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Linear adaptive control of a class of SISO nonaffine nonlinear systems

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  • Ahsene Boubakir
  • Salim Labiod
  • Fares Boudjema
  • Franck Plestan

Abstract

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.

Suggested Citation

  • Ahsene Boubakir & Salim Labiod & Fares Boudjema & Franck Plestan, 2014. "Linear adaptive control of a class of SISO nonaffine nonlinear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 2490-2498, December.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:12:p:2490-2498
    DOI: 10.1080/00207721.2013.772259
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    References listed on IDEAS

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    1. Xiao-Dong Li & Tommy Chow & L.L. Cheng, 2013. "Adaptive iterative learning control of non-linear MIMO continuous systems with iteration-varying initial error and reference trajectory," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(4), pages 786-794.
    2. Yi-Shao Huang & Xiaoxin Chen & Shao-Wu Zhou & Ling-Li Yu & Zheng-Wu Wang, 2012. "HGO-based decentralised indirect adaptive fuzzy control for a class of large-scale nonlinear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(6), pages 1133-1145.
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