang, 2023. "Mixture Basis Function Approximation and Neural Network Embedding Control for Nonlinear Uncertain Systems with Disturbances," Mathematics, MDPI, vol. 11(13), pages 1-24, June.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2823-:d:1177819
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