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Impulsive method to reliable sampled-data control for uncertain fractional-order memristive neural networks with stochastic sensor faults and its applications

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Abstract

This paper is devoted to investigate the issue of fault-tolerant sampled-data control for a class of uncertain fractional-order memristive neural networks with random switching topologies subject to stochastic sensor faults via impulsive method. Firstly, a fault detection sampled-data control strategy is proposed for sensor failure. Then, by utilizing the constructed quasi-periodic polynomial Lyapunov function, the criterion for ensuring that the transformed pulse system achieves asymptotic stability is established. Moreover, based on this criterion and with the help of the mechanism of sum of squares (SSs), the desired reliable control gain matrix is obtained. Finally, a numerical example is employed to demonstrate the validity of our method, and this method is applied to the well-known fractional-order Chua’s circuit system. Compared to large quantities of results for integer-order memristive neural networks, only a small number of results are for fractional order. In particular, the sampling-controlled fractional-order memristive neural networks have not been solved until now, let alone the novel impulive approach designed in this paper. This paper is the first attempt to make up for this vacancy in this topic.

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Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China (61773217), Hunan Provincial Science and Technology Project Foundation (2019RS1033), the Scientific Research Fund of Hunan Provincial Education Department (18A013), Hunan Normal University National Outstanding Youth Cultivation Project (XP1180101) and the Construct Program of the Key Discipline in Hunan Province.

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  1. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, China

    Kui Ding & Quanxin Zhu

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, Jiangsu, China

    Kui Ding

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  1. Kui Ding
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Correspondence to Quanxin Zhu.

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Ding, K., Zhu, Q. Impulsive method to reliable sampled-data control for uncertain fractional-order memristive neural networks with stochastic sensor faults and its applications. Nonlinear Dyn 100, 2595–2608 (2020). https://doi.org/10.1007/s11071-020-05670-y

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