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.
Download or read book Controlled Markov Processes and Viscosity Solutions written by Wendell H. Fleming and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
Download or read book Optimal Stochastic Control Stochastic Target Problems and Backward SDE written by Nizar Touzi and published by Springer Science & Business Media. This book was released on 2012-09-25 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects some recent developments in stochastic control theory with applications to financial mathematics. We first address standard stochastic control problems from the viewpoint of the recently developed weak dynamic programming principle. A special emphasis is put on the regularity issues and, in particular, on the behavior of the value function near the boundary. We then provide a quick review of the main tools from viscosity solutions which allow to overcome all regularity problems. We next address the class of stochastic target problems which extends in a nontrivial way the standard stochastic control problems. Here the theory of viscosity solutions plays a crucial role in the derivation of the dynamic programming equation as the infinitesimal counterpart of the corresponding geometric dynamic programming equation. The various developments of this theory have been stimulated by applications in finance and by relevant connections with geometric flows. Namely, the second order extension was motivated by illiquidity modeling, and the controlled loss version was introduced following the problem of quantile hedging. The third part specializes to an overview of Backward stochastic differential equations, and their extensions to the quadratic case.
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Download or read book Numerical Methods for Viscosity Solutions and Applications written by Maurizio Falcone and published by World Scientific. This book was released on 2001 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometrical optics and viscosity solutions / A.-P. Blanc, G. T. Kossioris and G. N. Makrakis -- Computation of vorticity evolution for a cylindrical Type-II superconductor subject to parallel and transverse applied magnetic fields / A. Briggs ... [et al.] -- A characterization of the value function for a class of degenerate control problems / F. Camilli -- Some microstructures in three dimensions / M. Chipot and V. Lecuyer -- Convergence of numerical schemes for the approximation of level set solutions to mean curvature flow / K. Deckelnick and G. Dziuk -- Optimal discretization steps in semi-lagrangian approximation of first-order PDEs / M. Falcone, R. Ferretti and T. Manfroni -- Convergence past singularities to the forced mean curvature flow for a modified reaction-diffusion approach / F. Fierro -- The viscosity-duality solutions approach to geometric pptics for the Helmholtz equation / L. Gosse and F. James -- Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations / L. Grune -- Solution and application of anisotropic curvature driven evolution of curves (and surfaces) / K. Mikula -- An adaptive scheme on unstructured grids for the shape-from-shading problem / M. Sagona and A. Seghini -- On a posteriori error estimation for constant obstacle problems / A. Veeser.
Download or read book Mathematics Applied to Engineering Modelling and Social Issues written by Frank T. Smith and published by Springer. This book was released on 2019-03-14 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several aspects of research on mathematics that have significant applications in engineering, modelling and social matters, discussing a number of current and future social issues and problems in which mathematical tools can be beneficial. Each chapter enhances our understanding of the research problems in a particular an area of study and highlights the latest advances made in that area. The self-contained contributions make the results and problems discussed accessible to readers, and provides references to enable those interested to follow subsequent studies in still developing fields. Presenting real-world applications, the book is a valuable resource for graduate students, researchers and educators. It appeals to general readers curious about the practical applications of mathematics in diverse scientific areas and social problems.
Download or read book An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L written by Nikos Katzourakis and published by Springer. This book was released on 2014-11-26 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.
Download or read book Controlled Markov Processes written by E. B. Dynkin and published by Springer. This book was released on 2012-04-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi nology multistage Markovian decision processes. We discuss the applications of this theory to various concrete problems. Particular attention is paid to mathe matical models of economic planning, taking account of stochastic factors. The authors strove to construct the exposition in such a way that a reader interested in the applications can get through the book with a minimal mathe matical apparatus. On the other hand, a mathematician will find, in the appropriate chapters, a rigorous theory of general control models, based on advanced measure theory, analytic set theory, measurable selection theorems, and so forth. We have abstained from the manner of presentation of many mathematical monographs, in which one presents immediately the most general situation and only then discusses simpler special cases and examples. Wishing to separate out difficulties, we introduce new concepts and ideas in the simplest setting, where they already begin to work. Thus, before considering control problems on an infinite time interval, we investigate in detail the case of the finite interval. Here we first study in detail models with finite state and action spaces-a case not requiring a departure from the realm of elementary mathematics, and at the same time illustrating the most important principles of the theory.
Download or read book Stochastic and Differential Games written by Martino Bardi and published by Springer Science & Business Media. This book was released on 1999-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.
Download or read book Viscosity Solutions and Optimal Control written by Robert James Elliott and published by Harlow, England : Longman Scientific & Technical. This book was released on 1987 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.
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.
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.
Download or read book Controlled Diffusion Processes written by N. V. Krylov and published by Springer Science & Business Media. This book was released on 2008-09-26 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.
Download or read book Nonlinear Optimal Control Theory written by Leonard David Berkovitz and published by CRC Press. This book was released on 2012-08-25 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.
Download or read book Applied Stochastic Control of Jump Diffusions written by Bernt Øksendal and published by Springer Science & Business Media. This book was released on 2007-04-26 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Download or read book Hamilton Jacobi Equations Approximations Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
