Download or read book Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Dynamical Systems written by Allen Russell LaBryer and published by . This book was released on 2012 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modeling Simulation and Control of Nonlinear Engineering Dynamical Systems written by Jan Awrejcewicz and published by Springer Science & Business Media. This book was released on 2008-12-26 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the invited papers presented at the 9th International Conference "Dynamical Systems — Theory and Applications" held in Lódz, Poland, December 17-20, 2007, dealing with nonlinear dynamical systems. The conference brought together a large group of outstanding scientists and engineers, who deal with various problems of dynamics encountered both in engineering and in daily life. Topics covered include, among others, bifurcations and chaos in mechanical systems; control in dynamical systems; asymptotic methods in nonlinear dynamics; stability of dynamical systems; lumped and continuous systems vibrations; original numerical methods of vibration analysis; and man-machine interactions. Thus, the reader is given an overview of the most recent developments of dynamical systems and can follow the newest trends in this field of science. This book will be of interest to to pure and applied scientists working in the field of nonlinear dynamics.

Download or read book Spatio Temporal Modeling of Nonlinear Distributed Parameter Systems written by Han-Xiong Li and published by Springer Science & Business Media. This book was released on 2011-02-24 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein systems and their identifi cation methods. Then, the traditional Volterra model is extended to DPS, which results in the spatio-temporal Volterra model and its identification algorithm. All these methods are based on linear time/space separation. Sometimes, the nonlinear time/space separation can play a better role in modeling of very complex processes. Thus, a nonlinear time/space separation based neural modeling is also presented for a class of DPS with more complicated dynamics. Finally, all these modeling approaches are successfully applied to industrial thermal processes, including a catalytic rod, a packed-bed reactor and a snap curing oven. The work is presented giving a unifi ed view from time/space separation. The book also illustrates applications to thermal processes in the electronics packaging and chemical industry. This volume assumes a basic knowledge about distributed parameter systems, system modeling and identifi cation. It is intended for researchers, graduate students and engineers interested in distributed parameter systems, nonlinear systems, and process modeling and control.

Download or read book Data driven Reduced order Modeling for Symmetrical Systems written by Ariana Mendible and published by . This book was released on 2021 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatiotemporal dynamical systems are ubiquitous across all areas of science and engineering. While some systems of interest can be studied through first-principles governing equations, often, the underlying dynamics are unknown. Furthermore, even for problems where equations are known, analytical solutions are rare. Computational solutions are then plagued by issues of nonlinearity, multiple relevant scales of time and space, chaos, and high-dimensionality. When parametric studies are needed, these simulations become prohibitively expensive, even under the most advance computational architectures. Often, even the most complex dynamical systems contain inherent low-dimensional coherent structure. Reduced-order models (ROMs) attempt to ease the computation burden of such simulations by uncovering this low-rank subspace, reducing the overall size of such models while retaining the critical dynamics. Many ROMs leverage the proper orthogonal decomposition (POD) to produce a linear dimensionality reduction, where a dominant set of correlated modes provide a subspace in which to project the dynamics. Dimensionality reduction techniques then enable downstream tasks such as prediction, estimation, and low-latency control. However, many dimensionality reduction techniques rely on separation of time and space variables. This assumption does not hold in systems with underlying symmetry, because the time and space variables are inherently coupled. Namely translation, or traveling waves, scaling, and rotation inhibit the effectiveness of dimensionality reduction techniques. The focus of this thesis is to develop an approach to make spatiotemporal systems with underlying symmetry amenable to traditional ROM architectures. Three objectives are addressed (1) developing a method to address translations in one spatial dimension, (2) demonstrating the effectiveness of such a method on complex dynamics in experimental data, and (3) expanding the method to approach higher-dimensional data with scaling symmetries. The Unsupervised Traveling Wave Identification with Shifting and Truncation (UnTWIST) method can be applied to pure data, yielding interpretable models for wave speeds. Several examples are explored, showing that even for systems with multiple waves, non-constant wave speeds, and nonlinear wave phenomenon, UnTWIST enables the use of traditional methods like POD for dimensionality reduction. Further, the method is demonstrated on experimental data from a rotating detonation engine, presenting complex nonlinear dynamics. UnTWIST enables the discovery of interpretable linear and nonlinear models for the traveling detonation speeds, and yields meaningful spatial modes to describe the wave shapes. Lastly, the method is augmented to accommodate higher-dimensional data and an arbitrary number of symmetries. Two-dimensional data with a scaling symmetry are investigated, and accurate models are found to improve the dimensionality reductions. Lastly, limitations to the method in the presence of interacting waves are explored, and improvements and expansions are discussed.

Download or read book Nonlinear Time Scale Systems in Standard and Nonstandard Forms written by Anshu Narang-Siddarth and published by SIAM. This book was released on 2014-01-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces key concepts for systematically controlling engineering systems that possess interacting phenomena occurring at widely different speeds. The aim is to present the reader with control techniques that extend the benefits of model reduction of singular perturbation theory to a larger class of nonlinear dynamical systems. New results and relevant background are presented through insightful examples that cover a wide range of applications from different branches of engineering. This book is unique because it: presents a new perspective on existing control methods and thus broadens their application to a larger class of nonlinear dynamical systems; discusses general rather than problem-specific developments to certain applications or disciplines in order to provide control engineers with useful analytical tools ; addresses new control problems using singular perturbation methods, including closed-form results for control of nonminimum phase systems.

Download or read book Linear Time varying Approximations to Nonlinear Dynamical Systems written by Maria Tomas-Rodriguez and published by Springer Science & Business Media. This book was released on 2010-02-04 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Download or read book Regularity and Stochasticity of Nonlinear Dynamical Systems written by Dimitri Volchenkov and published by Springer. This book was released on 2017-07-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems. This book covers integro-differential equation solvability, Poincare recurrences in ergodic systems, orientable horseshoe structure, analytical routes of periodic motions to chaos, grazing on impulsive differential equations, from chaos to order in coupled oscillators, and differential-invariant solutions for automorphic systems, inequality under uncertainty.

Download or read book Continuous Time Dynamical Systems written by B. M. Mohan and published by CRC Press. This book was released on 2017-11-22 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents the developments in problems of state estimation and optimal control of continuous-time dynamical systems using orthogonal functions since 1975. It deals with both full and reduced-order state estimation and problems of linear time-invariant systems. It also addresses optimal control problems of varieties of continuous-time systems such as linear and nonlinear systems, time-invariant and time-varying systems, as well as delay-free and time-delay systems. Content focuses on development of recursive algorithms for studying state estimation and optimal control problems"--

Download or read book Model Reduction of Nonlinear Dynamical Systems by System theoretic Methods written by Maria Cruz Varona and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A New Framework for Model Reduction of Complex Nonlinear Dynamical Systems written by Shahab Ilbeigi and published by . This book was released on 2017 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Regulation of Nonlinear Dynamical Systems on a Finite Interval written by A. P. Willemstein and published by . This book was released on 1976 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Effect of Problem Perturbations on Nonlinear Dynamical Systems and Their Reduced Order Models written by and published by . This book was released on 2005 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: 'What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?' and 'To what extent does the reduced order model capture this effect?'

Download or read book A Trajectory Piecewise linear Approach to Model Order Reduction of Nonlinear Dynamical Systems written by Michał Jerzy Rewieński and published by . This book was released on 2003 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) Finally, we present projection schemes which result in improved accuracy of the reduced order TPWL models, as well as discuss approaches leading to guaranteed stable and passive TPWL reduced-order models.

Download or read book Simplification and Order Reduction of Parametrically Excited Nonlinear Dynamical Systems written by Amit P. Gabale and published by . This book was released on 2010 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonlinear Galerkin Methods for the Model Reduction of Nonlinear Dynamical Systems written by Hermann G. Matthies and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reduced Order Models and Their Use in Design of Dynamical Systems written by G. F. Bryant and published by . This book was released on 1975 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stability Regions of Nonlinear Dynamical Systems written by Hsiao-Dong Chiang and published by . This book was released on 2015 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation problems"--