Abstract
This paper addresses the problem of stochastic sampled-data stabilization for neural-network-based control systems (NNBCSs) with an optimal guaranteed cost. In order to stabilize the closed-loop system, continuous-time nonlinear plant and three-layer fully connected feed-forward neural networks based on stochastic sampling are connected to the closed loop. By introducing new Lyapunov–Krasovskii functional with triple integral terms and by using second-order reciprocal convex technique, new stability and stabilization criteria for NNBCSs are derived in terms of linear matrix inequalities (LMIs). The desired stochastic sampled-data controllers can be calculated by solving these LMIs. Finally, physical example is given to verify the effectiveness and usefulness of the obtained results.
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References
He, Y., Liu, G.P., Rees, D., Wu, M.: Stability analysis for neural networks with time-varying interval delay. IEEE Trans. Neural Netw. 18, 1850–1854 (2007)
Rakkiyappan, R., Balasubramaniam, P.: Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Appl. Math. Comput. 198, 526–533 (2008)
Huang, C., He, Y., Huang, L.: Stability analysis of non-autonomous stochastic Cohen–Grossberg neural networks. Nonlinear Dyn. 57, 469–478 (2009)
Zhu, Q., Cao, J.: Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays. IEEE Trans. Neural Netw. Learn. Syst. 23, 467–479 (2012)
Shen, Y., Wang, J.: Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances. IEEE Trans. Neural Netw. Learn. Syst. 23, 87–96 (2012)
Zhou, L.: Global asymptotic stability of cellular neural networks with proportional delays. Nonlinear Dyn. 77, 41–47 (2014)
Astrom, K., Wittenmark, B.: Adaptive Control Reading. Addison-Wesley, MA (1989)
Mikheev, Y., Sobolev, V., Fridman, E.: Asymptotic analysis of digital control systems. Autom. Remote Control 49, 1175–1180 (1988)
Lam, H.: Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach. IEEE Trans. Syst. Man Cybern. B Cybern. 42, 258–267 (2012)
Wu, Z.G., Shi, P., Su, H., Chu, J.: Local synchronization of chaotic neural networks with sampled-data and saturating actuators. IEEE Trans. Cybern. (2014). doi:10.1109/TCYB.2014.2312004
Gao, H., Meng, X., Chen, T.: Stabilization of networked control systems with new delay characterization. IEEE Trans. Autom. Control 53, 2142–2148 (2008)
Gao, H., Chen, T., Lam, J.: A new delay system approach to network-based control. Automatica 44, 39–52 (2008)
Gao, H., Wu, J., Shi, P.: Robust sampled-data \(H_{\infty }\) control with stochastic sampling. Automatica 45, 1729–1736 (2009)
Lee, T.H., Park, J.H., Lee, S.M., Kwon, O.M.: Robust synchronization of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control. Int. J. Control 86, 107–119 (2013)
Lee, T.H., Park, J.H., Kwon, O.M., Lee, S.M.: Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw. 46, 99–108 (2013)
Revathi, V.M., Balasubramaniam, P., Park, J.H., Lee, T.H.: \(H_{\infty }\) filtering for sample data systems with stochastic sampling and Markovian jumping parameters. Nonlinear Dyn. (2014). doi:10.1007/s11071-014-1479-x
Patino, H.D., Carelli, R., Kuchen, B.R.: Neural network for advanced control of robot manipulators. IEEE Trans. Neural Netw. 13, 343–354 (2002)
Hwang, J.D., Hsiao, F.H.: Stability analysis of neural-network interconnected systems. IEEE Trans. Neural Netw. 14, 201–208 (2003)
Lam, H.K., Leung, F.H.F.: Design and stabilization of sampled-data neural-network-based control systems. IEEE Trans. Syst. Man Cybern. B Cybern. 36, 995–1005 (2006)
Zhu, X., Wang, Y.: Stabilization for sampled-data neural-network-based control systems. IEEE Trans. Syst. Man Cybern. B Cybern. 41, 210–221 (2011)
Zhou, Q., Shi, P., Liu, H., Xu, S.: Neural-network-based decentralized adaptive output-feedback control for large-scale stochastic nonlinear systems. IEEE Trans. Syst. Man Cybern. B Cybern. 42, 1608–1619 (2012)
Eski, I., Temurlenk, A.: Design of neural network-based control systems for active steering system. Nonlinear Dyn. 73, 1443–1454 (2013)
Wu, Z.G., Shi, P., Su, H., Chu, J.: Exponential stabilization for sampled-data neural-network-based control systems. IEEE Trans. Neural Netw. Learn. Syst. (2014). doi:10.1109/TNNLS.2014.2306202
Park, P.G., Ko, J.W., Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 7, 235–238 (2011)
Liu, J., Zhang, J.: Note on stability of discrete-time time-varying delay systems. IET Control Theory Appl. 6, 335–339 (2012)
Lee, W., Park, P.: Second-order reciprocally convex approach to stability of systems with interval time-varying delays. Appl. Math. Comput. 229, 245–253 (2014)
Tian, J.K., Zhong, S.M.: Improved delay-dependent stability criterion for neural networks with time-varying delay. Appl. Math. Comput. 217, 10278–10288 (2011)
Gao, H., Meng, X., Chen, T.: Stabilization of networked control systems with new delay characterization. IEEE Trans. Autom. Control 53, 2142–2148 (2008)
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Rakkiyappan, R., Sivasamy, R. & Cao, J. Stochastic sampled-data stabilization of neural-network-based control systems. Nonlinear Dyn 81, 1823–1839 (2015). https://doi.org/10.1007/s11071-015-2110-5
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DOI: https://doi.org/10.1007/s11071-015-2110-5