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Parameter optimization in large-scale dynamical systems: A method of contractive mapping. (English) Zbl 1050.65069

Summary: A new method is given to optimize parameters in dynamical systems by supplementing conventional methods with a procedure of contractive mapping. The dynamical system is first decoupled in order to reduce the search size. The reference curves and the simulation curves are obtained with the pre-optimization. A contractive mapping procedure is designed to asymptotically reduce the differences between the curves, whereby the parameters are further optimized. Numerical results indicate that the present method can solve some large-scale problems that are difficult for the previous methods.

MSC:

65K10 Numerical optimization and variational techniques
93B30 System identification
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[1] Lewis, R. M.; Torczon, V.; Trosset, M. W., Direct search method: then and now, J. Comput. Appl. Math., 124, 191-207 (2000) · Zbl 0969.65055
[2] E.K.P. Chong, S.H. Zak, An Introduction to Optimization, Wiley, NY, 2001.; E.K.P. Chong, S.H. Zak, An Introduction to Optimization, Wiley, NY, 2001. · Zbl 1056.90129
[3] Stortelder, W. J.H., Parameter estimation in dynamic system, Math. Comput. Simul., 42, 135-142 (1996) · Zbl 0862.92025
[4] K. Schittkowski, Numerical Data Fitting in Dynamical Systems, Kluwer Academic Publishers, Dordrecht, Holland, 2002.; K. Schittkowski, Numerical Data Fitting in Dynamical Systems, Kluwer Academic Publishers, Dordrecht, Holland, 2002. · Zbl 1018.65077
[5] Mahnken, M.; Stein, E., Parameter identification for finite deformation elasto-plasticity in principal directions, Comput. Methods Appl. Mech. Eng., 147, 1, 17-39 (1997) · Zbl 0896.73024
[6] Xiu, N.; Zhang, J., A smoothing Gauss-Newton method for the generalized HLCP, J. Comput. Appl. Math., 129, 1-2, 195-208 (2001) · Zbl 0985.65070
[7] E. Zeidler, Applied Functional Analysis, Springer-Verlag, New York, 1995.; E. Zeidler, Applied Functional Analysis, Springer-Verlag, New York, 1995. · Zbl 0834.46003
[8] Cao, H. Q.; Kang, L. S.; Guo, T.; Chen, Y. P.; Garis, H. D., A two-level hybrid evolutionary algorithm for modeling one-dimensional dynamic systems by higher-order ODE models, IEEE Trans. Syst., Man Cybern., 30, 351-357 (2000)
[9] E. Falkenauer, Genetic Algorithms and Grouping Problems, Wiley, Chichester, 1998.; E. Falkenauer, Genetic Algorithms and Grouping Problems, Wiley, Chichester, 1998. · Zbl 0803.68037
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