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Aperiodic Sampled-data Control for Exponential Synchronization of Chaotic Delayed Neural Networks with Exponentially Decaying Gain

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Abstract

This paper studies the exponential synchronization of chaotic delayed neural networks (CDNNs) under aperiodic sampled-data control. First, an aperiodic sampled-data controller with exponentially decaying gain is designed to enlarge the maximum sampling period and the maximum allowable delay while still preserving the stability of the closed-loop system. Then, a novel time-dependent Lyapunov functional that consists of the information of the exponential decay rate η is elaborately designed to analyze the stability of the closed-loop system instead of using the common “change of coordinates” method.With the aid of Lyapunov theory and some inequality techniques, the sufficient conditions are established to guarantee the exponential synchronization of master-slave CDNNs. Based on matrix transformation, the equivalent conditions in LMI form are established to design the feedback gain. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed controller and the obtained synchronization criteria.

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Author information

Authors and Affiliations

  1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Jikai Wang & Xia Huang

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhen Wang

  3. College of Mathematic Science, Liaocheng university, Liaocheng, 252000, China

    Jianwei Xia

  4. School of Electrical Engineering and Information, Anhui University of Technology, Ma’anshan, 243002, China

    Hao Shen

Authors
  1. Jikai Wang
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  2. Xia Huang
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  3. Zhen Wang
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  4. Jianwei Xia
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  5. Hao Shen
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Corresponding author

Correspondence to Xia Huang.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Mathiyalagan Kalidass under the direction of Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China under Grants 61973199, 61573008, and the Taishan Scholar Project of Shandong Province of China.

Jikai Wang received his B.Eng. degree in information and electrical engineering from Shandong Jianzhu University, Jinan, China, in 2018. He is currently pursuing the M.Eng. degree with the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China. His current research interests include neural networks, sampled-data control and switched systems.

Xia Huang received hher M.S. and Ph.D. degrees in applied mathematics from Southeast University, Nanjing, China, in 2004 and 2007, respectively. She has been a Professor with the College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China, since 2018. Her current research interests include neural networks, fractional-order nonlinear systems, and memristor-based circuits and systems.

Zhen Wang received his B.S. degree in mathematics from Ocean University of China, Qingdao, China in 2004 and the Ph.D. degree in the School of Automation, Nanjing University of Science and Technology, Nanjing, China in 2014. Since 2004, he has been with Shandong University of Science and Technology, Qingdao 266590, China, where he is currently a Professor and a Doctoral Supervisor. His current research interests include nonlinear control, neural networks, fractional order systems.

Jianwei Xia received his Ph.D. degree in control theory and control engineering from the Nanjing University of Science and Technology, Nanjing, China, in 2007. He is a Professor with the School of Mathematics Science, Liaocheng University, Liaocheng, China. From 2010 to 2012, he was a Post-Doctoral Research Associate with the School of Automation, Southeast University, Nanjing. From 2013 to 2014, he was a Post-Doctoral Research Associate with the Department of Electrical Engineering, Yeungnam University, Gyeongsan, South Korea. His current research interests include robust control, stochastic systems, and neural networks.

Hao Shen received his Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China, in 2011. From February 2013 to March 2014, he was a Post-Doctoral Fellow with the Department of Electrical Engineering, Yeungnam University, Korea. Since 2011, he has been with Anhui University of Technology, China, where he is currently a Professor and a Doctoral Supervisor. His current research interests include stochastic hybrid systems, complex networks, fuzzy systems and control, nonlinear control.

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Wang, J., Huang, X., Wang, Z. et al. Aperiodic Sampled-data Control for Exponential Synchronization of Chaotic Delayed Neural Networks with Exponentially Decaying Gain. Int. J. Control Autom. Syst. 18, 2898–2906 (2020). https://doi.org/10.1007/s12555-019-0818-6

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  • DOI: https://doi.org/10.1007/s12555-019-0818-6

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