Commenced in January 2007
Paper Count: 30172
Regularization of the Trajectories of Dynamical Systems by Adjusting Parameters
Abstract:A gradient learning method to regulate the trajectories of some nonlinear chaotic systems is proposed. The method is motivated by the gradient descent learning algorithms for neural networks. It is based on two systems: dynamic optimization system and system for finding sensitivities. Numerical results of several examples are presented, which convincingly illustrate the efficiency of the method.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335520Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1023
 E. Ott, C. Grebogy, J. A. Yorke, "Controlling chaos," Phys. Rev. Lett., vol. 64, pp. 1196- 1199, 1990.
 J. Singer, Y. Z. Wang, H. H. Bau, ÔÇ×Controlling chaotic system," Phys. Rev. Lett., vol. 66, pp. 1123- 1125, 1991.
 K. Pyragas, "Continuous control of chaos by self-controlling feedback," Phys. Lett., A, vol. 170, pp. 421-428, 1992.
 C. C. Hwang, R. F. Fung, J. Y. Hsieh, W. J. Li, ÔÇ×A nonlinear feedback control of the Lorenz equation," Int. J. Eng. Sci., vol. 37, pp 1893-1900, 1999.
 Y. Braiman, I. Goldhirsh, "Taming chaotic dynamic with weak periodic perturbations," Phys. Rev. Lett., vol. 66, pp. 2545- 2548, 1991.
 T. Kapitaniak, "The loss of chaos in a quasiperiodically-forced nonlinear oscillator," Int. J. Bifurcation and Chaos, vol. 1, pp357-362, 1991.
 ├£. Lepik, H. Hein, "On response of nonlinear oscillators with random frequency of excitation," J. Sound and Vibration, vol. 288, pp. 275-292, 2005.
 H. Hein, ├£. Lepik, "Response of nonlinear oscillators with random frequency of excitation," revisited., Journal of Sound and Vibration, vol. 301, pp. 1040-1049, 2007.
 P. Baldi, "Gradient descent learning algorithm overview: A general dynamical perspective," IEEE Transactions on neural networks, vol. 6, no. 1, January 1995.
 I. P. Marino, J. Miguez, "An approximate gradient-descent method for joint parameter estimation and synchronization of coupled chaotic systems," Phys. Lett., A, vol. 351, pp. 262-267, 2006.
 A. Bryson, H. Yu-Chi, Applied optimal control, New York: Wiley, 1975.
 C. Sparrow, The Lorenz equations: Bifurcations, chaos and strange attractors, Berlin: Springer, 1982.
 Y. Yao, "Dynamic tunneling algorithm for global optimization," IEEE Transactions on systems, Man and Cybernetics, vol. 19, no. 5, pp. 1222- 1230, October, 1989.
 P. RoyChowdhury, Y. P. Singh and R. A. Chansarkar, "Dynamic tunneling technique for efficient training of multilayer perceptrons," IEEE Transactions on neural networks, vol. 10, no. 1, pp.48-55, January, 1999.