Robust adaptive nonlinear observer design via multi-time scales neural network

Zhi Jun Fu*, Wen Fang Xie, Jing Na

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)


This paper deals with the robust adaptive observer design for nonlinear dynamic systems that have an underlying multiple time-scales structure via different time-scales neural network. The Lyapunov function method is used to develop a novel stable updating law for the multi-time scales neural networks model and prove that the state error, output estimation error and the neural network weights errors are all uniformly ultimately bounded around the zero point during the entire learning process. Furthermore, passivity-based approach is used to derive the robust property of the proposed multi-time scales neural networks observer. Compared with the other nonlinear observers without considering the time scales, the proposed observer demonstrates faster convergence and more accurate properties. Two examples are presented confirming the validity of the above approach.

Original languageEnglish
Pages (from-to)217-225
Number of pages9
Early online date1 Feb 2016
Publication statusPublished - 19 May 2016


  • Adaptive learning
  • Multi-time scale neural networks
  • Nonlinear observer
  • Nonlinear systems


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