Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion
El tema principal de la tesis es la identificación basada en datos de la región de atracción (ROA por sus siglas en ingles) de puntos de equilibrio asintóticamente estables. Aunque esta es la principal contribución computacional, la mayoría del trabajo de la tesis constituye en satisfacer las condic...
- Autores:
-
García Tenorio, Camilo
- Tipo de recurso:
- Doctoral thesis
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/80692
- Palabra clave:
- 620 - Ingeniería y operaciones afines
Region of Attraction
Koopman Operator
Extended Dynamic Mode Decomposition
Anaerobic Digestion
Región de Atración
Operador de Koopman
Digestión Anaerobia
Région d’attraction
Opérateur de Koopman
Digestion Anaérobie
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
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Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| dc.title.translated.eng.fl_str_mv |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| title |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| spellingShingle |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion 620 - Ingeniería y operaciones afines Region of Attraction Koopman Operator Extended Dynamic Mode Decomposition Anaerobic Digestion Región de Atración Operador de Koopman Digestión Anaerobia Région d’attraction Opérateur de Koopman Digestion Anaérobie |
| title_short |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| title_full |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| title_fullStr |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| title_full_unstemmed |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| title_sort |
Contribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestion |
| dc.creator.fl_str_mv |
García Tenorio, Camilo |
| dc.contributor.advisor.none.fl_str_mv |
Mojica-Nava, Eduardo |
| dc.contributor.author.none.fl_str_mv |
García Tenorio, Camilo |
| dc.contributor.researchgroup.spa.fl_str_mv |
Programa de Investigacion sobre Adquisicion y Analisis de Señales Paas-Un |
| dc.subject.ddc.spa.fl_str_mv |
620 - Ingeniería y operaciones afines |
| topic |
620 - Ingeniería y operaciones afines Region of Attraction Koopman Operator Extended Dynamic Mode Decomposition Anaerobic Digestion Región de Atración Operador de Koopman Digestión Anaerobia Région d’attraction Opérateur de Koopman Digestion Anaérobie |
| dc.subject.proposal.eng.fl_str_mv |
Region of Attraction Koopman Operator Extended Dynamic Mode Decomposition Anaerobic Digestion |
| dc.subject.proposal.spa.fl_str_mv |
Región de Atración Operador de Koopman Digestión Anaerobia |
| dc.subject.proposal.fra.fl_str_mv |
Région d’attraction Opérateur de Koopman Digestion Anaérobie |
| description |
El tema principal de la tesis es la identificación basada en datos de la región de atracción (ROA por sus siglas en ingles) de puntos de equilibrio asintóticamente estables. Aunque esta es la principal contribución computacional, la mayoría del trabajo de la tesis constituye en satisfacer las condiciones subyacentes para lograr aproximar la ROA\@. Para obtener una aproximación precisa basada en datos del ROA en sistemas con múltiples puntos fijos o de equilibrio es necesario completar apropiadamente una serie de pasos partiendo de algunas trayectorias del sistema, i.e., asumiendo que no hay ningún acceso al modelo de ecuaciones diferenciales. La condición principal es una aproximación precisa del operador de Koopman ya que proporciona un grupo de eigenfunciones donde una composición particular de las mismas proporciona otra eingenfunción no trivial con eigenvalor asociado unitario. La principal propiedad de esta eingenfunción es que proporciona el ``manifold'' estable de los puntos de silla en el perímetro de la ROA\@. Por esta razón, para todo este procedimiento de trabajo, también es necesario tener una aproximación de la ubicación y estabilidad de los puntos fijos del sistema, recordando que la única entrada al algoritmo es un conjunto de trayectorias del sistema. Por consiguiente, el algoritmo debe ser una aproximación apropiada de las dinámicas del sistema y ser capaz de proporcionar una ecuación de diferencia que pueda proporcionar la ubicación y estabilidad de puntos fijos basándose en el análisis tradicional de sistemas no lineales. El algoritmo que tiene el potencial de alcanzar estos requisitos es el ``extended dynamics mode decomposition'' (EDMD), en donde la mayor parte del trabajo de esta tesis se enfoca en transformar el potencial que tiene este algoritmo en una realidad. En su mayor parte, el enfoque del desarrollo es sobre la estabilidad numérica del algoritmo, reduciendo el esfuerzo computacional y pasos necesarios para llevar a cabo la aproximación. Técnicos como la reducción de los polinomios ortogonales bas\'andose en las casi normas p-q y la eliminaci\'on de elementos polinomiales segur su error, aseguran que bases mas pequeños realicen las aproximaciones garantizando la existencia de soluciones debido a la propiedad de ortogonalidad. Mejoras como la recuperaron del estado a troves de la función inversa de los polinomios de una sola variable reducen el numero necesario de inversiones de matrices. Finalmente, las expansiones a priori del estado con funciones trigonométricas arbitrarias o cualquier otro tipo de funciones elementales, expanden los tipos posibles de sistemas que el algoritmo puede manejar. Como consecuencia de estas mejoras, la tesis logra los objetivos originales de analizar sistemas y controlar conjuntos de sistemas interconectados en un contexto basado en datos. Finalmente, la aplicación principal de la tesis es el análisis de la ROA en el proceso de digestión anaerobia, donde el análisis del fenómeno de multi-estabilidad que garantiza la operación correcta del reactor es de suma importancia. |
| publishDate |
2021 |
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2021-11-18T00:16:19Z |
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2021-11-18T00:16:19Z |
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2021 |
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Trabajo de grado - Doctorado |
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info:eu-repo/semantics/doctoralThesis |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/80692 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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eng |
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eng |
| dc.relation.references.spa.fl_str_mv |
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Vector Lyanpunov Functions. Journal of the Society for Industrial and Applied Mathematics Series A Control, 1(1):32–34, jan 1962. ISSN 0887-4603. Olivier Bernard, Zakaria Hadj-Sadok, Denis Dochain, Antoine Genovesi, and Jean Philippe Steyer. Dynamical model development and parameter identification for an anaerobic wastewater treatment process. Biotechnology and Bioengineering, 75(4):424–438, 2001. Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, and J. Nathan Kutz. Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control. PLoS ONE, 11(2):1–19, 2016a. Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15):3932–3937, apr 2016b. Marko Budišic, Ryan Mohr, and Igor Mezic. Applied koopmanism. Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4): 47510, 2012. Vijaysekhar Chellaboina, Sanjay Bhat, Wassim Haddad, and Dennis Bernstein. Modeling and analysis of mass-action kinetics. IEEE Control Systems Magazine, 29(4):60–78, aug 2009. H D Chiang and L F C Alberto. Stability Regions of Nonlinear Dynamical Systems: Theory, Estimation, and Applications. Cambridge University Press, 2015. ISBN 9781316374320. Edson A. Coayla-Teran, S. E A Mohammed, and P. R C Ruffino. Hartman-Grobman theorems along hyperbolic stationary trajectories. Discrete and Continuous Dynamical Systems, 17(2):281–292, 2007. Federico Cuesta, Francisco Gordillo, Javier Aracil, and Anibal Ollero. Stability analysis of nonlinear multivariable Takagi-Sugeno fuzzy control systems. IEEE Transactions on Fuzzy Systems, 7(5):508–520, 1999. David Di Ruscio. Model Predictive Control with Integral Action: A simple MPC algorithm. Modeling, Identification and Control, 34(3): 119–129, 2013. Georgi M Dimirovski. 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In 2016 IEEE Conference on Control Applications (CCA), pages 1098–1103. IEEE, sep 2016. ISBN 978-1-5090-0755-4. Camilo Garcia-Tenorio, Duvan Tellez-Castro, Eduardo Mojica-Nava, and Alain Vande Wouwer. Analysis of a Class of Hyperbolic Systems via Data-Driven Koopman Operator. In International Conference on System Theory, Control and Computing (ICSTCC), pages 566–571, 2019. Hugues Garnier and LiupingWang, editors. Identification of Continuoustime Models from Sampled Data. Advances in Industrial Control. Springer-Verlag London, London, 1 edition, 2008. Peter Giesl and Sigurdur Hafstein. Review on computational methods for Lyapunov functions. Discrete and Continuous Dynamical Systems- Series B, 20(8):2291–2331, 2015. L. Grujic and D. Siljak. Asymptotic stability and instability of largescale systems. IEEE Transactions on Automatic Control, 18(6):636– 645, dec 1973. ISSN 0018-9286. Wassim M Haddad and VijaySekhar Chellaboina. Nonlinear dynamical systems and control : a Lyapunov-based approach. Princeton University Press, 2008. ISBN ISBN-13: 978-0-6911-3329-4. P. Ioannou. Decentralized adaptive control of interconnected systems. IEEE Transactions on Automatic Control, 31(4):291–298, apr 1986. ISSN 0018-9286. E. Kaiser, J. N. Kutz, and S. L. Brunton. Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474(2219), 2018. Hassan K Khalil. Nonlinear systems. Prentice Hall, 3rd edition, 2002. Stefan Klus, Péter Koltai, and Christof Schütte. On the numerical approximation of the Perron-Frobenius and Koopman operator. Journal of Computational Dynamics, 3(1):51–79, 2016. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw. Hypergeometric Orthogonal Polynomials and Their q-Analogues. Springer Monographs in Mathematics. Springer Berlin Heidelberg, Berlin, Heidelberg, 2010. Katerina Konakli and Bruno Sudret. Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions. Journal of Computational Physics, 321:1144–1169, sep 2016a. Katerina Konakli and Bruno Sudret. Reliability analysis of highdimensional models using low-rank tensor approximations. Probabilistic Engineering Mechanics, 46:18–36, 2016b. Bernard O. Koopman. Hamiltonian Systems and Transformation in Hilbert Space. Proceedings of the National Academy of Sciences, 17 (5):315–318, may 1931. Milan Korda and Igor Mezic. On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator. Journal of Nonlinear Science, 28(2):687–710, apr 2018a. Milan Korda and Igor Mezic. Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control. Automatica, 93:149–160, 2018b. Yueheng Lan and Igor Mezic. Linearization in the large of nonlinear systems and Koopman operator spectrum. Physica D: Nonlinear Phenomena, 242(1):42–53, 2013. A Lasota and James A. Yorke. Exact dynamical systems and the frobenius-perron operator. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 273(1):375–384, 1982. Qianxiao Li, Felix Dietrich, Erik M. Bollt, and Ioannis G. Kevrekidis. Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the koopman operator. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27 (10):103111, 2017. A. Linnemann. Decentralized control of dynamically interconnected systems. IEEE Transactions on Automatic Control, 29(11):1052–1054, nov 1984. ISSN 0018-9286. Ludovic Mailleret, Olivier Bernard, and J. P. Steyer. Robust regulation of anaerobic digestion processes. Water Science and Technology, 48(6): 87–94, 2003. Anirudha Majumdar, Amir Ali Ahmadi, and Russ Tedrake. Control and verification of high-dimensional systems with dsos and sdsos programming. 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Discrete & Continuous Dynamical Systems - B, 20:2291, 2015. Joshua L. Proctor, Steven L. Brunton, and J. Nathan Kutz. Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems, 15(1):142–161, 2016. Nicanor Quijano, Carlos Ocampo-Martinez, Julian Barreiro-Gomez, German Obando, Andres Pantoja, and Eduardo Mojica-Nava. The Role of Population Games and Evolutionary Dynamics in Distributed Control Systems: The Advantages of Evolutionary Game Theory. IEEE Control Systems, 37(1):70–97, feb 2017. Lorenzo Rosasco, Ernesto De Vito, Andrea Caponnetto, Michele Piana, and Alessandro Verri. Are Loss Functions All the Same? Neural Computation, 16(5):1063–1076, 2004. M. Sbarciog, M. Loccufier, and E. Noldus. Determination of appropriate operating strategies for anaerobic digestion systems. Biochemical Engineering Journal, 51(3):180–188, 2010a. Mihaela Sbarciog, Mia Loccufier, and Erik Noldus. The estimation of stability boundaries for an anaerobic digestion system. IFAC Proceedings Volumes, 43(6):359 – 364, 2010b. ISSN 1474-6670. 11th IFAC Symposium on Computer Applications in Biotechnology. Mihaela Sbarciog, Mia Loccufier, and Alain Vande Wouwer. On the optimization of biogas production in anaerobic digestion systems*. IFAC Proceedings Volumes, 44(1):7150 – 7155, 2011. ISSN 1474-6670. 18th IFAC World Congress. Peter J. Schmid. Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, 656:5–28, aug 2010. M. Erol Sezer and Özay Hüseyin. Stabilization of Linear Time-Invariant Interconnected Systems Using Local State Feedback. IEEE Transactions on Systems, Man, and Cybernetics, 8(10):751–756, 1978. ISSN 0018-9472. Shuiwen Shen, Giuliano C Premier, Alan Guwy, and Richard Dinsdale. Bifurcation and stability analysis of an anaerobic digestion model. Nonlinear Dynamics, 48(4):391–408, 2007. Shih-Ho Wang and E. Davison. On the stabilization of decentralized control systems. IEEE Transactions on Automatic Control, 18(5):473–478, oct 1973. ISSN 0018-9286. Dragoslav D. Siljak. Stability of Large-Scale Systems under Structural Perturbations. IEEE Transactions on Systems, Man, and Cybernetics, 2(5):657–663, 1972. ISSN 0018-9472. Dragoslav D Siljak. Decentralized Control of Complex Systems. Mathematics in science and engineering. Academic Press, 1991. S. J. Skar, R. K. Miller, and A. N. Michel. On Nonexistence of Limit Cycles in Interconnected Systems. IEEE Transactions on Automatic Control, 26(3):669–676, 1981. Bruno Sudret. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering and System Safety, 93(7):964–979, 2008. Eric Walter and Luc Pronzato. Identification of parametric models from experimental data. Springer-Verlag London, London, 1 edition, 1997. Jan C. Willems. Dissipative dynamical systems Part II: Linear systems with quadratic supply rates. Archive for Rational Mechanics and Analysis, 45(5):352–393, 1972a. JanC. Willems. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis, 45(5):321–351, 1972b. Matthew O. Williams, Ioannis G Kevrekidis, and Clarence W Rowley. A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition. Journal of Nonlinear Science, 25(6): 1307–1346, dec 2015. Matthew O. Williams, Clarence W. Rowley, and Ioannis G. Kevrekidis. A kernel-based method for data-driven koopman spectral analysis. Journal of Computational Dynamics, 2(2):247–265, may 2016. ISSN 2158- 2491. |
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Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Mojica-Nava, Eduardoe4a1a8ad2ab3b2c45a8785177a841de1600García Tenorio, Camilo3cce8b1d5fc4f9a2938970337cdd0016Programa de Investigacion sobre Adquisicion y Analisis de Señales Paas-Un2021-11-18T00:16:19Z2021-11-18T00:16:19Z2021https://repositorio.unal.edu.co/handle/unal/80692Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/El tema principal de la tesis es la identificación basada en datos de la región de atracción (ROA por sus siglas en ingles) de puntos de equilibrio asintóticamente estables. Aunque esta es la principal contribución computacional, la mayoría del trabajo de la tesis constituye en satisfacer las condiciones subyacentes para lograr aproximar la ROA\@. Para obtener una aproximación precisa basada en datos del ROA en sistemas con múltiples puntos fijos o de equilibrio es necesario completar apropiadamente una serie de pasos partiendo de algunas trayectorias del sistema, i.e., asumiendo que no hay ningún acceso al modelo de ecuaciones diferenciales. La condición principal es una aproximación precisa del operador de Koopman ya que proporciona un grupo de eigenfunciones donde una composición particular de las mismas proporciona otra eingenfunción no trivial con eigenvalor asociado unitario. La principal propiedad de esta eingenfunción es que proporciona el ``manifold'' estable de los puntos de silla en el perímetro de la ROA\@. Por esta razón, para todo este procedimiento de trabajo, también es necesario tener una aproximación de la ubicación y estabilidad de los puntos fijos del sistema, recordando que la única entrada al algoritmo es un conjunto de trayectorias del sistema. Por consiguiente, el algoritmo debe ser una aproximación apropiada de las dinámicas del sistema y ser capaz de proporcionar una ecuación de diferencia que pueda proporcionar la ubicación y estabilidad de puntos fijos basándose en el análisis tradicional de sistemas no lineales. El algoritmo que tiene el potencial de alcanzar estos requisitos es el ``extended dynamics mode decomposition'' (EDMD), en donde la mayor parte del trabajo de esta tesis se enfoca en transformar el potencial que tiene este algoritmo en una realidad. En su mayor parte, el enfoque del desarrollo es sobre la estabilidad numérica del algoritmo, reduciendo el esfuerzo computacional y pasos necesarios para llevar a cabo la aproximación. Técnicos como la reducción de los polinomios ortogonales bas\'andose en las casi normas p-q y la eliminaci\'on de elementos polinomiales segur su error, aseguran que bases mas pequeños realicen las aproximaciones garantizando la existencia de soluciones debido a la propiedad de ortogonalidad. Mejoras como la recuperaron del estado a troves de la función inversa de los polinomios de una sola variable reducen el numero necesario de inversiones de matrices. Finalmente, las expansiones a priori del estado con funciones trigonométricas arbitrarias o cualquier otro tipo de funciones elementales, expanden los tipos posibles de sistemas que el algoritmo puede manejar. Como consecuencia de estas mejoras, la tesis logra los objetivos originales de analizar sistemas y controlar conjuntos de sistemas interconectados en un contexto basado en datos. Finalmente, la aplicación principal de la tesis es el análisis de la ROA en el proceso de digestión anaerobia, donde el análisis del fenómeno de multi-estabilidad que garantiza la operación correcta del reactor es de suma importancia.Le sujet principal de cette thèse de doctorat est la détermination de la région d’attraction des points d’équilibre asymptotiquement stables d’un système dynamique non linéaire. Cette détermination est réalisée numériquement sans avoir recours à la connaissance explicite d’un modèle mathématique du système, mais sur base d’un ensemble de trajectoires de celui-ci. Ces trajectoires peuvent être soit collectées expérimentalement au départ du système physique, soit obtenues par simulation numérique d’un modèle de forme arbitraire qui serait déjà disponible mais dont la structure ne doit pas être connue. A cette fin, le système dynamique non linéaire est représenté par un opérateur de Koopman. Cet opérateur est linéaire mais de dimension infinie et en pratique il est nécessaire de procéder à une approximation en dimension finie. Celle-ci est fournie par la méthode ``extended dynamic mode decomposition'' (EDMD), qui permet de construire une matrice de Koopman et de calculer les fonctions propres et les valeurs propres associées à celle-ci. En particulier, les fonctions propres associées à la valeur propre unitaire apparaissent comme étant particulièrement utiles. Ces fonctions propres permettent en effet de déterminer les « manifolds » stables des points selle qui se trouvent à la frontière de la région d’attraction. Outre cette détermination des points d’équilibre et de leur région d’attraction, ce travaille de thèse s’intéresse aux aspects numériques de la méthode EDMD, notamment le choix de bases polynomiales performantes et la réduction de l’ordre de l’approximation en utilisant des techniques telles que les quasi-normes p-q. Le choix des bases polynomiales est aussi important pour la représentation des entrées de commande des systèmes ou de leur couplages, dans le contexte de l’interconnexion de plusieurs systèmes dynamiques. Les dernières considérations théoriques de ce travail concernent donc les systèmes avec des entrées de commande et la possibilité de développer une commande prédictive en relation avec la représentation de Koopman. Enfin ce travail contient plusieurs illustrations dont une application à la détermination des points d’équilibre et des régions d’attraction du processus de digestion anaérobie, ainsi qu’un pendule inversé approximé par la méthode EDMD utilisant des fonctions de base trigonométriques, ainsi que des oscillateurs de Duffing couplés.The main topic of the thesis is the data-driven identification of the region of attraction (ROA) of asymptotically stable equilibrium points. Although this is the main computational contribution, satisfying the underlying conditions to make this possible constitutes most of the work of the thesis. To achieve an accurate data-driven approximation of the ROA in systems with multiple fixed or equilibrium points it is necessary to properly complete a series of steps parting from some trajectories of the system, i.e., assuming there is no access to the differential or difference model equation. The main condition is an accurate approximation of the Koopman operator because it provides a set of eigenfunctions where a particular composition of them gives another non-trivial eigenfunction with an associated eigenvalue that is unitary. The main property of this eigenfunction is that it gives the stable manifold of saddle points in the boundary of the ROA, where this stable manifold is in fact, the actual boundary of the ROA\@. Therefore, for this whole procedure to work, it also necessary to have an approximation of the location and stability of the fixed points of the system, recalling that the only input to the algorithm is a set of trajectories of the system. Consequently, the algorithm must be an appropriate approximation of the dynamics of the system and be able to provide a difference equation able to give the location and stability of fixed points upon further traditional non-linear system analysis. The algorithm that has the potential to achieve these requisites is the extended dynamics mode decomposition (EDMD) algorithm, where most of the work of this thesis focuses in transforming the potential into actual. For the most part, the development focus is on the numerical stability of the algorithm, reducing the computational effort and necessary steps to perform the approximation. Techniques such as the p-q-quasi norm reduction of orthogonal polynomials and polynomial element elimination according to its error, ensures that smaller bases perform the approximations while guaranteeing the existence of solutions because of the orthogonality property. Improvements such as the recovery of the state via the inverse of univariate order-one polynomials reduce the number of necessary matrix inversions. Finally, a priori expansions of the state with arbitrary trigonometric functions or any other kind of elemental functions, expand the possible types of systems that the algorithm can handle. As a consequence of these improvements, the thesis achieves the original objectives of analyzing systems and controlling sets of interconnected systems in a data-driven context. Finally, the main application of the thesis is the analysis of the ROA to the anaerobic digestion process, where the analysis of multi-stability phenomena that guarantees the proper operation of the reactor is of paramount importance. (Text taken from source)DoctoradoDoctor en Ingenieríaxxviii, 148 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ingeniería - Doctorado en Ingeniería - Ingeniería Mecánica y MecatrónicaDepartamento de Ingeniería Mecánica y MecatrónicaFacultad de IngenieríaBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá620 - Ingeniería y operaciones afinesRegion of AttractionKoopman OperatorExtended Dynamic Mode DecompositionAnaerobic DigestionRegión de AtraciónOperador de KoopmanDigestión AnaerobiaRégion d’attractionOpérateur de KoopmanDigestion AnaérobieContribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestionContribution to the computation of regions of attraction of nonlinear systems based on the extended dynamic mode decomposition - Application to the anaerobic digestionTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDAmir Ali Ahmadi and Pablo A. 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ISSN 2158- 2491.Colciencias - ColfuturoPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/80692/1/license.txt8153f7789df02f0a4c9e079953658ab2MD51U.FT.09.006.004 Licencia y autorización para publicación de obras en el repositorio institucional UN v3.pdfU.FT.09.006.004 Licencia y autorización para publicación de obras en el repositorio institucional UN v3.pdfapplication/pdf226615https://repositorio.unal.edu.co/bitstream/unal/80692/5/U.FT.09.006.004%20Licencia%20y%20autorizaci%c3%b3n%20para%20publicaci%c3%b3n%20de%20obras%20en%20el%20repositorio%20institucional%20UN%20v3.pdfc613149b24e80fa95072d8f302a7ed35MD55ORIGINAL1020722818.2021.pdf1020722818.2021.pdfDocumento de Tesisapplication/pdf5639049https://repositorio.unal.edu.co/bitstream/unal/80692/4/1020722818.2021.pdfcc45b3445f1232fcfe037884dbf8299aMD54THUMBNAIL1020722818.2021.pdf.jpg1020722818.2021.pdf.jpgGenerated 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