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Finite-time Synchronization of Neural Networks with Multiple Proportional Delays via Non-chattering Control

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Abstract

This paper investigates finite-time synchronization of neural networks (NNs) with multiple proportional delays. In order to cope with the difficulties induced by multiple proportional delays, suitable nonlinear variable transformations and new 1-norm-based analytical techniques are developed. By constructing Lyapunov functional and designing new designed controllers, several new sufficient conditions are derived to realize synchronization in finite time. Moreover, estimation of the upper bound of synchronization time is also provided for NNs with bounded delays or proportional delays. The designed controllers without sign function are simple, which means the chattering phenomenon in most of the existing results can be overcome. A numerical simulation is offered to verify the effectiveness of the theoretical analysis.

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Author information

Authors and Affiliations

  1. National & Local Joint Engineering Laboratory of Intelligent Transmission and Control Technology (Chongqing), College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China

    Wanli Zhang & Chuandong Li

  2. Texas A & M University at Qatar, Doha, 23874, Qatar

    Tingwen Huang

  3. Key Laboratory of Machine Perception and Children’s Intelligence Development, Chongqing University of Education, Chongqing, 400067, China

    Junjian Huang

Authors
  1. Wanli Zhang
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  2. Chuandong Li
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  3. Tingwen Huang
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  4. Junjian Huang
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Corresponding author

Correspondence to Chuandong Li.

Additional information

Recommended by Editor Jessie (Ju H.) Park. This work was jointly supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61374078, 61403050, 61633011, the Foundation and Frontier Project of Chongqing under Grant No. cstc2015jcyjA00027 and Research Foundation of Key Laboratory of Machine Perception and Children’s Intelligence Development Funded by CQUE (16xjpt07), China.

Wanli Zhang received the B.S. and M.S. degrees in mathematics from Chongqing Normal University, Chongqing, China, in 2013 and 2016, respectively. He is currently pursuing the Ph.D. degree with the College of Electronic and Information Engineering, Southwest University, Chongqing, China. His current research interests include chaos synchronization, discontinuous dynamical systems, optimization method and neural networks.

Chuandong Li received the B.S. degree in Applied Mathematics from Sichuan University, Chengdu, China, in 1992, and M.S. degree in Operational Research and Control Theory and Ph.D. degree in Computer Software and Theory from Chongqing University, Chongqing, China, in 2001 and 2005, respectively. He has been a Professor at the College of Electronic and Information Engineering, Southwest University, Chongqing, China, since 2012, and been the IEEE Senior member since 2010. From November 2006 to November 2008, he serves as a research fellow in the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China. He has published about more than 100 journal papers. His current research interest covers computational intelligence, neural networks, memristive systems, chaos control and synchronization, and impulsive dynamical systems.

Tingwen Huang received his B.S. degree from Southwest Normal University in 1990, M.S. from Sichuan University in 1993 and Ph.D. degree from Texas A&M University in 2002. After he graduated at Texas A&M University, he has been working in Mathematics Department of Texas A&M University as Visiting Assistant Professor. In 2003, he started to work at Texas A&M University at Qatar until now. He is now a Professor of Mathematics. His research fields include neural networks, chaos and its applications. He has published about more than 30 journal papers on neural networks and nonlinear dynamics.

Junjian Huang received his B.S. degree in Chongqing Communication Institute, Chongqing, China, in 2002, M.S. degree and Ph.D. degree from Chongqing University, Chongqing, China, in 2008 and 2014, respectively. He has been a Professor at Chongqing University of Education, China, since 2014. His current research interest covers neural networks, memristive systems, intermittent control and synchronization.

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Zhang, W., Li, C., Huang, T. et al. Finite-time Synchronization of Neural Networks with Multiple Proportional Delays via Non-chattering Control. Int. J. Control Autom. Syst. 16, 2473–2479 (2018). https://doi.org/10.1007/s12555-017-0622-0

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  • DOI: https://doi.org/10.1007/s12555-017-0622-0

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