Resilient Asynchronous $H_{\infty }$ Filtering for Markov Jump Neural Networks With Unideal Measurements and Multiplicative Noises

This paper is concerned with the resilient H∞ filtering problem for a class of discrete-time Markov jump neural networks (NNs) with time-varying delays, unideal measurements, and multiplicative noises. The transitions of NNs modes and desired mode-dependent filters are considered to be asynchronous, and a nonhomogeneous mode transition matrix of filters is used to model the asynchronous jumps to different degrees that are also mode-dependent. The unknown time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. The unideal measurements model includes the phenomena of randomly occurring quantization and missing measurements in a unified form. The desired resilient filters are designed such that the filtering error system is stochastically stable with a guaranteed H∞ performance index. A monotonicity is disclosed in filtering performance index as the degree of asynchronous jumps changes. A numerical example is provided to demonstrate the potential and validity of the theoretical results.

[1]  Mark H. Davis.  Markov Models and Optimization , 1995 .

[2]  Yun Xie,et al.  Analysis of the effects of quantization in multilayer neural networks using a statistical model , 1992, IEEE Trans. Neural Networks.

[3]  Isaac Yaesh,et al.  Markovian jump delayed Hopfield networks with multiplicative noise , 2008, Autom..

[4]  Masahiro Tanaka,et al.  Pattern classification by stochastic neural network with missing data , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[5]  Marius Iosifescu,et al.  Finite Markov Processes and Their Applications , 1981 .

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

[7]  Alessandro N. Vargas,et al.  On the control of Markov jump linear systems with no mode observation: application to a DC Motor device , 2013 .

[8]  Ricardo C. L. F. Oliveira,et al.  Mode-Independent ${\cal H}_{2}$ -Control of a DC Motor Modeled as a Markov Jump Linear System , 2014, IEEE Transactions on Control Systems Technology.

[9]  Shankar P. Bhattacharyya,et al.  Robust, fragile or optimal? , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[10]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Complex Networks With Uncertain Inner Coupling and Incomplete Measurements , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Mariesa L. Crow,et al.  Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks , 2010, IJCNN.

[12]  Lihua Xie,et al.  The sector bound approach to quantized feedback control , 2005, IEEE Transactions on Automatic Control.

[13]  Guang-Hong Yang,et al.  Non-fragile Hinfinity filter design for linear continuous-time systems , 2008, Autom..

[14]  Zidong Wang,et al.  Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays , 2013, IEEE Transactions on Cybernetics.

[15]  C. Lee Giles,et al.  An analysis of noise in recurrent neural networks: convergence and generalization , 1996, IEEE Trans. Neural Networks.

[16]  Huijun Gao,et al.  New Delay-Dependent Exponential H ∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2009 .

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

[18]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

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

[20]  Oswaldo Luiz V. Costa,et al.  Robust mode-independent filtering for discrete-time Markov jump linear systems with multiplicative noises , 2013, Int. J. Control.

[21]  Shengyuan Xu,et al.  Neural-Network-Based Decentralized Adaptive Output-Feedback Control for Large-Scale Stochastic Nonlinear Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  Fei Liu,et al.  H∞ Filtering for Discrete-Time Systems With Stochastic Incomplete Measurement and Mixed Delays , 2012, IEEE Trans. Ind. Electron..

[23]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[24]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.

[25]  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.

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

[27]  Magdi S. Mahmoud,et al.  Resilient linear filtering of uncertain systems , 2004, Autom..

[28]  Monique Frize,et al.  Influence of Missing Values on Artificial Neural Network Performance , 2001, MedInfo.

[29]  Alessandro N. Vargas,et al.  Second moment constraints and the control problem of Markov jump linear systems , 2013, Numer. Linear Algebra Appl..

[30]  Günhan Dündar,et al.  The effects of quantization on multilayer neural networks , 1995, IEEE Trans. Neural Networks.

[31]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[32]  Volker Tresp,et al.  Training Neural Networks with Deficient Data , 1993, NIPS.

[33]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[34]  Peter Ti.  Markovian Architectural Bias of Recurrent Neural Networks , 2004 .

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