Indirect adaptive self-organizing RBF neural controller design with a dynamical training approach

Chun Fei Hsu, Chien Jung Chiu, Jang Zern Tsai

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


This study proposes an indirect adaptive self-organizing RBF neural control (IASRNC) system which is composed of a feedback controller, a neural identifier and a smooth compensator. The neural identifier which contains a self-organizing RBF (SORBF) network with structure and parameter learning is designed to online estimate a system dynamics using the gradient descent method. The SORBF network can add new hidden neurons and prune insignificant hidden neurons online. The smooth compensator is designed to dispel the effect of minimum approximation error introduced by the neural identifier in the Lyapunov stability theorem. In general, how to determine the learning rate of parameter adaptation laws usually requires some trial-and-error tuning procedures. This paper proposes a dynamical learning rate approach based on a discrete-type Lyapunov function to speed up the convergence of tracking error. Finally, the proposed IASRNC system is applied to control two chaotic systems. Simulation results verify that the proposed IASRNC scheme can achieve a favorable tracking performance.

Original languageEnglish
Pages (from-to)564-573
Number of pages10
JournalExpert Systems with Applications
Issue number1
StatePublished - Jan 2012


  • Adaptive control
  • Dynamical learning rate
  • Neural control
  • RBF network
  • Self-organizing


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