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Adaptive Backstepping Control for Nonlinear Systems Using Support Vector Regression

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Intelligence Computation and Evolutionary Computation

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 180))

Abstract

A nonlinear adaptive backstepping control approach is designed for a class of n-th order nonlinear systems. Support Vector Regression (SVR) is employed to adaptively approximate the unknown nonlinear functions composed of unknown uncertainties and disturbances. Unlike neural networks, no number of hidden units has to be determined for the controller and that no centers have to be specified for the Gaussian kernels when applying Mercer’s condition. The curse of dimensionality is avoided in comparison with defining a regular grid for the centers in classical radial basis function networks. The closed-loop system is guaranteed to be bounded and tracking errors are also proved to converge exponentially to a small residual set around the origin by Lyapunov theory. Simulation results demonstrate the effectiveness of the approach proposed.

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Author information

Authors and Affiliations

  1. Xi’an Research Inst. of Hi-Tech, Hongqing Town, Xi’an, 710025, PR China

    Liu Yinan, Zhang Shengxiu, Cao Lijia & Zhang Chao

Authors
  1. Liu Yinan
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  2. Zhang Shengxiu
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  3. Cao Lijia
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  4. Zhang Chao
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Corresponding author

Correspondence to Liu Yinan .

Editor information

Editors and Affiliations

  1. Industrial Engineering Research Center, Information Technology &, Room 301, Unit 2, Building 1, Wuhan, China, People's Republic

    Zhenyu Du

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© 2013 Springer-Verlag Berlin Heidelberg

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Yinan, L., Shengxiu, Z., Lijia, C., Chao, Z. (2013). Adaptive Backstepping Control for Nonlinear Systems Using Support Vector Regression. In: Du, Z. (eds) Intelligence Computation and Evolutionary Computation. Advances in Intelligent Systems and Computing, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31656-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-31656-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31655-5

  • Online ISBN: 978-3-642-31656-2

  • eBook Packages: EngineeringEngineering (R0)

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