Semiconcave Functions Hamilton Jacobi Equations And Optimal Control
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Semiconcave Functions Hamilton Jacobi Equations And Optimal Control
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Author : Piermarco Cannarsa
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31
Semiconcave Functions Hamilton Jacobi Equations And Optimal Control written by Piermarco Cannarsa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.
Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations. The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions.
Semi Lagrangian Approximation Schemes For Linear And Hamilton Jacobi Equations
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Author : Maurizio Falcone
language : en
Publisher: SIAM
Release Date : 2014-01-31
Semi Lagrangian Approximation Schemes For Linear And Hamilton Jacobi Equations written by Maurizio Falcone and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with Mathematics categories.
This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.
Stochastic Optimal Control In Infinite Dimension
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Author : Giorgio Fabbri
language : en
Publisher: Springer
Release Date : 2017-06-22
Stochastic Optimal Control In Infinite Dimension written by Giorgio Fabbri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Mathematics categories.
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Optimization And Operations Research Volume Iii
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Author : Ulrich Derigs
language : en
Publisher: EOLSS Publications
Release Date : 2009-02-09
Optimization And Operations Research Volume Iii written by Ulrich Derigs and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with categories.
Optimization and Operations Research is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Optimization and Operations Research is organized into six different topics which represent the main scientific areas of the theme: 1. Fundamentals of Operations Research; 2. Advanced Deterministic Operations Research; 3. Optimization in Infinite Dimensions; 4. Game Theory; 5. Stochastic Operations Research; 6. Decision Analysis, which are then expanded into multiple subtopics, each as a chapter. These four volumes are aimed at the following five major target audiences: University and College students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.
Advances In Mathematical Economics
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Author : Toru Maruyama
language : en
Publisher: Springer Nature
Release Date : 2020-02-20
Advances In Mathematical Economics written by Toru Maruyama and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-20 with Mathematics categories.
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
Optimal Control Novel Directions And Applications
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Author : Daniela Tonon
language : en
Publisher: Springer
Release Date : 2017-09-01
Optimal Control Novel Directions And Applications written by Daniela Tonon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-01 with Mathematics categories.
Focusing on applications to science and engineering, this book presents the results of the ITN-FP7 SADCO network’s innovative research in optimization and control in the following interconnected topics: optimality conditions in optimal control, dynamic programming approaches to optimal feedback synthesis and reachability analysis, and computational developments in model predictive control. The novelty of the book resides in the fact that it has been developed by early career researchers, providing a good balance between clarity and scientific rigor. Each chapter features an introduction addressed to PhD students and some original contributions aimed at specialist researchers. Requiring only a graduate mathematical background, the book is self-contained. It will be of particular interest to graduate and advanced undergraduate students, industrial practitioners and to senior scientists wishing to update their knowledge.
Trends In Control Theory And Partial Differential Equations
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Author : Fatiha Alabau-Boussouira
language : en
Publisher: Springer
Release Date : 2019-07-04
Trends In Control Theory And Partial Differential Equations written by Fatiha Alabau-Boussouira and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-04 with Mathematics categories.
This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.
Numerical Control Part B
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Author : Emmanuel Trélat
language : en
Publisher: Elsevier
Release Date : 2023-02-20
Numerical Control Part B written by Emmanuel Trélat and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-20 with Mathematics categories.
Numerical Control: Part B, Volume 24 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Control problems in the coefficients and the domain for linear elliptic equations, Computational approaches for extremal geometric eigenvalue problems, Non-overlapping domain decomposition in space and time for PDE-constrained optimal control problems on networks, Feedback Control of Time-dependent Nonlinear PDEs with Applications in Fluid Dynamics, Stabilization of the Navier-Stokes equations - Theoretical and numerical aspects, Reconstruction algorithms based on Carleman estimates, and more. Other sections cover Discrete time formulations as time discretization strategies in data assimilation, Back and forth iterations/Time reversal methods, Unbalanced Optimal Transport: from Theory to Numerics, An ADMM Approach to the Exact and Approximate Controllability of Parabolic Equations, Nonlocal balance laws -- an overview over recent results, Numerics and control of conservation laws, Numerical approaches for simulation and control of superconducting quantum circuits, and much more. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Numerical Analysis series - Updated release includes the latest information on Numerical Control
Analysis And Geometry In Control Theory And Its Applications
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Author : Piernicola Bettiol
language : en
Publisher: Springer
Release Date : 2015-09-01
Analysis And Geometry In Control Theory And Its Applications written by Piernicola Bettiol and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-01 with Mathematics categories.
Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.
Hamiltonian Systems
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Author : Albert Fathi
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-09
Hamiltonian Systems written by Albert Fathi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-09 with Mathematics categories.
Dynamical systems that are amenable to formulation in terms of a Hamiltonian function or operator encompass a vast swath of fundamental cases in applied mathematics and physics. This carefully edited volume represents work carried out during the special program on Hamiltonian Systems at MSRI in the Fall of 2018. Topics covered include KAM theory, polygonal billiards, Arnold diffusion, quantum hydrodynamics, viscosity solutions of the Hamilton–Jacobi equation, surfaces of locally minimal flux, Denjoy subsystems and horseshoes, and relations to symplectic topology.