Abstract
In this paper, the sampled-data state estimation problem is investigated for a class of recurrent neural networks with time-varying delay. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. By converting the sampling period into a bounded time-varying delay, the error dynamics of the considered neural network is derived in terms of a dynamic system with two different time-delays. Subsequently, by choosing an appropriate Lyapunov functional and using the Jensen’s inequality, a sufficient condition depending on the sampling period is obtained under which the resulting error system is exponentially stable. Then a sampled-data estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using available software. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed sampled-data estimation approach.
Similar content being viewed by others
References
Ahn, C.K.: Robust stability of recurrent neural networks with ISS learning algorithm. Nonlinear Dyn. 65(4), 413–419 (2011)
Balasubramaniam, P., Lakshmanan, S., Jeeva Sathya Theesar, S: State estimation for Markovian jumping recurrent neural networks with interval time-varying delays. Nonlinear Dyn. 60(4), 661–675 (2010)
Basheer, I.A., Hajmeer, M.: Artificial neural networks: fundamentals, computing, design, and application. J. Microbiol. Methods 43(1), 3–31 (2000)
Forti, M., Tesi, A.: New conditions for global stability of neural network with application to linear and quadratic-programming problems. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42(7), 354–366 (1995)
Fridman, E., Shaked, U., Suplin, V.: Input/output delay approach to robust sampled-data H ∞ control. Syst. Control Lett. 54(3), 271–282 (2005)
Gao, H., Sun, W., Shi, P.: Robust sampled-data H ∞ control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 18(1), 238–245 (2010)
Gao, H., Wu, J., Shi, P.: Robust sampled-data H ∞ control with stochastic sampling. Automatica 45(7), 1729–1736 (2009)
Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proc. 39th IEEE Conf. Decision and Control, Dec. 2000, Sydney, Australia, pp. 2805–2810 (2010)
Haken, H.: Pattern recognition and synchronization in pulse-coupled neural networks. Nonlinear Dyn. 44(1–4), 269–276 (2006)
He, Y., Wang, Q., Wu, M., Lin, C.: Delay-dependent state estimation for delayed neural networks. IEEE Trans. Neural Netw. 17(4), 1077–1081 (2006)
Hendzel, Z.: An adaptive critic neural network for motion control of a wheeled mobile robot. Nonlinear Dyn. 50(4), 849–855 (2007)
Huang, H., Feng, G.: Scaling parameter approach to delay-dependent state estimation of delayed neural networks. IEEE Trans. Circuits Syst. II, Express Briefs 57(1), 36–40 (2010)
Hush, D.R., Horne, B.G.: Progress in supervised neural networks. IEEE Signal Process. Mag. 10(1), 8–39 (1993)
Karimi, H., Gao, H.: New delay-dependent exponential H ∞ synchronization for uncertain neural networks with mixed time delays. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(1), 173–185 (2010)
Lam, H.K., Leung Frank, H.F.: Design and stabilization of sampled-data neural-network-based control systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 36(5), 995–1005 (2006)
Liang, J., Cao, J.: Global output convergence of recurrent neural networks with distributed delays. Nonlinear Anal., Real World Appl. 8(1), 187–197 (2007)
Liang, J., Lam, J.: Robust state estimation for stochastic genetic regulatory networks. Int. J. Syst. Sci. 41(1), 47–63 (2010)
Liu, Y., Wang, Z., Liu, X.: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 19(5), 667–675 (2006)
Liu, Y., Wang, Z., Liu, X.: State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays. Phys. Lett. A 372(48), 7147–7155 (2008)
Park, J., Kwon, O., Lee, S.: State estimation for neural networks of neutral-type with interval time-varying delays. Appl. Math. Comput. 203(1), 217–223 (2008)
Shen, B., Wang, Z., Liang, J., Liu, X.: Sampled-data H ∞ filtering for stochastic genetic regulatory networks. Int. J. Robust Nonlinear Control 21(15), 1759–1777 (2011)
Shen, B., Wang, Z., Liu, X.: A stochastic sampled-data approach to distributed H ∞ filtering in sensor networks. IEEE Trans. Circuits Syst. I, Regul. Pap. 58(9), 2237–2246 (2011)
Tian, J., Zhou, X.: Improved asymptotic stability criteria for neural networks with interval time-varying delay. Expert Syst. Appl. 37(12), 7521–7525 (2010)
Tong, S., Shi, P.: Sampled-data filtering framework for cardiac motion recovery: Optimal estimation of continuous dynamics from discrete measurements. IEEE Trans. Biomed. Eng. 54(10), 1750–1761 (2007)
Wang, Z., Ho, D.W.C., Liu, X.: State estimation for delayed neural networks. IEEE Trans. Neural Netw. 16(1), 279–284 (2005)
Wang, Z., Liu, Y., Li, M., Liu, X.: Stability analysis for stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans. Neural Netw. 17(3), 814–820 (2006)
Wang, Z., Liu, Y., Liu, X.: On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4–6), 299–308 (2005)
Wang, Y., Wang, Z., Liang, J.: A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances. Phys. Lett. A 372(39), 6066–6073 (2008)
Wang, Y., Wang, Z., Liang, J.: On robust stability of stochastic genetic regulatory networks with time delays: a delay fractioning approach. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(3), 729–740 (2010)
Wu, J., Chen, X., Gao, H.: H ∞ filtering with stochastic sampling. Signal Process. 90(4), 1131–1145 (2010)
Yildirim, S.: A proposed hybrid neural network for position control of a walking robot. Nonlinear Dyn. 52(3), 207–215 (2008)
Zhu, X.L., Wang, Y.: Stabilization for sampled-data neural-network-based control systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 41(1), 210–221 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, N., Hu, J., Hu, J. et al. Exponential state estimation for delayed recurrent neural networks with sampled-data. Nonlinear Dyn 69, 555–564 (2012). https://doi.org/10.1007/s11071-011-0286-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-011-0286-x