Controlling chaotic systems is very often investigated by using empirical laws, without taking advantage of the structure of the governing equations. There are two concepts, observability and controllability, which are inherited from control theory, for selecting the best placement of sensors and actuators. These two concepts can be combined (extended) into flatness, which provides the conditions to fulfill for designing a feedback linearization or another classical control law for which the system is always fully observable and fully controllable. We here design feedback linearization control laws using flatness for the three popular chaotic systems, namely, the Rössler, the driven van der Pol, and the Hénon–Heiles systems. As developed during the last two decades for observability, symbolic controllability coefficients and symbolic flatness coefficients are introduced here and their meanings are tested with numerical simulations. We show that the control law works for every initial condition when the symbolic flatness coefficient is equal to 1.
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October 2021
Research Article|
October 12 2021
Optimal flatness placement of sensors and actuators for controlling chaotic systems
Christophe Letellier
;
Christophe Letellier
a)
1
Rouen Normandie University—CORIA
, Avenue de l’Université, F-76800 Saint-Etienne du Rouvray, France
a)Author to whom correspondence should be addressed: [email protected]
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Jean-Pierre Barbot
Jean-Pierre Barbot
b)
2
QUARTZ EA7393 Laboratory, ENSEA
, 6 Avenue du Ponceau, 95014 Cergy-Pontoise, France
3
LS2N, UMR 6004, CNRS, École Centrale de Nantes
, 1 rue de la Noë, Nantes, France
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a)Author to whom correspondence should be addressed: [email protected]
b)
Electronic mail: [email protected]
Chaos 31, 103114 (2021)
Article history
Received:
May 04 2021
Accepted:
September 20 2021
Citation
Christophe Letellier, Jean-Pierre Barbot; Optimal flatness placement of sensors and actuators for controlling chaotic systems. Chaos 1 October 2021; 31 (10): 103114. https://doi.org/10.1063/5.0055895
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