Robust Stability of Inertial BAM Neural Networks with Time Delays and Uncertainties via Impulsive Effect

This paper investigates the robust stability of inertial bidirectional association memory (BAM) neural networks with time delays and uncertainties via impulsive control. Firstly, utilizing suitable variable substitution, the seconded-order inertial BAM neural networks can be transformed into first-order differential equations. Secondly, Under the framework of Lyapunov stability method, Halanay inequality and impulsive differential inequations, we develop some techniques of impulsive to achieve the robust stability of inertial BAM neural networks. These obtained criteria are capable of reducing computational burden in the theoretical part. Some effective sufficient conditions are established for the realization of stability of the underlying network. Finally, an illustrative example is given to verify the validity of the obtained results.

[1]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[2]  Jun Tani,et al.  Model-based learning for mobile robot navigation from the dynamical systems perspective , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[3]  J. Ashmore,et al.  The fast activating potassium current, IK,f, in guinea-pig inner hair cells is regulated by protein kinase A , 1999, Neuroscience Letters.

[4]  Guanrong Chen,et al.  On delayed impulsive Hopfield neural networks , 1999, Neural Networks.

[5]  Kate Smith-Miles,et al.  A unified framework for chaotic neural-network approaches to combinatorial optimization , 1999, IEEE Trans. Neural Networks.

[6]  M. Magnasco,et al.  Evidence of a Hopf bifurcation in frog hair cells. , 2001, Biophysical journal.

[7]  J.A. Anderson,et al.  Neural Network Models for Pattern Recognition and Associative Memory , 2002 .

[8]  Ashraf Elazouni,et al.  Progress Monitoring of Construction Projects Using Neural Networks Pattern Recognition , 2009 .

[9]  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).

[10]  Jinde Cao,et al.  Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[11]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[12]  Chuandong Li,et al.  Bogdanov-Takens bifurcation in a single inertial neuron model with delay , 2012, Neurocomputing.

[13]  Jinde Cao,et al.  Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Xuerui Wei.  Exponential stability of periodic solutions for inertial Cohen-Grossberg-type BAM neural networks with time delays , 2013 .

[15]  Yang Tang,et al.  Exponential Synchronization of Coupled Switched Neural Networks With Mode-Dependent Impulsive Effects , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Tingwen Huang,et al.  Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Jinde Cao,et al.  Synchronization of Coupled Reaction-Diffusion Neural Networks with Time-Varying Delays via Pinning-Impulsive Controller , 2013, SIAM J. Control. Optim..

[18]  Shiji Song,et al.  Research on synchronization of chaotic delayed neural networks with stochastic perturbation using impulsive control method , 2014, Commun. Nonlinear Sci. Numer. Simul..

[19]  Zhigang Zeng,et al.  Exponential Adaptive Lag Synchronization of Memristive Neural Networks via Fuzzy Method and Applications in Pseudorandom Number Generators , 2014, IEEE Transactions on Fuzzy Systems.

[20]  Chuandong Li,et al.  A Recurrent Neural Network for Solving Bilevel Linear Programming Problem , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[22]  Zhigang Zeng,et al.  Observer-based synchronization of memristive systems with multiple networked input and output delays , 2014 .

[23]  Jinde Cao,et al.  Pinning synchronization of coupled inertial delayed neural networks , 2014, Cognitive Neurodynamics.

[24]  Changjin Xu,et al.  Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay , 2015, Neurocomputing.

[25]  Tingwen Huang,et al.  Event-Triggering Sampling Based Leader-Following Consensus in Second-Order Multi-Agent Systems , 2015, IEEE Transactions on Automatic Control.

[26]  Zhigang Zeng,et al.  Circuit design and exponential stabilization of memristive neural networks , 2015, Neural Networks.

[27]  Quanxin Zhu,et al.  Synchronization of reaction–diffusion neural networks with time-varying delays via stochastic sampled-data controller , 2014, Nonlinear Dynamics.

[28]  Tingwen Huang,et al.  Second-Order Global Consensus in Multiagent Networks With Random Directional Link Failure , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Jinde Cao,et al.  Finite-time synchronization of fractional-order memristor-based neural networks with time delays , 2016, Neural Networks.

[30]  Jinde Cao,et al.  Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays , 2016, Neurocomputing.

[31]  Xinghuo Yu,et al.  A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Xinghuo Yu,et al.  Distributed Event-Triggered Scheme for Economic Dispatch in Smart Grids , 2016, IEEE Transactions on Industrial Informatics.

[33]  Jinde Cao,et al.  Pinning Controllability Scheme of Directed Complex Delayed Dynamical Networks via Periodically Intermittent Control , 2016 .

[34]  Wei Yan,et al.  A Rising E-Channel Tide Lifts All Boats? The Impact of Manufacturer Multi-Channel Encroachment on Traditional Selling and Leasing , 2016 .

[35]  Xinghuo Yu,et al.  Asynchronous impulsive containment control in switched multi-agent systems , 2016, Inf. Sci..

[36]  Tingwen Huang,et al.  Event-Triggered Distributed Average Consensus Over Directed Digital Networks With Limited Communication Bandwidth , 2016, IEEE Transactions on Cybernetics.

[37]  Jinde Cao,et al.  Matrix measure based dissipativity analysis for inertial delayed uncertain neural networks , 2016, Neural Networks.

[38]  Kexue Zhang,et al.  Pinning Impulsive Synchronization of Reaction–Diffusion Neural Networks With Time-Varying Delays , 2017, IEEE Transactions on Neural Networks and Learning Systems.