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Robust Adaptive Limit Cycle Controller Design for Nonlinear Time-delay Systems

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Abstract

This paper studies the adaptive limit cycle controller design for shaping stable output oscillations through creating stable limit cycles. For this purpose, a class of time-delay nonlinear systems with multiple time delays and external disturbances is considered. The desirable limit cycle is shaped in the first step by using an extended Lyapunov theorem for stability analysis of positive limit sets. The Lyapunov–Krasovskii theorem is also employed to handle the difficulties raised by multiple time delays. Besides, an adaptive approach is developed to deal with unknown but bounded external disturbances. Unlike the classic approaches, the upper bounds of disturbances are not required to be known in advance. The method is discussed for the second-order system, firstly and then, developed for higher-order systems by the recursive procedure of the backstepping technique. It will be shown that the closed-loop system is practically stable and the phase trajectories of the system converge to an arbitrarily small neighborhood of the target limit cycle. Simulation results are provided to show the effectiveness of the proposed approach.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran

    A. R. Hakimi & T. Binazadeh

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  1. A. R. Hakimi
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  2. T. Binazadeh
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Correspondence to T. Binazadeh.

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Hakimi, A.R., Binazadeh, T. Robust Adaptive Limit Cycle Controller Design for Nonlinear Time-delay Systems. Circuits Syst Signal Process 41, 57–76 (2022). https://doi.org/10.1007/s00034-021-01787-6

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  • DOI: https://doi.org/10.1007/s00034-021-01787-6

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