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Adaptive Stabilization of Feedforward Time-delay Systems with Uncertain Output Equation

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  • Control Theory and Applications
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Abstract

In this work, the problem of global adaptive stabilization is solved by output feedback for a family of feedforward nonlinear time-delay systems with uncertain output equation and unknown growth rate. To deal with system uncertainty, a low-gain observer incorporating with novel adaptive gain is first proposed. Next, via output feedback, an adaptive delay-free controller is constructed by combining scaling change with backstepping algorithm. Compared with existing results, the controller proposed is capable of handling both uncertain output equation and unknown delay. With the aid of Lyapunov-Krasovskii functional and Barbălat’s lemma, it is shown that the state and its estimate converge asymptotically to zero, and the adaptive gain is bounded. Furthermore, by numerical simulations, the usefulness of the control scheme is illustrated.

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Funding

This work was supported by the Fundamental Research Funds for the Provincial Universities of Zhejiang (GK219909299001-002), the Zhejiang Provincial Natural Science Foundation of China (LY21F030008), the National Natural Science Foundation of China (61773146, 61803208, 62003168), the Jiangsu Provincial Natural Science Foundation of China (BK20180726), and the Natural Science Research Project of Jiangsu Higher Education Institutions (20KJB120003).

Author information

Authors and Affiliations

  1. School of Automation, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, China

    Yiming Shao & Xianglei Jia

  2. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, Jiangsu, 210023, China

    Wenhui Liu & Guobao Liu

Authors
  1. Yiming Shao
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  2. Xianglei Jia
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  3. Wenhui Liu
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  4. Guobao Liu
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Corresponding author

Correspondence to Xianglei Jia.

Additional information

Yiming Shao received his B.S degree in Automation from Hangzhou Dianzi University in 2019. He is currently pursuing a Master’s degree in Control Science and Engineering from Hangzhou Dianzi University in 2021 with a focus on the nonlinear control system.

Xianglei Jia received his Ph.D. degree from the Nanjing University of Science and Technology, Nanjing, China, in 2017. From November 2015 to May 2016, he was a visiting scholar with the Department of Electronic and Information Systems, Shibaura Institute of Technology, Japan. He joined the School of Automation, Hangzhou Dianzi University, as an Associate Professor, in 2017. His current research interests include nonlinear adaptive control, observer design of nonlinear systems, and control of time-delay systems.

Wenhui Liu received her B.S. degree in School of Science, and Ph.D. degree in School of Automation, Nanjing University of Science and Technology, in 2012 and 2017, respectively. She is currently an associate professor in School of Electrical and Automation Engineering, Nanjing Normal University. From December 2014 to June 2016 and December 2016 to March 2017, she was a joint supervisory Ph.D. student in School of Electrical and Electronic Engineering at the University of Adelaide. Her research interests include adaptive control, fuzzy control, fault-tolerant control, and quantized control of nonlinear systems.

Guobao Liu received his B.S. degree and Ph.D. degree from Nanjing University of Science and Technology, Nanjing, China, in 2014 and 2019, respectively. He joined the School of Electrical and Automation Engineering as Lecturer in October 2019. His research interests include time-delay systems, singular systems, singular perturbed systems, and robust control and filtering.

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Shao, Y., Jia, X., Liu, W. et al. Adaptive Stabilization of Feedforward Time-delay Systems with Uncertain Output Equation. Int. J. Control Autom. Syst. 20, 1194–1204 (2022). https://doi.org/10.1007/s12555-021-0046-8

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  • DOI: https://doi.org/10.1007/s12555-021-0046-8

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