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2 - nonlinear system identification via recurrent neural networks. (English) Zbl 1209.93035
Summary: This paper proposes an 2 - identification scheme as a new robust identification method for nonlinear systems via recurrent neural networks. Based on linear matrix inequality (LMI) formulation, for the first time, the 2 - learning algorithm is presented to reduce the effect of disturbance to an 2 - induced norm constraint. New stability results, such as boundedness, input-to-state stability (ISS), and convergence, are established in some senses. It is shown that the design of the 2 - identification method can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed identification scheme.
93B30System identification
93B36H -control
[1]Hunt, K.J., Sbarbaro, D., Zbikowski, R., Gawthrop, P.J.: Neural networks for control systems–a survey. Automatica 28, 1083–1112 (1992) · Zbl 0763.93004 · doi:10.1016/0005-1098(92)90053-I
[2]Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall, Upper Saddle River (1996)
[3]Egardt, B.: Stability of Adaptive Controllers. Lecture Notes in Control and Information Sciences, vol. 20. Springer, Berlin (1979)
[4]Polycarpou, M.M., Ioannou, P.A.: Learning and convergence analysis of neural-type structured networks. IEEE Trans. Neural Netw. 3, 39–50 (1992) · doi:10.1109/72.105416
[5]Jin, L., Gupta, M.M.: Stable dynamic backpropagation learning in recurrent neural networks. IEEE Trans. Neural Netw. 10, 1321–1334 (1999) · doi:10.1109/72.809078
[6]Suykens, J.A.K., Vandewalle, J., De Moor, B.: nl q theory: checking and imposing stability of recurrent neural networks for nonlinear modelling. IEEE Trans. Signal Process. 45, 2682–2691 (1997) · doi:10.1109/78.650094
[7]Kosmatopoulos, E.B., Polycarpou, M.M., Christodoulou, M.A., Ioannou, P.A.: High-order neural network structures for identification of dynamical systems. IEEE Trans. Neural Netw. 6, 431–442 (1995) · doi:10.1109/72.363477
[8]Jagannathan, S., Lewis, F.L.: Identification of nonlinear dynamical systems using multilayered neural networks. Automatica 32, 1707–1712 (1996) · Zbl 0879.93010 · doi:10.1016/S0005-1098(96)80007-0
[9]Song, Q.: Robust training algorithm of multilayered neural networks for identification of nonlinear dynamic systems. IEE Proc. Control Theory Appl. 145, 41–46 (1998) · Zbl 0900.93062 · doi:10.1049/ip-cta:19981614
[10]Yu, W., Li, X.: Discrete-time neuro identification without robust modification. IEE Proc. Control Theory Appl. 150, 311–316 (2003) · doi:10.1049/ip-cta:20030204
[11]Rubio, J.J., Yu, W.: Stability analysis of nonlinear system identification via delayed neural networks. IEEE Trans. Circuits Syst. II 57, 161–165 (2007) · doi:10.1109/TCSII.2006.886464
[12]Grigoriadis, K.M., Watson, J.T.: Reduced-order and 2–filtering via linear matrix inequalities. IEEE Trans. Aerosp. Electron. Syst. 33, 1326–1338 (1997) · doi:10.1109/7.625133
[13]Watson, J.T., Grigoriadis, K.M.: Optimal unbiased filtering via linear matrix inequalities. Syst. Control Lett. 35, 111–118 (1998) · Zbl 0909.93069 · doi:10.1016/S0167-6911(98)00042-5
[14]Palhares, R.M., Peres, P.L.D.: Robust filtering with guaranteed energy-to-peak performance–an LMI approach. Automatica 36, 851–858 (2000) · Zbl 0953.93067 · doi:10.1016/S0005-1098(99)00211-3
[15]Gao, H., Wang, C.: Robust 2–filtering for uncertain systems with multiple time-varying state delays. IEEE Trans. Circuits Syst. I 50, 594–599 (2003) · doi:10.1109/TCSI.2003.809816
[16]Gao, H., Wang, C.: Delay-dependent robust and 2–filtering for a class of uncertain nonlinear time-delay systems. IEEE Trans. Autom. Control 48, 1661–1666 (2003) · doi:10.1109/TAC.2003.817012
[17]Mahmoud, M.S.: Resilient 2–filtering of polytopic systems with state delays. IET Control Theory Appl. 1(1), 141–154 (2007) · doi:10.1049/iet-cta:20045281
[18]Qiu, J., Feng, G., Yang, J.: New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay. IET Control Theory Appl. 2(9), 795–806 (2008) · doi:10.1049/iet-cta:20070361
[19]Zhou, Y., Li, J.: Energy-to-peak filtering for singular systems: the discrete-time case. IET Control Theory Appl. 2(9), 773–781 (2008) · doi:10.1049/iet-cta:20070432
[20]Boyd, S., Ghaoui, L.E., Feron, E., Balakrishinan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)
[21]Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The Mathworks, Natick (1995)
[22]Hopfield, J.J.: Neurons with grade response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA 81, 3088–3092 (1984) · doi:10.1073/pnas.81.10.3088
[23]Sontag, E.D., Wang, Y.: On characterizations of the input-to-state stability property. Syst. Control Lett. 24, 351–359 (1995) · Zbl 0877.93121 · doi:10.1016/0167-6911(94)00050-6
[24]Zeng, Y., Singh, S.N.: Adaptive control of chaos in Lorenz system. Dyn. Control 7, 143–154 (1997) · Zbl 0875.93191 · doi:10.1023/A:1008275800168