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Generalized Lag Synchronization of Neural Networks with Discontinuous Activations and Bounded Perturbations

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Abstract

In this paper, generalized lag synchronization (GLS) for a class of neural networks with discontinuous activation functions and bounded external disturbances is studied under the framework of Filippov solutions. The external disturbances to the driver and response neural networks are nonidentical. A simple discontinuous adaptive controller is designed to overcome the difficulty induced by the nonidentical perturbations and the uncertainties of the Filippov solutions. Based on the concept of Filippov solutions, differential inclusion, nonsmooth analysis, and Lyapunov function method, sufficient conditions are obtained to guarantee the GLS of the discontinuous neural networks. Some existing results on synchronization of neural networks with discontinuous activations are extended and improved. Results of this paper are also applicable to nonlinear continuous systems. Numerical simulations are given to show the effectiveness of the theoretical results.

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Acknowledgments

The authors would like to thank the Editor-in-Chief, Prof. M.N.S. Swamy, for his helpful comments in improving the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Chongqing Normal University, Chongqing, 401331, China

    Enli Wu & Xinsong Yang

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  1. Enli Wu
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  2. Xinsong Yang
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Correspondence to Xinsong Yang.

Additional information

This work was jointly supported by the National Natural Science Foundation of China (NSFC) under Grants No. 61263020, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant No. KJ130613, and the Program of Chongqing Innovation Team Project in University under Grant No. KJTD201308.

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Wu, E., Yang, X. Generalized Lag Synchronization of Neural Networks with Discontinuous Activations and Bounded Perturbations. Circuits Syst Signal Process 34, 2381–2394 (2015). https://doi.org/10.1007/s00034-014-9962-7

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  • DOI: https://doi.org/10.1007/s00034-014-9962-7

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