Data Driven Modeling For Analysis And Control Of Dynamical Systems
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Author | : Steven L. Brunton |
Publisher | : Cambridge University Press |
Total Pages | : 615 |
Release | : 2022-05-05 |
Genre | : Computers |
ISBN | : 1009098489 |
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Author | : J. Nathan Kutz |
Publisher | : SIAM |
Total Pages | : 241 |
Release | : 2016-11-23 |
Genre | : Science |
ISBN | : 1611974496 |
Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.
Author | : Damien Gueho |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : |
This dissertation advances the understanding of data-driven modeling and delivers tools to pursue the ambition of complete unsupervised identification of dynamical systems. From measured data only, the proposed framework consists of a series of modules to derive accurate mathematical models for the state prediction of a wide range of linear and nonlinear dynamical systems. Identified models are constructed to be of low complexity and amenable for analysis and control. This developed framework provides a unified mathematical structure for the identification of nonlinear systems based on the Koopman operator. A main contribution of this dissertation is to introduce the concept of time-varying Koopman operator for accurate modeling of dynamical systems in a given domain around a reference trajectory. Subspace identification methods coupled with sparse approximation techniques deliver accurate models both in the continuous and discrete time domains. This allows for perfect reconstruction of several classes of nonlinear dynamical systems, from the chaotic behavior of the Lorenz oscillator to identifying the Newton's law of gravitation. The connection between the Koopman operator and higher-order state transition matrices (STMs) is explicitly discussed. It is shown that subspace methods based on the Koopman operator are able to accurately identify the linear time varying model for the propagation of higher order STMs when polynomial basis are used as lifting functions. Such algorithms are validated on a wide range of nonlinear dynamical systems of varying complexity and are proven to be very effective on nonlinear systems of higher dimension where traditional methods either fail or perform poorly. Applications include model-order reduction in hypersonic aerothermoelasticity and reduced-order dynamics in a high-dimensional finite-element model of the Von Kàrmàn Beam. Numerical simulation results confirm better prediction accuracy by several orders of magnitude using this framework. Additionally, a major objective of this research is to enhance the field of data-driven uncertainty quantification for nonlinear dynamical systems. Uncertainty propagation through nonlinear dynamics is computationally expensive. Conventional approaches focus on finding a reduced order model to alleviate the computational complexity associated with the uncertainty propagation algorithms. This dissertation exploits the fact that the moment propagation equations form a linear time-varying (LTV) system and use system theory to identify this LTV system from data only. By estimating and propagating higher-order moments of an initial probability density function, two new approaches are presented and compared to analytical and quadrature-based methods for estimating the uncertainty associated with a system's states. In all test cases considered in this dissertation, a newly-introduced indirect method using a time-varying subspace identification technique jointly with a quadrature method achieved the best results. This dissertation also extends the Koopman operator theoretic framework for controlled dynamical systems and offers a global overview of bilinear system identification techniques as well as perspectives and advances for bilinear system identification. Nonlinear dynamics with a control action are approximated as a bilinear system in a higher-dimensional space, leading to increased accuracy in the prediction of the system's response. In the same context, a data-driven parameter sensitivity method is developed using bilinear system identification algorithms. Finally, this dissertation investigates new ways to alleviate the effect of noise in the data, leading to new algorithms with data-correlations and rank optimization for optimal subspace identification.
Author | : J. Nathan Kutz |
Publisher | : SIAM |
Total Pages | : 241 |
Release | : 2016-11-23 |
Genre | : Science |
ISBN | : 161197450X |
Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.
Author | : Wang Jianhong |
Publisher | : CRC Press |
Total Pages | : 363 |
Release | : 2023-03-31 |
Genre | : Computers |
ISBN | : 1000860272 |
A key challenge in science and engineering is to provide a quantitative description of the systems under investigation, leveraging the noisy data collected. Such a description may be a complete mathematical model or a mechanism to return controllers corresponding to new, unseen inputs. Recent advances in the theories are described in detail, along with their applications in engineering. The book aims to develop model-free system analysis and control strategies, i.e., data-driven control from theoretical analysis and engineering applications based only on measured data. The study aims to develop system identification, and combination in advanced control theory, i.e., data-driven control strategy as system and controller are generated from measured data directly. The book reviews the development of system identification and its combination in advanced control theory, i.e., data-driven control strategy, as they all depend on measured data. Firstly, data-driven identification is developed for the closed-loop, nonlinear system and model validation, i.e., obtaining model descriptions from measured data. Secondly, the data-driven idea is combined with some control strategies to be considered data-driven control strategies, such as data-driven model predictive control, data-driven iterative tuning control, and data-driven subspace predictive control. Thirdly data-driven identification and data-driven control strategies are applied to interested engineering. In this context, the book provides algorithms to perform state estimation of dynamical systems from noisy data and some convex optimization algorithms through identification and control problems.
Author | : Steven L. Brunton |
Publisher | : Cambridge University Press |
Total Pages | : 495 |
Release | : 2019-02-28 |
Genre | : Computers |
ISBN | : 1108422098 |
This beginning graduate textbook teaches data science and machine learning methods for modeling, prediction, and control of complex systems.
Author | : Xiaolin Hu |
Publisher | : World Scientific |
Total Pages | : 329 |
Release | : 2023-03-21 |
Genre | : Computers |
ISBN | : 9811267197 |
This comprehensive book systematically introduces Dynamic Data Driven Simulation (DDDS) as a new simulation paradigm that makes real-time data and simulation model work together to enable simulation-based prediction/analysis.The text is significantly dedicated to introducing data assimilation as an enabling technique for DDDS. While data assimilation has been studied in other science fields (e.g., meteorology, oceanography), it is a new topic for the modeling and simulation community.This unique reference text bridges the two study areas of data assimilation and modelling and simulation, which have been developed largely independently from each other.
Author | : Peter Benner |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 346 |
Release | : 2021-11-08 |
Genre | : Mathematics |
ISBN | : 3110497719 |
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.
Author | : Carlo Novara |
Publisher | : Control, Robotics and Sensors |
Total Pages | : 300 |
Release | : 2019-09 |
Genre | : Technology & Engineering |
ISBN | : 1785617125 |
Using important examples, this book showcases the potential of the latest data-based and data-driven methodologies for filter and control design. It discusses the most important classes of dynamic systems, along with the statistical and set membership analysis and design frameworks.
Author | : Ricardo Zavala Yoe |
Publisher | : Springer Science & Business Media |
Total Pages | : 164 |
Release | : 2008-05-30 |
Genre | : Computers |
ISBN | : 3540787348 |
The Behavioral Approach for systems and control deals directly with the solution of the differential equations which represent the system. This book reviews this approach and offers new theoretic results. The programs and algorithms are MATLAB based.