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Hamilton-Jacobi-Bellman Equations

Numerical Methods and Applications in Optimal Control

Edited by: Dante Kalise, Karl Kunisch and Zhiping Rao
With contributions of: Marianne Akian, Jan Blechschmidt, Nikolai D. Botkin, Jochen Garcke, 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
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
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Audience: Researchers and graduate students in applied and computational mathematics, physics, and engineering.