Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal Control

Published by De Gruyter 2018

Hamilton-Jacobi-Bellman Equations

Numerical Methods and Applications in Optimal Control

Edited by: Dante Kalise , Karl Kunisch and Zhiping Rao
With contributions by: Marianne Akian , Jan Blechschmidt , Nikolai D. Botkin , Max Jensen , Axel Kröner , Athena Picarelli , Iain Smears , Karsten Urban , Mickaël D. Chekroun , Roland Herzog , Ilja Kalmykov , Johannes Diepolder , Eric Fodjo , Honghu Liu , Christoph Reisinger , Julen Rotaetxe Arto , Sebastian Steck and Varvara L. Turova

Volume 21 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110543599

Overview
Contents

About this book

Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations.

Contents
From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations
Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing
Viability approach to simulation of an adaptive controller
Galerkin approximations for the optimal control of nonlinear delay differential equations
Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods
Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains
On the notion of boundary conditions in comparison principles for viscosity solutions
Boundary mesh refinement for semi-Lagrangian schemes
A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme

A collection of original survey articles on the numerics of Hamilton-Jacobi-Bellman equations
Presents a variety of numerical and computational techniques
Of interest to applied mathematicians as well as to engineers and applied scientists

Author / Editor information

Dante Kalise and Zhiping Rao, Radon Institute, Austria; Karl Kunisch, University of Graz and Radon Institute, Austria.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Dante Kalise, Karl Kunisch and Zhiping Rao Requires Authentication Unlicensed Licensed Download PDF	V
Contents Publicly Available Download PDF	VII
List Of Contributing Authors Requires Authentication Unlicensed Licensed Download PDF	XI
1. From A Monotone Probabilistic Scheme To A Probabilistic Max-Plus Algorithm For Solving Hamilton–Jacobi–Bellman Equations Marianne Akian and Eric Fodjo Requires Authentication Unlicensed Licensed Download PDF	1
2. Improving Policies For Hamilton–Jacobi–Bellman Equations By Postprocessing Jan Blechschmidt and Roland Herzog Requires Authentication Unlicensed Licensed Download PDF	25
3. Viability Approach To Simulation Of An Adaptive Controller Nikolai D. Botkin, Johannes Diepolder and Varvara L. Turova Requires Authentication Unlicensed Licensed Download PDF	43
4. Galerkin Approximations For The Optimal Control Of Nonlinear Delay Differential Equations Mickaël D. Chekroun, Axel Kröner and Honghu Liu Requires Authentication Unlicensed Licensed Download PDF	61
5. Efficient Higher Order Time Discretization Schemes For Hamilton–Jacobi–Bellman Equations Based On Diagonally Implicit Symplectic Runge–Kutta Methods Jochen Garcke and Ilja Kalmykov Requires Authentication Unlicensed Licensed Download PDF	97
6. Numerical Solution Of The Simple Monge–Ampère Equation With Nonconvex Dirichlet Data On Nonconvex Domains Max Jensen Requires Authentication Unlicensed Licensed Download PDF	129
7. On The Notion Of Boundary Conditions In Comparison Principles For Viscosity Solutions Max Jensen and Iain Smears Requires Authentication Unlicensed Licensed Download PDF	143
8. Boundary Mesh Refinement For Semi-Lagrangian Schemes Athena Picarelli, Christoph Reisinger and Julen Rotaetxe Arto Requires Authentication Unlicensed Licensed Download PDF	155
9. A Reduced Basis Method For The Hamilton–Jacobi–Bellman Equation Within The European Union Emission Trading Scheme Sebastian Steck and Karsten Urban Requires Authentication Unlicensed Licensed Download PDF	175
Index Requires Authentication Unlicensed Licensed Download PDF	197

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in applied and computational mathematics, physics, and engineering.
Pages
- Front matter: 12
- Main content: 197
Illustrations
- Illustrations: 54
- Tables: 20
Keywords: Dynamische Optimierung; Finite-Elemente-Methode; Hamilton-Jacobi-Differentialgleichung; Numerische Mathematik; Optimale Kontrolle

eBook

Published: August 6, 2018
ISBN: 9783110543599

Hardcover

Published: August 6, 2018
ISBN: 9783110542639