SCIENCE CHINA Information Sciences, Volume 59 , Issue 11 : 112201(2016) https://doi.org/10.1007/s11432-016-5568-y

A framework for stability analysis of high-order nonlinear systems based on the CMAC method

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  • ReceivedJan 21, 2016
  • AcceptedMar 16, 2016
  • PublishedSep 30, 2016


A framework for analyzing the stability of a class of high-order minimum-phase nonlinear systems of relative degree two based on the characteristic model-based adaptive control (CMAC) method is presented. In particular, concerning the tracking problem for such high-order nonlinear systems, by introducing a consistency condition for quantitatively describing modeling errors corresponding to a group of characteristic models together with a certain kind of CMAC laws, we prove closed-loop stability and show that such controllers can make output tracking error arbitrarily small. Furthermore, following this framework, with a specific characteristic model and a golden-section adaptive controller, detailed sufficient conditions to stabilize such groups of high-order nonlinear systems are presented and, at the same time, tracking performance is analyzed. Our results provide a new perspective for exploring the stability of some high-order nonlinear plants under CMAC, and lay certain theoretical foundations for practical applications of the CMAC method.

Funded by

National Natural Science Foundation of China(61333008)

National Key Basic Research Program and Development Program of China(973)




This work was supported by National Natural Science Foundation of China (Grant No. 61333008) and National Key Basic Research Program and Development Program of China (973) (Grant No. 2013CB733100). The authors would like to thank Professor Lei Guo for his helpful suggestions and comments on this paper.


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