Nonsmooth recursive identification of sandwich systems with backlash-like hysteresis. (English) Zbl 1251.93131

Summary: A recursive gradient identification algorithm based on the bundle method for sandwich systems with backlash-like hysteresis is presented in this paper. In this method, a dynamic parameter estimation scheme based on a subgradient is developed to handle the nonsmooth problem caused by the backlash embedded in the system. The search direction of the algorithm is estimated based on the so-called bundle method. Then, the convergence of the algorithm is discussed. After that, simulation results on a nonsmooth sandwich system are presented to validate the proposed estimation algorithm. Finally, the application of the proposed method to an \(X\)-\(Y\) moving positioning stage is illustrated.


93E12 Identification in stochastic control theory
90C30 Nonlinear programming
Full Text: DOI


[1] N. J. Bershad, P. Celka, and S. McLaughlin, “Analysis of stochastic gradient identification of Wiener-Hammerstein systems for nonlinearities with Hermite polynomial expansions,” IEEE Transactions on Signal Processing, vol. 49, no. 5, pp. 1060-1071, 2001. · doi:10.1109/78.917809
[2] A. H. Tan and K. Godfrey, “Identification of Wiener-Hammerstein models using linear interpolation in the frequency domain (LIFRED),” IEEE Transactions on Instrumentation and Measurement, vol. 51, no. 3, pp. 509-521, 2002. · doi:10.1109/TIM.2002.1017722
[3] M. Boutayeb and M. Darouach, “Recursive identification method for MISO Wiener-Hammerstein model,” IEEE Transactions on Automatic Control, vol. 40, no. 2, pp. 287-291, 1995. · Zbl 0819.93024 · doi:10.1109/9.341794
[4] V. Cerone and D. Regruto, “Bounding the parameters of linear systems with input backlash-like hysteresis,” in Proceedings of the American Control Conference, pp. 4476-4481, Portland, Ore, USA, June 2005.
[5] E.-W. Bai, “Identification of linear systems with hard input nonlinearities of known structure,” Automatica, vol. 38, no. 5, pp. 853-860, 2002. · Zbl 1010.93032 · doi:10.1016/S0005-1098(01)00281-3
[6] F. Giri, Y. Rochdi, F. Z. Chaoui, and A. Brouri, “Identification of Hammerstein systems in presence of hysteresis-backlash and hysteresis-relay nonlinearities,” Automatica, vol. 44, no. 3, pp. 767-775, 2008. · doi:10.1016/j.automatica.2007.07.005
[7] R. Dong, Y. Tan, and H. Chen, “Recursive identification for dynamic systems with backlash,” Asian Journal of Control, vol. 12, no. 1, pp. 26-38, 2010. · doi:10.1002/asjc.157
[8] R. Dong, Q. Tan, and Y. Tan, “Recursive identification for dynamic systems with output backlash-like hysteresis and its convergence,” International Journal of Applied Mathematics and Computer Science, vol. 19, no. 4, pp. 631-638, 2009. · Zbl 1300.93172
[9] R. Dong and R. Tan, “Online identification algorithm and convergence analysis for sandwich systems with backlash,” International Journal of Control, Automation and Systems, vol. 9, no. 3, pp. 1-7, 2011.
[10] C. Eitzinger, “Nonsmooth training of fuzzy neural networks,” Soft Computing, vol. 8, pp. 443-448.
[11] M. M. Mäkelä, M. Miettinen, L. Luk\vsan, and J. Vl\vcek, “Comparing nonsmooth nonconvex bundle methods in solving hemivariational inequalities,” Journal of Global Optimization, vol. 14, no. 2, pp. 117-135, 1999. · Zbl 0947.90125 · doi:10.1023/A:1008282922372
[12] S. A. Miller, An inexact bundle method for solving large structured linear matrix inequality [Doctoral dissertation], University of California, Santa Barbara, Calif, USA, 2001.
[13] C. Lemaréchal, “Nondifferentiable optimization,” in Optimization, G. L. Nemhauser, A. H. G. Rinnooy Kan, and M. J. Todd, Eds., vol. 1, pp. 529-572, North-Holland, Amsterdam, The Netherland, 1989. · doi:10.1016/S0927-0507(89)01008-X
[14] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, .Reading, Mass, USA, 1998.
[15] R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, Chichester, 2nd edition, 1987. · Zbl 0905.65002
[16] C.-C. Ku and K. Y. Lee, “Diagonal recurrent neural networks for dynamic systems control,” IEEE Transactions on Neural Networks, vol. 6, no. 1, pp. 144-156, 1995. · doi:10.1109/72.363441
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.