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Semicontinuous Solutions Of Hamilton Jacobi Bellman Equations With State Constraints
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Book Synopsis Variational Calculus, Optimal Control and Applications by : Leonhard Bittner
Download or read book Variational Calculus, Optimal Control and Applications written by Leonhard Bittner and published by Birkhäuser. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 12th conference on "Variational Calculus, Optimal Control and Applications" took place September 23-27, 1996, in Trassenheide on the Baltic Sea island of Use dom. Seventy mathematicians from ten countries participated. The preceding eleven conferences, too, were held in places of natural beauty throughout West Pomerania; the first time, in 1972, in Zinnowitz, which is in the immediate area of Trassenheide. The conferences were founded, and led ten times, by Professor Bittner (Greifswald) and Professor KlCitzler (Leipzig), who both celebrated their 65th birthdays in 1996. The 12th conference in Trassenheide, was, therefore, also dedicated to L. Bittner and R. Klotzler. Both scientists made a lasting impression on control theory in the former GDR. Originally, the conferences served to promote the exchange of research results. In the first years, most of the lectures were theoretical, but in the last few conferences practical applications have been given more attention. Besides their pioneering theoretical works, both honorees have also always dealt with applications problems. L. Bittner has, for example, examined optimal control of nuclear reactors and associated safety aspects. Since 1992 he has been working on applications in optimal control in flight dynamics. R. Klotzler recently applied his results on optimal autobahn planning to the south tangent in Leipzig. The contributions published in these proceedings reflect the trend to practical problems; starting points are often questions from flight dynamics.
Book Synopsis Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations by : Martino Bardi
Download or read book Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations written by Martino Bardi and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.
Author : Publisher :World Scientific ISBN 13 : Total Pages :1131 pages Book Rating :4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 1131 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities by : Guy Barles
Download or read book On Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities written by Guy Barles and published by Springer Nature. This book was released on 2024-01-30 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the most recent developments in the study of Hamilton-Jacobi Equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text. After an initial section that provides a “toolbox” containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text – such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization – and several key open problems are presented. This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi Equations, network problems, or scalar conservation laws.
Book Synopsis Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by : Maurizio Falcone
Download or read book Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations written by Maurizio Falcone and published by SIAM. This book was released on 2014-01-31 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Calculus of Variations and Optimal Control by : Alexander Ioffe
Download or read book Calculus of Variations and Optimal Control written by Alexander Ioffe and published by CRC Press. This book was released on 2021-02-27 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the referenced proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
Book Synopsis On the Numerical Solution of Nonlinear and Hybrid Optimal Control Problems by : Matthias Rungger
Download or read book On the Numerical Solution of Nonlinear and Hybrid Optimal Control Problems written by Matthias Rungger and published by kassel university press GmbH. This book was released on 2012 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control: Novel Directions and Applications by : Daniela Tonon
Download or read book Optimal Control: Novel Directions and Applications written by Daniela Tonon and published by Springer. This book was released on 2017-09-01 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Principles of Dynamic Optimization by : Piernicola Bettiol
Download or read book Principles of Dynamic Optimization written by Piernicola Bettiol and published by Springer Nature. This book was released on with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hamilton–Jacobi Equations: Theory and Applications by : Hung V. Tran
Download or read book Hamilton–Jacobi Equations: Theory and Applications written by Hung V. Tran and published by American Mathematical Soc.. This book was released on 2021-08-16 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an extensive survey of many important topics in the theory of Hamilton–Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton–Jacobi equations is covered. Then, the homogenization theory, a very active research topic since the late 1980s but not covered in any standard textbook, is discussed in depth. Afterwards, dynamical properties of solutions, the Aubry–Mather theory, and weak Kolmogorov–Arnold–Moser (KAM) theory are studied. Both dynamical and PDE approaches are introduced to investigate these theories. Connections between homogenization, dynamical aspects, and the optimal rate of convergence in homogenization theory are given as well. The book is self-contained and is useful for a course or for references. It can also serve as a gentle introductory reference to the homogenization theory.
Book Synopsis Advances in Mathematical Economics by : Toru Maruyama
Download or read book Advances in Mathematical Economics written by Toru Maruyama and published by Springer Nature. This book was released on 2020-02-20 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mutational and Morphological Analysis by : Jean-Pierre Aubin
Download or read book Mutational and Morphological Analysis written by Jean-Pierre Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis, processing, evolution, optimization and/or regulation, and control of shapes and images appear naturally in engineering (shape optimization, image processing, visual control), numerical analysis (interval analysis), physics (front propagation), biological morphogenesis, population dynamics (migrations), and dynamic economic theory. These problems are currently studied with tools forged out of differential geometry and functional analysis, thus requiring shapes and images to be smooth. However, shapes and images are basically sets, most often not smooth. J.-P. Aubin thus constructs another vision, where shapes and images are just any compact set. Hence their evolution -- which requires a kind of differential calculus -- must be studied in the metric space of compact subsets. Despite the loss of linearity, one can transfer most of the basic results of differential calculus and differential equations in vector spaces to mutational calculus and mutational equations in any mutational space, including naturally the space of nonempty compact subsets. "Mutational and Morphological Analysis" offers a structure that embraces and integrates the various approaches, including shape optimization and mathematical morphology. Scientists and graduate students will find here other powerful mathematical tools for studying problems dealing with shapes and images arising in so many fields.
Book Synopsis Large-Scale Scientific Computing by : Ivan Lirkov
Download or read book Large-Scale Scientific Computing written by Ivan Lirkov and published by Springer Nature. This book was released on 2020-02-13 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes revised papers from the 12th International Conference on Large-Scale Scientific Computing, LSSC 2019, held in Sozopol, Bulgaria, in June 2019. The 70 papers presented in this volume were carefully reviewed and selected from 81 submissions. The book also contains two invited talks. The papers were organized in topical sections named as follows: control and optimization of dynamical systems; meshfree and particle methods; fractional diffusion problems: numerical methods, algorithms and applications; pore scale flow and transport simulation; tensors based algorithms and structures in optimization and applications; HPC and big data: algorithms and applications; large-scale models: numerical methods, parallel computations and applications; monte carlo algorithms: innovative applications in conjunctions with other methods; application of metaheuristics to large-scale problems; large scale machine learning: multiscale algorithms and performance guarantees; and contributed papers.
Book Synopsis Control and Optimization with PDE Constraints by : Kristian Bredies
Download or read book Control and Optimization with PDE Constraints written by Kristian Bredies and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems. These contributions originate from the “International Workshop on Control and Optimization of PDEs” in Mariatrost in October 2011. This book is an excellent resource for students and researchers in control or optimization of differential equations. Readers interested in theory or in numerical algorithms will find this book equally useful.
Book Synopsis Tychastic Measure of Viability Risk by : Jean-Pierre Aubin
Download or read book Tychastic Measure of Viability Risk written by Jean-Pierre Aubin and published by Springer. This book was released on 2014-08-06 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a forecasting mechanism of the price intervals for deriving the SCR (solvency capital requirement) eradicating the risk during the exercise period on one hand and measuring the risk by computing the hedging exit time function associating with smaller investments the date until which the value of the portfolio hedges the liabilities on the other. This information, summarized under the term “tychastic viability measure of risk” is an evolutionary alternative to statistical measures, when dealing with evolutions under uncertainty. The book is written by experts in the field and the target audience primarily comprises research experts and practitioners.
Book Synopsis SIAM Journal on Control and Optimization by : Society for Industrial and Applied Mathematics
Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 2006 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Traffic Networks as Information Systems by : Jean-Pierre Aubin
Download or read book Traffic Networks as Information Systems written by Jean-Pierre Aubin and published by Springer. This book was released on 2016-07-13 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authored monograph covers a viability to approach to traffic management by advising to vehicles circulated on the network the velocity they should follow for satisfying global traffic conditions;. It presents an investigation of three structural innovations: The objective is to broadcast at each instant and at each position the advised celerity to vehicles, which could be read by auxiliary speedometers or used by cruise control devices. Namely, 1. Construct regulation feedback providing at each time and position advised velocities (celerities) for minimizing congestion or other requirements. 2. Taking into account traffic constraints of different type, the first one being to remain on the roads, to stop at junctions, etc. 3. Use information provided by the probe vehicles equipped with GPS to the traffic regulator; 4. Use other global traffic measures of vehicles provided by different types of sensors; These results are based on convex analysis, intertemporal optimization and viability theory as mathematical tools as well as viability algorithms on the computing side, instead of conventional techniques such as partial differential equations and their resolution by finite difference or finite elements algorithms. The target audience primarily covers researchers and mathematically oriented engineers but the book may also be beneficial for graduate students.
