Adaptive State Estimation of Stochastic Delayed Neural Networks with Fractional Brownian Motion

Abstract

This paper considers the adaptive state estimation problem for stochastic neural networks with fractional Brownian motion (FBM). The problem for the stochastic neural networks with FBM is handled according to the theory of Hilbert–Schmidt and the principle of analytic semigroup. Using the stochastic analytic technique and adaptive control method, the asymptotic stability and the exponential stability criteria are established. Finally, a simulation example is given to prove the efficiency of developed criteria.

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Correspondence to Dongbing Tong or Qiaoyu Chen.

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This work is partially supported by the National Natural Science Foundation of China (61673257; 11501367; 61573095; 61673221); the Natural Science Foundation of Jiangsu Province (BK20181418); the fifteenth batch of Six Talent Peaks project in Jiangsu Province (DZXX-019).

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Yan, X., Tong, D., Chen, Q. et al. Adaptive State Estimation of Stochastic Delayed Neural Networks with Fractional Brownian Motion. Neural Process Lett 50, 2007–2020 (2019). https://doi.org/10.1007/s11063-018-9960-z

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Keywords

  • State estimation
  • Neural networks
  • Fractional Brownian motion (FBM)
  • Asymptotic stability
  • Exponential stability