Some novel approaches on state estimation of delayed neural networks

This paper studies the issue of state estimation for a class of neural networks (NNs) with time-varying delay. A novel Lyapunov-Krasovskii functional (LKF) is constructed, where triple integral terms are used and a secondary delay-partition approach (SDPA) is employed. Compared with the existing delay-partition approaches, the proposed approach can exploit more information on the time-delay intervals. By taking full advantage of a modified Wirtinger's integral inequality (MWII), improved delay-dependent stability criteria are derived, which guarantee the existence of desired state estimator for delayed neural networks (DNNs). A better estimator gain matrix is obtained in terms of the solution of linear matrix inequalities (LMIs). In addition, a new activation function dividing method is developed by bringing in some adjustable parameters. Three numerical examples with simulations are presented to demonstrate the effectiveness and merits of the proposed methods.

[1]  Yongduan Song,et al.  A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays , 2013, IEEE Transactions on Fuzzy Systems.

[2]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[3]  Jun Wang,et al.  A recurrent neural network for solving a class of generalized convex optimization problems , 2013, Neural Networks.

[4]  Tibor Kmet,et al.  Adaptive critic design and Hopfield neural network based simulation of time delayed photosynthetic production and prey-predator model , 2015, Inf. Sci..

[5]  Gang Feng,et al.  State estimation of recurrent neural networks with time-varying delay: A novel delay partition approach , 2011, Neurocomputing.

[6]  Ju H. Park,et al.  Extended Dissipative Analysis for Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Tingwen Huang,et al.  Exponential stabilization of delayed recurrent neural networks: A state estimation based approach , 2013, Neural Networks.

[8]  Fen Zhang,et al.  State estimation of neural networks with both time-varying delays and norm-bounded parameter uncertainties via a delay decomposition approach , 2013, Commun. Nonlinear Sci. Numer. Simul..

[9]  Hieu Trinh,et al.  NEW H1 CONTROL DESIGN FOR POLYTOPIC SYSTEMS WITH MIXED TIME-VARYING DELAYS IN STATE AND INPUT , 2015 .

[10]  Xiaodi Li,et al.  Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays , 2015, Inf. Sci..

[11]  Dan Zhang,et al.  Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays , 2012, Neural Networks.

[12]  Michael Egmont-Petersen,et al.  Image processing with neural networks - a review , 2002, Pattern Recognit..

[13]  Ju H. Park,et al.  New results on exponential passivity of neural networks with time-varying delays , 2012 .

[14]  Dianhui Wang,et al.  An iterative learning algorithm for feedforward neural networks with random weights , 2016, Inf. Sci..

[15]  Ligang Wu,et al.  Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems , 2014, IEEE Transactions on Cybernetics.

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

[17]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[18]  Ju H. Park,et al.  Delay-dependent H∞ state estimation of neural networks with mixed time-varying delays , 2014, Neurocomputing.

[19]  Shouming Zhong,et al.  Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems , 2014, Autom..

[20]  John Cosmas,et al.  Time-Delay Neural Network for Continuous Emotional Dimension Prediction From Facial Expression Sequences , 2016, IEEE Transactions on Cybernetics.

[21]  Daoyun Xu,et al.  Vector Wirtinger-type inequality and the stability analysis of delayed neural network , 2013, Commun. Nonlinear Sci. Numer. Simul..

[22]  Yan Shi,et al.  Adaptive output-feedback neural tracking control for a class of nonstrict-feedback nonlinear systems , 2016, Inf. Sci..

[23]  Huaguang Zhang,et al.  Observer-Based Adaptive Neural Network Control for Nonlinear Systems in Nonstrict-Feedback Form , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Weisheng Chen,et al.  Global adaptive neural control for strict-feedback time-delay systems with predefined output accuracy , 2015, Inf. Sci..

[25]  Jing Xu,et al.  L∞ performance of single and interconnected neural networks with time-varying delay , 2016, Inf. Sci..

[26]  Ju H. Park,et al.  Stability for Neural Networks With Time-Varying Delays via Some New Approaches , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Guoping Liu,et al.  Improved delay-range-dependent stability criteria for linear systems with time-varying delays , 2010, Autom..

[28]  Qing-Guo Wang,et al.  Delay-Dependent State Estimation for Delayed Neural Networks , 2006, IEEE Transactions on Neural Networks.

[29]  Yong He,et al.  Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Neural Networks.

[30]  Jia Wang,et al.  Event-Triggered Generalized Dissipativity Filtering for Neural Networks With Time-Varying Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Rathinasamy Sakthivel,et al.  Design of state estimator for bidirectional associative memory neural networks with leakage delays , 2015, Inf. Sci..

[32]  Daniel W. C. Ho,et al.  State estimation for delayed neural networks , 2005, IEEE Transactions on Neural Networks.

[33]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[34]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[35]  Ju H. Park,et al.  Dissipativity analysis of stochastic neural networks with time delays , 2012 .

[36]  Xin-Ping Guan,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Ligang Wu,et al.  Induced l2 filtering of fuzzy stochastic systems with time-varying delays , 2013, IEEE Transactions on Cybernetics.

[38]  Fang Xu,et al.  Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays , 2014, Appl. Math. Comput..

[39]  Yingchun Wang,et al.  State estimation of recurrent neural networks with interval time-varying delay: an improved delay-dependent approach , 2012, Neural Computing and Applications.

[40]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[41]  Xinzhi Liu,et al.  Global convergence of neural networks with mixed time-varying delays and discontinuous neuron activations , 2012, Inf. Sci..

[42]  Hao Shen,et al.  Delay-difference-dependent robust exponential stability for uncertain stochastic neural networks with multiple delays , 2014, Neurocomputing.

[43]  Georges G. E. Gielen,et al.  A fast learning algorithm for time-delay neural networks , 2002, Inf. Sci..

[44]  Jinde Cao,et al.  An LMI approach to delay-dependent state estimation for delayed neural networks , 2008, Neurocomputing.

[45]  Nasser M. Nasrabadi,et al.  Object recognition using multilayer Hopfield neural network , 1997, IEEE Trans. Image Process..

[46]  Long Cheng,et al.  Decentralized Robust Adaptive Control for the Multiagent System Consensus Problem Using Neural Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[47]  Tingwen Huang,et al.  Guaranteed $H_{\infty}$ Performance State Estimation of Delayed Static Neural Networks , 2015, IEEE Transactions on Circuits and Systems II: Express Briefs.

[48]  Keith J. Burnham,et al.  On designing observers for time-delay systems with non-linear disturbances , 2002 .

[49]  Ju H. Park,et al.  A study on H∞ state estimation of static neural networks with time-varying delays , 2014, Appl. Math. Comput..

[50]  Yaochu Jin,et al.  Modeling neural plasticity in echo state networks for classification and regression , 2016, Inf. Sci..

[51]  Qiankun Song,et al.  Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales , 2013, Neurocomputing.