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Variance-Constrained Resilient \(H_{\infty }\) State Estimation for Time-Varying Neural Networks with Random Saturation Observation Under Uncertain Occurrence Probability

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Abstract

This paper studies the variance-constrained resilient \(H_{\infty }\) state estimation problem for discrete time-varying uncertain recurrent neural networks with random saturation observation under uncertain occurrence probability. In fact, the state estimation problem of stochastic recurrent neural networks with time-varying parameters has significant importance and wide applications. In order to characterize the realistic transmission process of neural signals, the phenomenon of random saturation observation is represented by introducing a random variable. In addition, the estimator gain is allowed to satisfy parameter perturbations to reflect the fragility of the estimator. The main objective is to present a finite-horizon resilient state estimation scheme without utilizing the augmentation method such that, in the presence of estimator parameter perturbations and random saturation observation, some sufficient criteria are obtained for the estimation error dynamical system satisfying both the pre-defined \(H_{\infty }\) performance constraint and the error variance boundedness. Finally, a numerical example demonstrates the feasibility of the presented resilient \(H_{\infty }\) SE method under variance constraint. From the engineering viewpoint, the proposed state estimation method under variance constraint has time-varying characteristics, which is suitable for online estimation applications. Moreover, both the state estimation and original neural state have the same order, which can reduce the computation burden.

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Authors and Affiliations

  1. Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, China

    Yan Gao, Jun Hu & Junhua Du

  2. School of Automation, Harbin University of Science and Technology, Harbin, 150080, China

    Jun Hu, Hui Yu & Chaoqing Jia

  3. Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems, Harbin University of Science and Technology, Harbin, 150080, China

    Jun Hu & Chaoqing Jia

  4. Heilongjiang Provincial Key Laboratory of Complex Intelligent System and Integration, Harbin University of Science and Technology, Harbin, 150080, China

    Hui Yu

  5. College of Science, Qiqihar University, Qiqihar, 161006, China

    Junhua Du

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  1. Yan Gao
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Correspondence to Jun Hu.

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This work was supported in part by the National Natural Science Foundation of China under Grant 12171124 and 72001059, the Natural Science Foundation of Heilongjiang Province of China under Grant ZD2022F003, the Heilongjiang Provincial Key Laboratory of Complex Intelligent System and Integration under Grant HPKL-CICS-202203, the Fundamental Research Funds in Heilongjiang Provincial Universities of China under Grant 135509121, the Educational Research Project of the Qiqihar University of China under Grant YB201904, and the Alexander von Humboldt Foundation of Germany.

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Gao, Y., Hu, J., Yu, H. et al. Variance-Constrained Resilient \(H_{\infty }\) State Estimation for Time-Varying Neural Networks with Random Saturation Observation Under Uncertain Occurrence Probability. Neural Process Lett 55, 5031–5054 (2023). https://doi.org/10.1007/s11063-022-11078-z

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