1
|
Letellier C, Mangiarotti S, Minati L, Frasca M, Barbot JP. Optimal placement of sensor and actuator for controlling low-dimensional chaotic systems based on global modeling. CHAOS (WOODBURY, N.Y.) 2023; 33:013140. [PMID: 36725621 DOI: 10.1063/5.0128471] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 12/30/2022] [Indexed: 06/18/2023]
Abstract
Controlling chaos is fundamental in many applications, and for this reason, many techniques have been proposed to address this problem. Here, we propose a strategy based on an optimal placement of the sensor and actuator providing global observability of the state space and global controllability to any desired state. The first of these two conditions enables the derivation of a model of the system by using a global modeling technique. In turn, this permits the use of feedback linearization for designing the control law based on the equations of the obtained model and providing a zero-flat system. The procedure is applied to three case studies, including two piecewise linear circuits, namely, the Carroll circuit and the Chua circuit whose governing equations are approximated by a continuous global model. The sensitivity of the procedure to the time constant of the dynamics is also discussed.
Collapse
Affiliation(s)
- Christophe Letellier
- Rouen Normandie University-CORIA, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France
| | - Sylvain Mangiarotti
- Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-IRD-INRAe, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France
| | - Ludovico Minati
- Center for Mind/Brain Sciences (CIMeC), University of Trento, 38123 Trento, Italy
| | - Mattia Frasca
- Dipartimento di Ingegneria Elettrica Elettronica e Informatica, University of Catania, 95131 Catania, Italy
| | - Jean-Pierre Barbot
- QUARTZ EA7393 Laboratory, ENSEA, 6 Avenue du Ponceau, 95014 Cergy-Pontoise, France
| |
Collapse
|
2
|
Mangiarotti S, Fu E, Jouquet P, Tran MT, Huc M, Bottinelli N. Earthworm activity and its coupling to soil hydrology: A deterministic analysis. CHAOS (WOODBURY, N.Y.) 2021; 31:013134. [PMID: 33754768 DOI: 10.1063/5.0029969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 12/29/2020] [Indexed: 06/12/2023]
Abstract
Considering in situ observations, chaos theory was taken as a basis to study the activity of anecic earthworms based on cast production from September 2016 to January 2018 in the Dong Cao watershed (Vietnam). To study this activity, the global modeling technique was used to obtain deterministic models of ordinary differential equations directly from observational time series. The obtained models show that the behavior of earthworms is chaotic; it is coupled to the dynamics of soil water content in a complex (integrative) way and can be interpreted as an habituation/sensitization process. However, this coupling is insufficient to explain the desynchronization of the cast production variations observed at different study sites. The retroaction of earthworm activity on soil is required to explain the spatiotemporal discrepancies.
Collapse
Affiliation(s)
- S Mangiarotti
- Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-IRD-INRAe, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France
| | - E Fu
- Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-IRD-INRAe, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France
| | - P Jouquet
- Institute of Ecology and Environmental Sciences (UMR 242 iEES-Paris), Sorbonne Université, 75252 Paris, France
| | - M T Tran
- Department of Soil Sciences, Soils and Fertilizers Research Institute, Bac Tu Liem District, Hanoi, Vietnam
| | - M Huc
- Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-IRD-INRAe, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France
| | - N Bottinelli
- Institute of Ecology and Environmental Sciences (UMR 242 iEES-Paris), Sorbonne Université, 75252 Paris, France
| |
Collapse
|
3
|
Letellier C, Leyva I, Sendiña-Nadal I. Dynamical complexity measure to distinguish organized from disorganized dynamics. Phys Rev E 2020; 101:022204. [PMID: 32168607 DOI: 10.1103/physreve.101.022204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Accepted: 01/17/2020] [Indexed: 11/07/2022]
Abstract
We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of the dynamics and the lack of describability of the structure in the Poincaré plane constructed from a given time series. As for the former, we use the permutation entropy S_{p}, while for the latter, we introduce an indicator, the structurality Δ, which accounts for the fraction of visited points in the Poincaré plane. The complexity measure thus defined as the sum of those two components is validated by classifying in the (S_{p},Δ) space the complexity of several benchmark dissipative and conservative dynamical systems. As an application, we show how the metric can be used as a powerful biomarker for different cardiac pathologies and to distinguish the dynamical complexity of two electrochemical dissolutions.
Collapse
Affiliation(s)
- Christophe Letellier
- Rouen Normandie University-CORIA, Avenue de l'Université, F-76800 Saint-Etienne du Rouvray, France
| | - I Leyva
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain and Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - I Sendiña-Nadal
- Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain and Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain
| |
Collapse
|
4
|
Mangiarotti S, Huc M. Can the original equations of a dynamical system be retrieved from observational time series? CHAOS (WOODBURY, N.Y.) 2019; 29:023133. [PMID: 30823741 DOI: 10.1063/1.5081448] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2018] [Accepted: 02/01/2019] [Indexed: 06/09/2023]
Abstract
The aim of the present work is to investigate the possibility to retrieve the original sets of dynamical equations directly from observational time series when all the system variables are observed. Time series are generated from chosen dynamical systems, and the global modeling technique is applied to obtain optimal models of parsimonious structure from these time series. The obtained models are then compared to the original equations to investigate if the original equations can be retrieved. Twenty-seven systems are considered in the study. The Rössler system is first used to illustrate the procedure and then to test the robustness of the approach under various conditions, varying the initial conditions, time series length, dynamical regimes, subsampling (and resampling), measurement noise, and dynamical perturbations. The other 26 systems (four rational ones included) of various algebraic structures, sizes, and dimensions are then considered to investigate the generality of the approach.
Collapse
Affiliation(s)
- Sylvain Mangiarotti
- Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-INRA-IRD, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France
| | - Mireille Huc
- Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-INRA-IRD, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France
| |
Collapse
|
5
|
Kevrekidis YG, Kiss IZ, Kori H, Krischer K. Introduction to Focus Issue: In Memory of John L. Hudson: Self-Organized Structures in Chemical Systems. CHAOS (WOODBURY, N.Y.) 2018; 28:045001. [PMID: 31906653 DOI: 10.1063/1.5033452] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Affiliation(s)
- Yannis G Kevrekidis
- Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA
| | - István Z Kiss
- Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, USA
| | - Hiroshi Kori
- Department of Information Sciences, Ochanomizu University, Tokyo 112-8610, Japan
| | - Katharina Krischer
- Department of Physics, Technical University of Munich, James-Franck-Str. 1, D-85748 Garching, Germany
| |
Collapse
|