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Robust adaptive nonlinear control for uncertain control-affine systems and its applications

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Abstract

This paper addresses the robust tracking control problem for a class of uncertain nonlinear systems with time-varying parameters, perturbed by external disturbances. The unknown time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Depending on the characteristics of disturbance signals, two adaptive-based control algorithms are developed. First, an adaptive H ∞ control is designed that achieves: (i) an H ∞ tracking performance when the external disturbances are L 2 signals, and (ii) the convergence of tracking error to zero if the disturbances are bounded and L 2 signals. Then a novel adaptive control algorithm is proposed, only with the assumption of boundedness of disturbances, to drive the tracking error to zero. The designed tracking controllers are then used for controlling a cart-pendulum system, as an underactuated mechanical system, and chaos synchronization of uncertain Genesio–Tesi chaotic system. Numerical simulations are also given to demonstrate the effectiveness of the proposed control schemes.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156, Iran

    Hamid R. Koofigar, Saeed Hosseinnia & Farid Sheikholeslam

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  1. Hamid R. Koofigar
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  2. Saeed Hosseinnia
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  3. Farid Sheikholeslam
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Correspondence to Farid Sheikholeslam.

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Koofigar, H.R., Hosseinnia, S. & Sheikholeslam, F. Robust adaptive nonlinear control for uncertain control-affine systems and its applications. Nonlinear Dyn 56, 13–22 (2009). https://doi.org/10.1007/s11071-008-9375-x

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  • DOI: https://doi.org/10.1007/s11071-008-9375-x

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