Similar articles

Abstract: A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constraints are shown to be a set of linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law. Most recurrent neural networks (including the chaotic neural network) and nonlinear systems modeled by neural networks or takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM. Finally, three numerical examples are provided to illustrate the design developed in this paper.

[1] Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V., 1994. Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, PA.

[2] Cao, J., Li, H.X., Ho, D.W.C., 2005. Synchronization criteria of Lur’e systems with time-delay feedback control. Chaos Solit. Fract., 23(4):1285-1298.

[3] Cao, J., Yuan, K., Li, H.X., 2006. Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. on Neural Networks, 17(6):1646-1651.

[4] Cheng, C.J., Liao, T.L., Hwang, C.C., 2005. Exponential synchronization of a class of chaotic neural networks. Chaos Solit. Fract., 24(1):197-206.

[5] Chua, L.O., Yang, L., 1988a. Cellular neural networks: theory. IEEE Trans. on Circuits Syst., 35(10):1257-1272.

[6] Chua, L.O., Yang, L., 1988b. Cellular neural networks: applications. IEEE Trans. on Circuits Syst., 35(10):1273-1290.

[7] Er, M.J., Gao, Y., 2003. Robust adaptive control of robot manipulators using generalized fuzzy neural networks. IEEE Trans. on Ind. Electr., 50(3):620-628.

[8] Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., 1995. LMI Control Toolbox for Use with Matlab. The MATH Works, Inc., Natick, MA.

[9] Hopfield, J.J., 1984. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA, 81(10):3088-3092.

[10] Hu, S., Wang, J., 2006. Global robust stability of a class of discrete-time interval neural networks. IEEE Trans. on Circuits Syst.-I: Regul. Papers, 53(1):129-138.

[11] Kosko, B., 1988. Adaptive bi-directional associative memories. IEEE Trans. on Syst. Man Cybern., 18(1):49-60.

[12] Limanond, S., Si, J., 1998. Neural-network-based control design: an LMI approach. IEEE Trans. on Neural Networks, 9(6):1422-1429.

[13] Lin, C.L., Lin, T.Y., 2001. An H₍ design approach for neural net-based control schemes. IEEE Trans. on Automatic Control, 46(10):1599-1605.

[14] Lin, C.M., Hsu, C.F., 2004. Supervisory recurrent fuzzy neural network control of wing rock for slender delta wings. IEEE Trans. on Fuzzy Syst., 12(5):733-742.

[15] Lin, C.M., Hsu, C.F., 2005. Recurrent-neural-network-based adaptive-backstepping control for induction servomotors. IEEE Trans. on Ind. Electr., 52(6):1677-1684.

[16] Liu, M., 2005. Discrete-time delayed standard neural network model and its application. Sci. China Ser. E-Inf. Sci., 35(10):1031-1048.

[17] Liu, M., 2006. Interval standard neural network models for nonlinear systems. J. Zhejiang Univ. Sci. A, 7(4):530-538.

[18] Liu, M., 2007. Delayed standard neural network models for control systems. IEEE Trans. on Neural Networks, 18(5):1376-1391.

[19] Ma, J., Feng, G., 2003. An approach to H₍ control of fuzzy dynamic systems. Fuzzy Sets Syst., 137(3):367-386.

[20] Nørgaard, M., Ravn, O., Poulsen, N.K., Hansen, L.K., 2000. Neural Networks for Modeling and Control of Dynamic Systems. Springer-Verlag, London, Berlin, Heidelberg.

[21] Sun, C., Zhang, K., Fei, S., Feng, C.B., 2002. On exponential stability of delayed neural networks with a general class of activation functions. Phys. Lett. A, 298(2-3):122-132.

[22] Suykens, J.A.K., Vandewalle, J.P.L., de Moor, B.L.R., 1996. Artificial Neural Networks for Modeling and Control of Non-linear Systems. Kluwer Academic Publishers, Boston, Dordrecht, London.

[23] Tanaka, K., 1995. Stability and stabilizability of fuzzy-neural-linear control systems. IEEE Trans. on Fuzzy Syst., 3(4):438-447.

[24] Tanaka, K., Sugeno, M., 1992. Stability and design of fuzzy control systems. Fuzzy Sets Syst., 45(2):135-156.

[25] Tanaka, K., Wang, H.O., 2001. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. John Wiley & Sons, Hoboken, New Jersey, USA.

[26] Wu, H.N., Cai, K.Y., 2004. H₂ guaranteed cost fuzzy control for uncertain nonlinear systems via linear matrix inequalities. Fuzzy Sets Syst., 148(3):411-429.

[27] Zhang, H., Wang, Z., Liu, D., 2007. Robust exponential stability of recurrent neural networks with multiple time-varying delays. IEEE Trans. on Circuits Syst.-II: Expr. Briefs, 54(8):730-734.

[28] Zhang, S., Liu, M., 2005. Stability analysis of discrete-time BAM neural networks based on standard neural network models. J. Zhejiang Univ. Sci., 6A(7):689-696.

[29] Zhou, W.N., Meng, P.Y., 2005. LMI-based H_∞ Control Design with Regional Stability Constraint for T-S Fuzzy System. Proc. Int. Conf. on Machine Learning and Cybernetics, Guangzhou, China, 2:868-873.