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1 L??ber, Jakob Optimal Trajectory Tracking of Nonlinear Dynamical Systems I09534 2017 eBook  
2 Nelles, Oliver Nonlinear System Identification I09519 2020 eBook  
3 Marmo, G Classical and Quantum Physics I08690 2019 eBook  
4 Mbiock, Aristide Radiation in Enclosures I11457 2000 eBook  
5 Lieb, Elliott H The Stability of Matter: From Atoms to Stars I11279 2001 eBook  
6 Tarasov, Vasily E Fractional Dynamics I08522 2010 eBook  
7 Chavent, Guy Nonlinear Least Squares for Inverse Problems I07718 2010 eBook  
8 Schulz, Michael Control Theory in Physics and other Fields of Science I07009 2006 eBook  
9 Basdevant, Jean-Louis Variational Principles in Physics I06783 2007 eBook  
10 Lieb, Elliott H The Stability of Matter: From Atoms to Stars I06244 2005 eBook  
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TitleOptimal Trajectory Tracking of Nonlinear Dynamical Systems
Author(s)L??ber, Jakob
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXIV, 243 p. 36 illus., 32 illus. in color : online resource
Abstract NoteBy establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e.g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry
ISBN,Price9783319465746
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. CALCULUS OF VARIATIONS 3. Calculus of Variations and Optimal Control; Optimization 4. DYNAMICAL SYSTEMS 5. Dynamical Systems and Ergodic Theory 6. DYNAMICS 7. EBOOK 8. EBOOK - SPRINGER 9. ERGODIC THEORY 10. STATISTICAL PHYSICS 11. VIBRATION 12. Vibration, Dynamical Systems, Control
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TitleNonlinear System Identification : From Classical Approaches to Neural Networks, Fuzzy Models, and Gaussian Processes
Author(s)Nelles, Oliver
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionX, 1203 p. 670 illus., 179 illus. in color : online resource
Abstract NoteThis book provides engineers and scientists in academia and industry with a thorough understanding of the underlying principles of nonlinear system identification. It equips them to apply the models and methods discussed to real problems with confidence, while also making them aware of potential difficulties that may arise in practice. Moreover, the book is self-contained, requiring only a basic grasp of matrix algebra, signals and systems, and statistics. Accordingly, it can also serve as an introduction to linear system identification, and provides a practical overview of the major optimization methods used in engineering. The focus is on gaining an intuitive understanding of the subject and the practical application of the techniques discussed. The book is not written in a theorem/proof style; instead, the mathematics is kept to a minimum, and the ideas covered are illustrated with numerous figures, examples, and real-world applications. In the past, nonlinear system identification was a field characterized by a variety of ad-hoc approaches, each applicable only to a very limited class of systems. With the advent of neural networks, fuzzy models, Gaussian process models, and modern structure optimization techniques, a much broader class of systems can now be handled. Although one major aspect of nonlinear systems is that virtually every one is unique, tools have since been developed that allow each approach to be applied to a wide variety of systems.
ISBN,Price9783030474393
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. CALCULUS OF VARIATIONS 3. Calculus of Variations and Optimal Control; Optimization 4. COMPLEXITY 5. COMPUTATIONAL COMPLEXITY 6. COMPUTER SIMULATION 7. Control and Systems Theory 8. Control engineering 9. Control, Robotics, Mechatronics 10. EBOOK 11. EBOOK - SPRINGER 12. Mechatronics 13. ROBOTICS 14. Simulation and Modeling 15. STATISTICAL PHYSICS
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TitleClassical and Quantum Physics : 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control
Author(s)Marmo, G;Mart??n de Diego, David;Mu??oz Lecanda, Miguel
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2019.
DescriptionXXVI, 374 p. 46 illus., 14 illus. in color : online resource
Abstract NoteThis proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas. Most of Albertos???s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics. Let us mention some of the fields of expertise of Alberto Ibort: Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others. In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic. His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed
ISBN,Price9783030247485
Keyword(s)1. Associative rings 2. Associative Rings and Algebras 3. CALCULUS OF VARIATIONS 4. Calculus of Variations and Optimal Control; Optimization 5. COMPLEX MANIFOLDS 6. DIFFERENTIAL GEOMETRY 7. EBOOK 8. EBOOK - SPRINGER 9. Manifolds (Mathematics) 10. Manifolds and Cell Complexes (incl. Diff.Topology) 11. MATHEMATICAL PHYSICS 12. Rings (Algebra) 13. Theoretical, Mathematical and Computational Physics
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TitleRadiation in Enclosures : Elliptic Boundary Value Problem
Author(s)Mbiock, Aristide;Weber, Roman
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2000.
DescriptionXIII, 211 p : online resource
Abstract NoteThis graduate textbook is concerned with both the formulation and the solution of radiation heat transfer problems in enclosures. The book is essentially self-contained and includes a brief historical survey. The foundations are carefully discussed from the point of view of the exact mathematical basis of boundary value problems and their variational solutions as well as of the physical foundations. The computational methods developed by the authors are used in engineering applications. The combinaton of exact mathematical modelling with numerical skills makes this a unique textbook
ISBN,Price9783642570940
Keyword(s)1. CALCULUS OF VARIATIONS 2. Calculus of Variations and Optimal Control; Optimization 3. Computational Science and Engineering 4. Computer mathematics 5. EBOOK 6. EBOOK - SPRINGER 7. EDUCATION 8. Engineering Thermodynamics, Heat and Mass Transfer 9. Heat engineering 10. HEAT TRANSFER 11. MASS TRANSFER 12. MATHEMATICAL PHYSICS 13. Popular Science in Education 14. Theoretical, Mathematical and Computational Physics 15. THERMODYNAMICS
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TitleThe Stability of Matter: From Atoms to Stars : Selecta of Elliott H. Lieb
Author(s)Lieb, Elliott H;Thirring, Walter
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2001.
DescriptionXIII, 812 p. 12 illus : online resource
Abstract NoteThis collection of papers -- starting with a brilliant article by one of the masters of the field -- gives an excellent current review of our knowledge of matter. Partially basing his work on a variational formulation of quantum mechanics, E.H. Lieb links the difficult question of the stability of matter with important problems in functional analysis. In this collection the reader will find general results together with deep insights into quantum systems combined with papers on the structure of atoms and molecules, the thermodynamic limit, and stellar structures. The book is suitable as an accompanying text for a graduate course in quantum mechanics. In this new edition two new sections have been added: Section 7 contains papers on quantum electrodynamics, and Section 8 on Boson systems.
ISBN,Price9783662043608
Keyword(s)1. ANALYSIS 2. Analysis (Mathematics) 3. CALCULUS OF VARIATIONS 4. Calculus of Variations and Optimal Control; Optimization 5. CONDENSED MATTER 6. CONDENSED MATTER PHYSICS 7. EBOOK 8. EBOOK - SPRINGER 9. MATHEMATICAL ANALYSIS 10. Mathematical Methods in Physics 11. PHYSICS 12. QUANTUM PHYSICS
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TitleFractional Dynamics : Applications of Fractional Calculus to Dynamics of Particles, Fields and Media
Author(s)Tarasov, Vasily E
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2010.
DescriptionXV, 505 p : online resource
Abstract Note"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute
ISBN,Price9783642140037
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. CALCULUS OF VARIATIONS 4. Calculus of Variations and Optimal Control; Optimization 5. COMPLEX SYSTEMS 6. DYNAMICAL SYSTEMS 7. EBOOK 8. EBOOK - SPRINGER 9. ENGINEERING MATHEMATICS 10. Mathematical and Computational Engineering 11. MATHEMATICAL PHYSICS 12. STATISTICAL PHYSICS 13. Statistical Physics and Dynamical Systems 14. Theoretical, Mathematical and Computational Physics
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TitleNonlinear Least Squares for Inverse Problems : Theoretical Foundations and Step-by-Step Guide for Applications
Author(s)Chavent, Guy
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2010.
DescriptionXIV, 360 p : online resource
Abstract NoteThis book provides an introduction into the least squares resolution of nonlinear inverse problems. The first goal is to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, i.e. both wellposedness and optimizability. Using the results, the applicability of various regularization techniques can be checked. The second objective of the book is to present frequent practical issues when solving NLS problems. Application oriented readers will find a detailed analysis of problems on the reduction to finite dimensions, the algebraic determination of derivatives (sensitivity functions versus adjoint method), the determination of the number of retrievable parameters, the choice of parametrization (multiscale, adaptive) and the optimization step, and the general organization of the inversion code. Special attention is paid to parasitic local minima, which can stop the optimizer far from the global minimum: multiscale parametrization is shown to be an efficient remedy in many cases, and a new condition is given to check both wellposedness and the absence of parasitic local minima. For readers that are interested in projection on non-convex sets, Part II of this book presents the geometric theory of quasi-convex and strictly quasi-convex (s.q.c.) sets. S.q.c. sets can be recognized by their finite curvature and limited deflection and possess a neighborhood where the projection is well-behaved. Throughout the book, each chapter starts with an overview of the presented concepts and results
ISBN,Price9789048127856
Keyword(s)1. APPLIED MATHEMATICS 2. CALCULUS OF VARIATIONS 3. Calculus of Variations and Optimal Control; Optimization 4. EBOOK 5. EBOOK - SPRINGER 6. ENGINEERING MATHEMATICS 7. Mathematical and Computational Engineering 8. Mathematical Methods in Physics 9. Mathematical Modeling and Industrial Mathematics 10. MATHEMATICAL MODELS 11. PHYSICS
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TitleControl Theory in Physics and other Fields of Science : Concepts, Tools, and Applications
Author(s)Schulz, Michael
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2006.
DescriptionIX, 296 p. 46 illus : online resource
Abstract NoteThis book covers systematically and in a simple language the mathematical and physical foundations of controlling deterministic and stochastic evolutionary processes in systems with a high degree of complexity. Strong emphasis is placed on concepts, methods and techniques for modelling, assessment and the solution or estimation of control problems in an attempt to understand the large variability of these problems in several branches of physics, chemistry and biology as well as in technology and economics. The main focus of the book is on a clear physical and mathematical understanding of the dynamics and kinetics behind several kinds of control problems and their relation to self-organizing principles in complex systems. The book is a modern introduction and a helpful tool for researchers, engineers as well as post-docs and graduate students interested in an application oriented control theory and related topics
ISBN,Price9783540324171
Keyword(s)1. CALCULUS OF VARIATIONS 2. Calculus of Variations and Optimal Control; Optimization 3. COMPLEX SYSTEMS 4. DYNAMICAL SYSTEMS 5. EBOOK 6. EBOOK - SPRINGER 7. STATISTICAL PHYSICS 8. Statistical Physics and Dynamical Systems
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TitleVariational Principles in Physics
Author(s)Basdevant, Jean-Louis
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2007.
DescriptionX, 183 p : online resource
Abstract NoteOptimization under constraints is an essential part of everyday life. Indeed, we routinely solve problems by striking a balance between contradictory interests, individual desires and material contingencies. This notion of equilibrium was dear to thinkers of the enlightenment, as illustrated by Montesquieu???s famous formulation: "In all magistracies, the greatness of the power must be compensated by the brevity of the duration." Astonishingly, natural laws are guided by a similar principle. Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be known as Fermat???s principle, a cornerstone of geometrical optics. Variational Principles in Physics explains variational principles and charts their use throughout modern physics. The heart of the book is devoted to the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. Prof. Basdevant also offers simple but rich first impressions of Einstein???s General Relativity, Feynman???s Quantum Mechanics, and more revealing and amazing interconnections between various fields of physics. A graduate of the Ecole Normale Superieure, Jean-Louis Basdevant is Professor and former Chair of the Department of Physics at the Ecole Polytechnique, and Director of Research for the CNRS. Specializing in the theoretical physics of elementary particles, quantum field theory and astrophysics, Prof. Basdevant works in the Leprince-Ringuet Laboratory at the Ecole Polytechnique
ISBN,Price9780387377483
Keyword(s)1. CALCULUS OF VARIATIONS 2. Calculus of Variations and Optimal Control; Optimization 3. CLASSICAL MECHANICS 4. EBOOK 5. EBOOK - SPRINGER 6. History and Philosophical Foundations of Physics 7. Mathematical Methods in Physics 8. MATHEMATICAL OPTIMIZATION 9. MECHANICS 10. Mechanics, Applied 11. OPTIMIZATION 12. PHYSICS 13. Theoretical and Applied Mechanics
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TitleThe Stability of Matter: From Atoms to Stars : Selecta of Elliott H. Lieb
Author(s)Lieb, Elliott H;Thirring, Walter
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2005.
DescriptionXVI, 932 p : online resource
Abstract NoteThis collection of papers -- starting with a brilliant article by one of the masters of the field -- gives an excellent current review of our knowledge of matter. Partially basing his own work on a variational formulation of quantum mechanics, E.H. Lieb links the difficult question of the stability of matter with important problems in functional analysis. Here the reader will find general results together with deep insights into quantum systems combined with papers on the structure of atoms and molecules, the thermodynamic limit, and stellar structures. The book is suitable as an accompanying text or recommended reading for a graduate course in quantum mechanics. In the third edition, two new sections were added: one contains papers on quantum electrodynamics, and the other on Boson systems. In this fourth edition, these topics have been further developed, extending the book by approximately 120 pages
ISBN,Price9783540270560
Keyword(s)1. ANALYSIS 2. Analysis (Mathematics) 3. CALCULUS OF VARIATIONS 4. Calculus of Variations and Optimal Control; Optimization 5. CONDENSED MATTER 6. CONDENSED MATTER PHYSICS 7. EBOOK 8. EBOOK - SPRINGER 9. Elementary particles (Physics) 10. Elementary Particles, Quantum Field Theory 11. MATHEMATICAL ANALYSIS 12. Mathematical Methods in Physics 13. PHYSICS 14. QUANTUM FIELD THEORY 15. QUANTUM PHYSICS
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