Controlling Chaos: The Example of an Impact Oscillator

[+] Author and Article Information
Jayant R. Kalagnanam

Department of Engineering & Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213

J. Dyn. Sys., Meas., Control 116(3), 557-564 (Sep 01, 1994) (8 pages) doi:10.1115/1.2899253 History: Received October 27, 1992; Revised August 18, 1993; Online March 17, 2008


The OGY algorithm (Ott et al., 1990) allows the conversion of a chaotic attractor to any one of a large number of periodic orbits by making small time-dependent perturbations of an available system parameter. We have applied this method to impact oscillators and stabilized its chaotic attractor on period-1 and period-2 orbits using small time-dependent pertubations of the driving frequency. We also demonstrate the ability to switch the chaotic system between the period-1 and period-2 orbits at will by controlled time-dependent perturbations. However, before the system settles on the stabilized orbit, it exhibits a long chaotic transient. We demonstrate how the exponential sensitivity of a chaotic system to small perturbations can be exploited to control the duration of this chaotic transient.

Copyright © 1994 by The American Society of Mechanical Engineers
Topics: Algorithms , Chaos , Switches
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