# eBook Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (Systems Control: Foundations Applications) download

## by Martino Bardi,Italo Capuzzo-Dolcetta

**ISBN:**0817636404

**Author:**Martino Bardi,Italo Capuzzo-Dolcetta

**Publisher:**Birkhäuser Boston; 1 edition (December 18, 1997)

**Language:**English

**Pages:**570

**ePub:**1165 kb

**Fb2:**1112 kb

**Rating:**4.3

**Other formats:**lit lrf docx rtf

**Category:**Math Sciences

**Subcategory:**Mathematics

Martino Bardi, Italo Capuzzo-Dolcetta.

Martino Bardi, Italo Capuzzo-Dolcetta. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about.

Authors: Bardi, Martino, Capuzzo Dolcetta, Italo Discontinuous viscosity solutions and applications. Bardi, Martino (et a.

Authors: Bardi, Martino, Capuzzo Dolcetta, Italo. Replete with exercises. Discontinuous viscosity solutions and applications.

In optimal control theory, the Hamilton–Jacobi–Bellman (HJB) equation gives a necessary and sufficient condition for optimality of a control with respect to a loss function. It is, in general, a nonlinear partial differential equation in the value function, which means its solution is the value function itself. Once the solution is known, it can be used to obtain the optimal control by taking the maximizer/minimizer of the Hamiltonian involved in the HJB equation.

Optimal Control and Viscosity Solutions of man Equations. Recently, Crandall and Lions introduced the notion of viscosity solution for Hamilton–Jacobi equations to settle the uniqueness problem of generalized solutions of Hamilton–Jacobi equations. The existence of viscosity solutions of Hamilton–Jacobi equations was established under the same hypotheses on the Hamiltonians as those for the uniqueness of viscosity solutions. Thus, the chapter presents.

by Martino Bardi (Author), Italo Capuzzo-Dolcetta (Author). ISBN-13: 978-0817647544.

Items related to Optimal Control and Viscosity Solutions of. .Martino Bardi; Italo Capuzzo-Dolcetta.

Items related to Optimal Control and Viscosity Solutions of Hamilton-Jacobi-B. Martino Bardi; Italo Capuzzo-Dolcetta Optimal Control and Viscosity Solutions of man Equations (Systems & Control: Foundations & Applications). ISBN 13: 9780817636401. Optimal Control and Viscosity Solutions of man Equations (Systems & Control: Foundations & Applications).

Continuous viscosity solutions of Hamilton-Jacobi equations. Approximation and perturbation problems. Optimal control problems with continuous value functions: unrestricted state space. Optimal control problems with continuous value functions: restricted state space. Asymptotic problems. Numerical solution of Dynamic Programming. Nonlinear H-infinity control by Pierpaolo Soravia.

The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The theory of viscosity solutions, initiated in the early 80's by the papers of .

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This 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, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions.

The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. 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.

"The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems…will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." — Mathematical Reviews

"With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises…Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." — ZAA

"The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." — Zentralblatt MATH

"The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." — Acta Applicandae Mathematicae