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Direct Adaptive Fuzzy Control of Nonlinear Descriptor Systems

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Abstract

This paper deals with direct adaptive fuzzy control for uncertain affine nonlinear descriptor systems. Two cases are considered: in the first one, it is assumed that the control gain is known, while in the second one, it is an unknown-but-bounded symmetric positive definite matrix. To account for uncertainties in the system dynamics, a fuzzy system is employed to directly approximate the unknown ideal controller. The adjustable parameters of the fuzzy system are updated by either a Lyapunov-based adaptative law in the first case, or a gradient descent algorithm minimizing a suitable quadratic cost function in the second case. Furthermore, an auxiliary compensating signal is designed to guarantee that the tracking error asymptotically vanishes in both cases. Simulation results show how the proposed methods exhibit satisfactory performance thus demonstrating their effectiveness.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Robotic, Shahrood University of Technology, Shahrood, Iran

    Naeimeh Fakhr Shamloo & Ali Akbarzadeh Kalat

  2. Department of Information Engineering (DINFO), Florence University, via di Santa Marta 3, 50139, Firenze, Italy

    Luigi Chisci

Authors
  1. Naeimeh Fakhr Shamloo
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  2. Ali Akbarzadeh Kalat
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  3. Luigi Chisci
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Correspondence to Ali Akbarzadeh Kalat.

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Shamloo, N.F., Kalat, A.A. & Chisci, L. Direct Adaptive Fuzzy Control of Nonlinear Descriptor Systems. Int. J. Fuzzy Syst. 21, 2588–2599 (2019). https://doi.org/10.1007/s40815-019-00702-1

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  • DOI: https://doi.org/10.1007/s40815-019-00702-1

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