NDLI: Control of delayed measured systems and impulse length limitations in difference control

Content Provider	IEEE Xplore Digital Library
Author	Claussen, J.C.
Copyright Year	2003
Description	Author affiliation: Inst. fur Theor. Phys. und Astrophys., Kiel Univ., Germany (Claussen, J.C.)
Abstract	When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi and Yorke (OGY) has to be based on a measurement delayed by /spl tau/ orbit lengths, unmodified OGY method fails beyond a maximal Lyapunov number of /spl lambda//sub max/ = 1+1//spl tau/. Therefore the question arises as to how the control of delayed measured chaotic systems can be improved. Apart from rhythmic control, OGY and difference control can be improved for this case by the memory methods discussed here, linear predictive logging control (LPLC) and memory difference control (MDC). These allow to overcome the measurement delay completely within the linear approximation around the orbit. Furthermore a new stability analysis of the two elementary Poincare-based chaos control schemes, OGY and difference control, is given by means of Floquet theory. This approach allows to calculate exactly the stability restrictions occurring for small measurement delays and for an impulse length shorter than the length of the orbit. As an unexpected result, while for OGY control the influence of the impulse length is marginal, difference control is shown to fail when the impulse length is taken longer than one half of the orbit length.
Starting Page	1296
Ending Page	1302
File Size	2561170
Page Count	7
File Format	PDF
ISBN	078037939X
DOI	10.1109/PHYCON.2003.1237095
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-08-20
Publisher Place	Russia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Chaos Stability Delay systems Delay effects Feedback Length measurement Control systems Extraterrestrial measurements Orbits Lenses
Content Type	Text
Resource Type	Article

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