Abstract
In this paper a global stochastic optimization algorithm, which is almost surely (a.s.) convergent, is applied to the model reduction problem. The proposed method is compared with the balanced truncation and Hankel norm approximation methods by examples in step responses and in approximation errors as well. Simulation shows that the proposed algorithm provides better results.
Similar content being viewed by others
References
J. Koronacki, Some remarks on stochastic approximation methods, In F. Archetti and M. Cugiani, editors, Numerical Techniques for Stochastic Systems, North-Holland, Amsterdam, 1980
M. B. Nevelson and R. Z. Hasminskii, Stochastic approximation and recursive estimation, Am. Math. Soc. Transl. Math. Monographs 47, 1976.
H. J. Kushner and G. Yin, Stochastic Approximation, Springer, New York, 1997.
H. F. Chen and Y. M. Zhu, Stochastic Approximation (in Chinese), Shanghai Scientific and Technical Publishers, Shanghai, 1996.
H. F. Chen, Stochastic approximation and its new applications, in Proc. 1994 Hong Kong International Workshop on New Directions of Control and Manufacturing, 1994, 2–12.
S. B. Gelfand and S. K. Mitter, Recursive stochastic algorithms for global optimization in ℝn, SIAM J. Control and Optim. 29: 999–1018, 1991.
V. Fabian, Simulated annealing simulated, Computers Math. Applic. 33: 81–94, 1997.
H. T. Fang, G. L. Gong and M. P. Qian, Annealing of iterative stochastic schemes, SIAM J. Control and Optim. 35: 1886–1907, 1997.
H. F. Chen, T. E. Duncan and B. Pasik-Duncan, A Kiefer-Wolfowitz algorithm with randomized differences, IEEE Trans. Autom. Control 44: 442–453, 1999.
J. C. Spall, Multivariate stochastic approximation using a simultaneous perturbation gradient approximation, IEEE Trans. Autom. Control 37: 332–341, 1992.
H. T. Fang and H. F. Chen, Almost surely convergent global optimization algorithm using noise-corrupted observations, J. of Optim. Theory and Appl. 104: 343–376, 2000.
Zhigljavsky, A. A. Theory of Global Random Search. Kluwer Acdemic Publishers, Dordrecht, 1991.
K. Zhou, J. C. Doyle and K. Glover, Robust Optimal Control, Prentice Hall, Englewood Cliffs, NJ, 1996.
B. A. Francis, A course in H ? control theory, Lecture Notes in Control and Information Sciences 18, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chen, HF., Fang, HT. Nonconvex Stochastic Optimization for Model Reduction. Journal of Global Optimization 23, 359–372 (2002). https://doi.org/10.1023/A:1016591031998
Issue Date:
DOI: https://doi.org/10.1023/A:1016591031998