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Adaptive asymptotic stabilization of uncertain nonstrict feedback nonlinear HOFA systems with time delays

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A Correction to this article was published on 27 June 2023

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Abstract

We consider the adaptive control for the nonstrict-feedback uncertain nonlinear high-order fully actuated (HOFA) systems with either uncertain constant delay or time-varying delay. Different from the previous works, the most difficult point is that the uncertain nonlinear function in the HOFA systems contains nonstrict feedback form and time delay in system states. In order to overcome this difficulty, the arbitrary approximation property of the radial basis function neural network (RBF NN) is used to estimate the unknown nonlinear functions. What’s more, the nonstrict-feedback form is transformed into strict-feedback strcture by using the property of Gaussian function. In addition, the appropriate Lyapunov-Krasovskii functions and separation techniques are used to compensate the effect of the unknown constant time delay or time-varying delay. Based on the HOFA system approaches, two adaptive NN controllers are proposed to ensure the system with constant time-delay and time-varying delay to be stabilized asymptotically, respectively. Finally, the proposed control strategies are applied to the thermoacoustic instability systems to demonstrate the feasibility and effectiveness of the obtained results.

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Acknowledgements

This work was supported by NSFC under grant 61973060.

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Authors and Affiliations

  1. The State Key Laboratory of Synthetical Automation for Process Industries and College of Information Science and Engineering Northeastern University, Shenyang, 110819, China

    Yu-Zhuo Zhao, Dan Ma & Ying-Wei Zhang

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  1. Yu-Zhuo Zhao
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  2. Dan Ma
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  3. Ying-Wei Zhang
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Correspondence to Dan Ma.

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Zhao, YZ., Ma, D. & Zhang, YW. Adaptive asymptotic stabilization of uncertain nonstrict feedback nonlinear HOFA systems with time delays. Nonlinear Dyn 111, 14139–14153 (2023). https://doi.org/10.1007/s11071-023-08593-6

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  • DOI: https://doi.org/10.1007/s11071-023-08593-6

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