Finite-time stochastic stabilization for BAM neural networks with uncertainties

Abstract This paper is concerned with the finite-time stabilization for a class of stochastic BAM neural networks with parameter uncertainties. Compared with the previous references, a continuous stabilizator is designed for stabilizing the states of stochastic BAM neural networks in finite time. Based on the finite-time stability theorem of stochastic nonlinear systems, several sufficient conditions are proposed for guaranteeing the finite-time stability of the controlled neural networks in probability. Meanwhile, the gains of the finite-time controller could be designed by solving some linear matrix inequalities. Furthermore, for the stochastic BAM neural networks with uncertain parameters, the problem of robust finite-time stabilization could also be ensured as well. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

[1]  V. Haimo.  Finite time controllers , 1986 .

[2]  Licheng Jiao,et al.  Authors' reply to "Comments on 'Finite-time stability theorem of stochastic nonlinear systems [Automatica 46 (2010) 2105-2108]"' , 2011, Autom..

[3]  Sanjay P. Bhat,et al.  Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks , 2008, IEEE Transactions on Automatic Control.

[4]  Daniel W. C. Ho,et al.  Pinning Stabilization of Linearly Coupled Stochastic Neural Networks via Minimum Number of Controllers , 2009, IEEE Transactions on Neural Networks.

[5]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[6]  Xiaodi Li,et al.  Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays , 2011, Appl. Math. Comput..

[7]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

[8]  Ju H. Park,et al.  On improved delay-dependent criterion for global stability of bidirectional associative memory neural networks with time-varying delays , 2008, Appl. Math. Comput..

[9]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

[10]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

[11]  S. Bhat,et al.  Finite-time stability of homogeneous systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[12]  Frank L. Lewis,et al.  Finite-time distributed consensus via binary control protocols , 2011, Autom..

[13]  Jinde Cao,et al.  Filippov systems and quasi-synchronization control for switched networks. , 2012, Chaos.

[14]  Zhihong Man,et al.  Robust Finite-Time Consensus Tracking Algorithm for Multirobot Systems , 2009, IEEE/ASME Transactions on Mechatronics.

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

[16]  V. S. Vaidhyanathan,et al.  Regulation and control mechanisms in biological systems , 1993 .

[17]  Xuyang Lou,et al.  Robust asymptotic stability of uncertain fuzzy BAM neural networks with time-varying delays , 2007, Fuzzy Sets Syst..

[18]  Tianyou Chai,et al.  Nonlinear indirect adaptive decoupling control based on neural networks and multiple models , 2006, 2006 American Control Conference.

[19]  Peng Shi,et al.  Delay-range-dependent stability for fuzzy BAM neural networks with time-varying delays , 2009 .

[20]  Ligang Wu,et al.  New global exponential stability criteria for interval-delayed neural networks , 2011 .

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

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

[23]  Ligang Wu,et al.  Exponential stabilization of switched stochastic dynamical networks , 2009 .

[24]  Qiankun Song,et al.  An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays☆ , 2007 .

[25]  Xuyang Lou,et al.  On the global robust asymptotic stability of BAM neural networks with time-varying delays , 2006, Neurocomputing.

[26]  Ju H. Park.  Robust stability of bidirectional associative memory neural networks with time delays , 2006 .

[27]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[28]  Jinde Cao,et al.  Finite-time stochastic synchronization of complex networks , 2010 .

[29]  Jinde Cao,et al.  Robust State Estimation for Neural Networks With Discontinuous Activations , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[31]  Xiaodi Li,et al.  New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays , 2010 .

[32]  Huijun Gao,et al.  Novel Robust Stability Criteria for Stochastic Hopfield Neural Networks With Time Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[34]  Yiguang Hong,et al.  Adaptive finite-time control of nonlinear systems with parametric uncertainty , 2006, IEEE Transactions on Automatic Control.

[35]  Wei Xing Zheng,et al.  Exponential Stability Analysis for Delayed Neural Networks With Switching Parameters: Average Dwell Time Approach , 2010, IEEE Transactions on Neural Networks.

[36]  Jinde Cao,et al.  Stability analysis for stochastic BAM neural networks with Markovian jumping parameters , 2009, Neurocomputing.

[37]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[38]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[39]  E. I. El-Masry,et al.  A switched capacitor bidirectional associative memory , 1990 .