Adaptive control for nonlinear pure-feedback systems with high-order sliding mode observer

Jing Na, Xuemei Ren, Dongdong Zheng

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

212 Citations (Scopus)


Most of the available control schemes for pure-feedback systems are derived based on the backstepping technique. On the contrary, this paper presents a novel adaptive control design for nonlinear pure-feedback systems without using backstepping. By introducing a set of alternative state variables and the corresponding transform, state-feedback control of the pure-feedback system can be viewed as output-feedback control of a canonical system. Consequently, backstepping is not necessary and the previously encountered explosion of complexity and circular issue are also circumvented. To estimate unknown states of the newly derived canonical system, a high-order sliding mode observer is adopted, for which finite-time observer error convergence is guaranteed. Two adaptive neural controllers are then proposed to achieve tracking control. In the first scheme, a robust term is introduced to account for the neural approximation error. In the second scheme, a novel neural network with only a scalar weight updated online is constructed to further reduce the computational costs. The closed-loop stability and the convergence of the tracking error to a small compact set around zero are all proved. Comparative simulation and practical experiments on a servo motor system are included to verify the reliability and effectiveness.

Original languageEnglish
Pages (from-to)370-382
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number3
Publication statusPublished - 8 Oct 2013


  • Adaptive control
  • High-order sliding mode (HOSM) observer
  • Neural networks
  • Pure-feedback systems


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