Research Papers

Nonlinear Control of Hyperchaotic System, Lie Derivative, and State Space Linearization

[+] Author and Article Information
Anirban Ray

High Energy Physics Division,Department of Physics,  Jadavpur University, Calcutta, 700 032, Indiaanirban.chaos@gmail.com

A. RoyChowdhury

High Energy Physics Division,Department of Physics,  Jadavpur University, Calcutta, 700 032, Indiaarc.roy@gmail.com

Indranil Mukherjee

 School of Management and Science,  West Bengal University of Technology, Calcutta, 700 064, Indiaindranil.m11@gmail.com

J. Comput. Nonlinear Dynam 7(3), 031002 (Mar 19, 2012) (4 pages) doi:10.1115/1.4005926 History: Received February 03, 2011; Revised December 03, 2011; Published March 13, 2012; Online March 19, 2012

State space linearization using the concept of Brunovsky form and Lie derivative is applied to the case of a Hyperchaotic Lorentz System. It is observed that the necessary and sufficient conditions can be satisfied, the analytic form of the controller ‘u’ and the final form of the linearized equations can be obtained. Numerical simulation is used to ascertain the feasibility of the procedure in practice. It may be added that the case of an ordinary Lorentz equation is distinctively different as the controller is to be added in a different manner. The most important aspect of the present analysis is that the controller can be determined and not chosen ad hoc.

Copyright © 2012 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Form of the time series before and after application of control signal



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