Hamilton-Jacobi-Bellman Equations Numerical Methods and Applications in Optimal Control |
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| Editor:
| Kalise, Dante
Kunisch, Karl
Rao, Zhiping |
| Contribution by:
| Akian, Marianne
Blechschmidt, Jan
Botkin, Nikolai D.
Jensen, Max
Kröner, Axel
Picarelli, Athena
Smears, Iain
Urban, Karsten
Chekroun, Mickaël D.
Herzog, Roland
Kalmykov, Ilja
Diepolder, Johannes
Fodjo, Eric
Liu, Honghu
Reisinger, Christoph
Rotaetxe Arto, Julen
Steck, Sebastian
Turova, Varvara L. |
| Series title: | Radon Series on Computational and Applied Mathematics Ser. |
| ISBN: | 978-3-11-054263-9 |
| Publication Date: | Aug 2018 |
| Publisher: | Walter de Gruyter GmbH
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| Book Format: | Hardback |
| List Price: | USD $166.99 |
Book Description:
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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...
More Description
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