Sliding Intermittent Control for BAM Neural Networks with Delays

This paper addresses the exponential stability problem for a class of delayed bidirectional associative memory (BAM) neural networks with delays. A sliding intermittent controller which takes the advantages of the periodically intermittent control idea and the impulsive control scheme is proposed and employed to the delayed BAM system. With the adjustable parameter taking different particular values, such a sliding intermittent control method can comprise several kinds of control schemes as special cases, such as the continuous feedback control, the impulsive control, the periodically intermittent control, and the semi-impulsive control. By using analysis techniques and the Lyapunov function methods, some sufficient criteria are derived for the closed-loop delayed BAM neural networks to be globally exponentially stable. Finally, two illustrative examples are given to show the effectiveness of the proposed control scheme and the obtained theoretical results.

[1]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[2]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[3]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[4]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[5]  V. Sree Hari Rao,et al.  Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones , 1999, Neural Networks.

[6]  S. Mohamad.  Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks , 2001 .

[7]  Jinde Cao,et al.  Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays , 2004 .

[8]  Jinde Cao,et al.  Exponential stability of high-order bidirectional associative memory neural networks with time delays , 2004 .

[9]  Sabri Arik,et al.  Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays , 2005, IEEE Transactions on Neural Networks.

[10]  K.M.K.H. Leong,et al.  A secure high-speed retrodirective communication link , 2005, IEEE Transactions on Microwave Theory and Techniques.

[11]  James Lam,et al.  Global exponential stability of impulsive high-order BAM neural networks with time-varying delays , 2006, Neural Networks.

[12]  Yao-tang Li,et al.  Global exponential stability analysis on impulsive BAM neural networks with distributed delays , 2006 .

[13]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[14]  Jinde Cao,et al.  Adaptive synchronization in tree-like dynamical networks , 2007 .

[15]  S. Cheng,et al.  Oscillation of Even Order Nonlinear Differential Equations with Impulses , 2007 .

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

[17]  Rajendran Samidurai,et al.  Global asymptotic stability of BAM neural networks with mixed delays and impulses , 2009, Appl. Math. Comput..

[18]  Jinde Cao,et al.  Pinning synchronization of delayed dynamical networks via periodically intermittent control. , 2009, Chaos.

[19]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[20]  Antonio M. Batista,et al.  Delayed feedback control of bursting synchronization in a scale-free neuronal network , 2010, Neural Networks.

[21]  Jan Lunze,et al.  A state-feedback approach to event-based control , 2010, Autom..

[22]  Zidong Wang,et al.  On Passivity and Passification of Stochastic Fuzzy Systems With Delays: The Discrete-Time Case , 2010, IEEE Trans. Syst. Man Cybern. Part B.

[23]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[24]  Ling Chen,et al.  Exponential stability for impulsive stochastic functional differential equations , 2011, 2011 International Conference on Multimedia Technology.

[25]  Xiwei Liu,et al.  Cluster Synchronization in Directed Networks Via Intermittent Pinning Control , 2011, IEEE Transactions on Neural Networks.

[26]  Jinde Cao,et al.  Anti-periodic solution for delayed cellular neural networks with impulsive effects , 2011 .

[27]  Zidong Wang,et al.  Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling , 2012, IEEE Transactions on Automatic Control.

[28]  Zidong Wang,et al.  Distributed H∞ state estimation with stochastic parameters and nonlinearities through sensor networks: The finite-horizon case , 2012, Autom..

[29]  Qintao Gan,et al.  Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control , 2012, Neural Networks.

[30]  Jun Hu,et al.  Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements , 2012, Autom..

[31]  James Lam,et al.  Fuzzy-Model-Based Robust Fault Detection With Stochastic Mixed Time Delays and Successive Packet Dropouts , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[32]  Huijun Gao,et al.  Fault Detection for Markovian Jump Systems With Sensor Saturations and Randomly Varying Nonlinearities , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  Zidong Wang,et al.  Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays , 2012, ACM Trans. Sens. Networks.

[34]  Zidong Wang,et al.  Probability‐dependent gain‐scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities , 2013 .

[35]  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.

[36]  Wei Xing Zheng,et al.  Hopf Bifurcation of an $(n+1)$ -Neuron Bidirectional Associative Memory Neural Network Model With Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Jun Hu,et al.  Gain-Constrained Recursive Filtering With Stochastic Nonlinearities and Probabilistic Sensor Delays , 2013, IEEE Transactions on Signal Processing.

[38]  Zidong Wang,et al.  Finite-horizon H∞ fault estimation for linear discrete time-varying systems with delayed measurements , 2013, Autom..

[39]  Yongkun Li,et al.  Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses , 2013, Fuzzy Sets Syst..