Exponential Synchronization of Neural Networks With Time-Varying Delays via Dynamic Intermittent Output Feedback Control

This paper addresses the exponential synchronization problem for neural networks with time-varying delays. First, a novel controller is presented by combining intermittent control with dynamic output feedback control. Next, a sufficient criterion is established based on the Lyapunov-Krasovskii functional approach and the lower bound lemma for reciprocally convex technique to ensure exponential stability of the resultant closed-loop system. Then, some solvable conditions of the proposed control problem are derived in terms of linear matrix inequalities. Notably, our results here extend the existing ones to the relaxed case because the derivative of time-varying delays is now an arbitrary bounded real number. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed method.

[1]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[2]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Zhigang Zeng,et al.  Second-Order Consensus for Multiagent Systems via Intermittent Sampled Position Data Control , 2018, IEEE Transactions on Cybernetics.

[4]  Qing-Long Han,et al.  Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach , 2014, Neural Networks.

[5]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[6]  Wang Yi-jing,et al.  Exponential Synchronization of Master-Slave Lur'e Systems via Intermittent Time-Delay Feedback Control , 2010 .

[7]  Pengcheng Wei,et al.  Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control , 2011 .

[8]  Yong He,et al.  Exponential synchronization of neural networks with time-varying mixed delays and sampled-data , 2010, Neurocomputing.

[9]  Hamid Reza Karimi,et al.  Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay , 2014, IEEE Transactions on Industrial Electronics.

[10]  Shouming Zhong,et al.  New delay-dependent exponential stability criteria for neural networks with discrete and distributed time-varying delays , 2011, Neurocomputing.

[11]  Xin-Ping Guan,et al.  Stability analysis of time-delay systems via free-matrix-based double integral inequality , 2017, Int. J. Syst. Sci..

[12]  Peter J. Gawthrop,et al.  Open-loop intermittent feedback control: practical continuous-time GPC , 1999 .

[13]  C. Deissenberg.  Optimal control of linear econometric models with intermittent controls , 1980 .

[14]  Qing-Guo Wang,et al.  Exponential synchronization of chaotic neural networks with time-varying delay via intermittent output feedback approach , 2017, Appl. Math. Comput..

[15]  Xin-Ping Guan,et al.  Synchronization of Chaotic Lur’e Systems With Time Delays Using Sampled-Data Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Alexander S. Mikhailov,et al.  Controlling Chemical Turbulence by Global Delayed Feedback: Pattern Formation in Catalytic CO Oxidation on Pt(110) , 2001, Science.

[17]  Xinghuo Yu,et al.  Pulse-Modulated Intermittent Control in Consensus of Multiagent Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[18]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Guang-Hong Yang,et al.  Observer-Based Output Feedback Control for Discrete-Time T-S Fuzzy Systems With Partly Immeasurable Premise Variables , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[21]  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.

[22]  Yasuyuki Inoue,et al.  Adaptive intermittent control: A computational model explaining motor intermittency observed in human behavior , 2015, Neural Networks.

[23]  Chen Xu,et al.  Exponential synchronization of stochastic perturbed complex networks with time-varying delays via periodically intermittent pinning , 2013, Commun. Nonlinear Sci. Numer. Simul..

[24]  Kok Lay Teo,et al.  Robust global exponential synchronization of general Lur’e chaotic systems subject to impulsive disturbances and time delays☆ , 2005 .

[25]  Jinde Cao,et al.  Robust synchronization of coupled neural networks with mixed delays and uncertain parameters by intermittent pinning control , 2014, Neurocomputing.

[26]  Yong He,et al.  Improved Conditions for Passivity of Neural Networks With a Time-Varying Delay , 2014, IEEE Transactions on Cybernetics.

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

[28]  Zhidong Teng,et al.  Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control , 2010 .

[29]  Qing-Long Han,et al.  Event-triggered dynamic output feedback control for networked control systems , 2014 .

[30]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[31]  Zhiyong Yu,et al.  Second-Order Consensus for Multiagent Systems via Intermittent Sampled Data Control , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[32]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[33]  Min Wu,et al.  Delay-Dependent Stability Criteria for Generalized Neural Networks With Two Delay Components , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[34]  T. Chai,et al.  Adaptive synchronization between two different chaotic systems with unknown parameters , 2006 .

[35]  Guodong Zhang,et al.  Exponential Stabilization of Memristor-based Chaotic Neural Networks with Time-Varying Delays via Intermittent Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[36]  Yong He,et al.  Stability analysis of systems with time-varying delay via relaxed integral inequalities , 2016, Syst. Control. Lett..

[37]  J. Kurths,et al.  Single impulsive controller for globally exponential synchronization of dynamical networks , 2013 .

[38]  Fuwen Yang,et al.  H∞ filtering for nonlinear networked systems with randomly occurring distributed delays, missing measurements and sensor saturation , 2016, Inf. Sci..

[39]  Jinde Cao,et al.  Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay , 2016, IEEE Transactions on Neural Networks and Learning Systems.

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

[41]  Ju H. Park,et al.  Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control , 2014 .

[42]  Ju H. Park,et al.  Nonfragile Exponential Synchronization of Delayed Complex Dynamical Networks With Memory Sampled-Data Control , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[43]  王一晶,et al.  Exponential Synchronization of Master-Slave Lur＇e Systems via Intermittent Time-Delay Feedback Control , 2010 .

[44]  V. Kapila,et al.  Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators , 2010 .

[45]  Hao Shen,et al.  Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[46]  Xinzhi Liu,et al.  Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control , 2012 .

[47]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[48]  Xian Zhang,et al.  Exponential Stabilization of Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays by Intermittent Control: A CCL Approach , 2014, Circuits Syst. Signal Process..

[49]  Huibin Zhu,et al.  Stabilization and synchronization of chaotic systems via intermittent control , 2010 .

[50]  Qing-Long Han,et al.  New Lyapunov-Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks , 2009, IEEE Trans. Neural Networks.

[51]  Ju H. Park,et al.  Analysis on delay-dependent stability for neural networks with time-varying delays , 2013, Neurocomputing.

[52]  Min Wu,et al.  Further results on exponential stability of neural networks with time-varying delay , 2015, Appl. Math. Comput..

[53]  Fuwen Yang,et al.  $H_{\infty }$ Fault Detection for Networked Mechanical Spring-Mass Systems With Incomplete Information , 2016, IEEE Transactions on Industrial Electronics.

[54]  Jin-Hua She,et al.  New results on stability analysis for systems with discrete distributed delay , 2015, Autom..

[55]  Chuandong Li,et al.  Stabilization of Nonlinear Systems via Periodically Intermittent Control , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[56]  Yong He,et al.  Exponential stabilization of neural networks with time-varying delay by periodically intermittent control , 2016, Neurocomputing.

[57]  Fuwen Yang,et al.  H∞ consensus of event-based multi-agent systems with switching topology , 2016, Inf. Sci..

[58]  Chuandong Li,et al.  Exponential stabilization of chaotic systems with delay by periodically intermittent control. , 2007, Chaos.

[59]  Min Wu,et al.  Novel stability criteria for recurrent neural networks with time-varying delay , 2014, Neurocomputing.

[60]  Henrik Gollee,et al.  Does the Motor System Need Intermittent Control? , 2014, Exercise and sport sciences reviews.

[61]  Peng Shi,et al.  Exponential Synchronization of Neural Networks With Discrete and Distributed Delays Under Time-Varying Sampling , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[62]  Qiankun Song,et al.  Stabilization and synchronization of chaotic systems with mixed time-varying delays via intermittent control with non-fixed both control period and control width , 2015, Neurocomputing.

[63]  Chuandong Li,et al.  Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period , 2016, Neurocomputing.

[64]  Wu-Hua Chen,et al.  Periodically Intermittent Stabilization of Delayed Neural Networks Based on Piecewise Lyapunov Functions/Functionals , 2014, Circuits Syst. Signal Process..

[65]  Taishin Nomura,et al.  Modeling human postural sway using an intermittent control and hemodynamic perturbations. , 2013, Mathematical biosciences.

[66]  Fuwen Yang,et al.  Event-Based Distributed $H_{\infty }$ Filtering Networks of 2-DOF Quarter-Car Suspension Systems , 2016, IEEE Transactions on Industrial Informatics.

[67]  Xin-Ping Guan,et al.  New stability criteria for neural networks with time-varying delays , 2012, Appl. Math. Comput..

[68]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[69]  Wu Jigang,et al.  Pinning Control for Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topologies , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[70]  Kanjian Zhang,et al.  Synchronization control of recurrent neural networks with distributed delays , 2008 .