Adaptive control of recurrent trajectories based on linearization of Poincare map

A.L. Fradkov, P. Guzenko, A. Pavlov

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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Uittreksel

The problem of adaptive output feedback control aimed at stabilization of a (periodic or chaotic) goal trajectory is considered. Advantages and drawbacks of chaos control method based on linearization of Poincaré map (first proposed by Ott, Grebogi and Yorke in 1990) are discussed. It is suggested that the recurrence of the goal trajectory is the key property for applicability of approach. Algorithms of adaptive control based on linearization of controlled Poincaré map and method of goal inequalities are proposed. It is shown that stabilization of recurrent trajectories is possible under additional controllability-like and observability-like conditions. Examples of stabilization of periodic and chaotic trajectories for forced brusselator and Rössler systems are studied by computer simulations.
Originele taal-2Engels
Pagina's (van-tot)621-637
Aantal pagina's17
TijdschriftInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume10
Nummer van het tijdschrift3
DOI's
StatusGepubliceerd - 2000

Vingerafdruk

Poincaré Map
Linearization
Adaptive Control
Trajectories
Trajectory
Stabilization
Control of Chaos
Output Feedback Control
Observability
Controllability
Chaos theory
Recurrence
Feedback control
Computer Simulation
Computer simulation

Citeer dit

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abstract = "The problem of adaptive output feedback control aimed at stabilization of a (periodic or chaotic) goal trajectory is considered. Advantages and drawbacks of chaos control method based on linearization of Poincar{\'e} map (first proposed by Ott, Grebogi and Yorke in 1990) are discussed. It is suggested that the recurrence of the goal trajectory is the key property for applicability of approach. Algorithms of adaptive control based on linearization of controlled Poincar{\'e} map and method of goal inequalities are proposed. It is shown that stabilization of recurrent trajectories is possible under additional controllability-like and observability-like conditions. Examples of stabilization of periodic and chaotic trajectories for forced brusselator and R{\"o}ssler systems are studied by computer simulations.",
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Adaptive control of recurrent trajectories based on linearization of Poincare map. / Fradkov, A.L.; Guzenko, P.; Pavlov, A.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 10, Nr. 3, 2000, blz. 621-637.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

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AU - Guzenko, P.

AU - Pavlov, A.

PY - 2000

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AB - The problem of adaptive output feedback control aimed at stabilization of a (periodic or chaotic) goal trajectory is considered. Advantages and drawbacks of chaos control method based on linearization of Poincaré map (first proposed by Ott, Grebogi and Yorke in 1990) are discussed. It is suggested that the recurrence of the goal trajectory is the key property for applicability of approach. Algorithms of adaptive control based on linearization of controlled Poincaré map and method of goal inequalities are proposed. It is shown that stabilization of recurrent trajectories is possible under additional controllability-like and observability-like conditions. Examples of stabilization of periodic and chaotic trajectories for forced brusselator and Rössler systems are studied by computer simulations.

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