Estimation of a class of stochastic switching neural networks with sensor saturations through a nonsynchronous filter

In this paper, the problem of energy-to-peak state estimation for a class of discrete-time Markov jump recurrent neural networks (RNNs) with randomly occurring sensor saturations is investigated. A practical phenomenon of nonsynchronous jumps between RNNs modes and desired mode-dependent filters is considered and a nonstationary mode transition among the filters is used to model the non-synchronous jumps to different degrees that are also mode-dependent. The sensor saturation occurs in a probabilistic way according to a Bernoulli sequence. Sufficient conditions on the existence of the nonsynchronous filters are obtained such that the filtering error system is stochastically stable and achieves a prescribed energy-to-peak performance index. A numerical example is presented to verify the theoretical findings.

[1]  Zidong Wang,et al.  State estimation for discrete-time delayed neural networks with fractional uncertainties and sensor saturations , 2013, Neurocomputing.

[2]  Peng Shi,et al.  A delay decomposition approach to L2-Linfinity filter design for stochastic systems with time-varying delay , 2011, Autom..

[3]  Jinde Cao,et al.  Robust State Estimation for Uncertain Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[4]  D.W.C. Ho,et al.  Design of Hºº filter for Markov jumping linear systems with non-accessible mode information. , 2008 .

[5]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[6]  J.C. Geromel,et al.  ${\cal H}_{\infty}$ Filtering of Discrete-Time Markov Jump Linear Systems Through Linear Matrix Inequalities , 2009, IEEE Transactions on Automatic Control.

[7]  Kay Chen Tan,et al.  Neural Networks: Computational Models and Applications , 2007 .

[8]  Wei Xing Zheng,et al.  Delay-Slope-Dependent Stability Results of Recurrent Neural Networks , 2011, IEEE Transactions on Neural Networks.

[9]  W. Fleming,et al.  Theory of Markov Processes , 1963 .

[10]  P. Whittle,et al.  Theory of Markov Processes. , 1962 .

[11]  Dan Zhang,et al.  Estimator Design for Discrete-Time Switched Neural Networks With Asynchronous Switching and Time-Varying Delay , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Alexandre Trofino,et al.  Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems , 2006, IEEE Transactions on Automatic Control.

[13]  Wei Xing Zheng,et al.  Stability and $L_{2}$ Performance Analysis of Stochastic Delayed Neural Networks , 2011, IEEE Transactions on Neural Networks.

[14]  Huijun Gao,et al.  Network-Induced Constraints in Networked Control Systems—A Survey , 2013, IEEE Transactions on Industrial Informatics.

[15]  Fuchun Sun,et al.  Design of Hinfinity filter for Markov jumping linear systems with non-accessible mode information , 2008, Autom..

[16]  Tingwen Huang,et al.  Brief Papers Further Result on Guaranteed H∞ Performance State Estimation of Delayed Static Neural Networks , 2015 .

[17]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[18]  Wei Xing Zheng,et al.  Discrete-Time Neural Network for Fast Solving Large Linear $L_{1}$ Estimation Problems and its Application to Image Restoration , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[20]  Wei Xing Zheng,et al.  Stochastic state estimation for neural networks with distributed delays and Markovian jump , 2012, Neural Networks.

[21]  Peter Tiño,et al.  Markovian architectural bias of recurrent neural networks , 2004, IEEE Transactions on Neural Networks.

[22]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.