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Hamilton-Jacobi-Bellman Equations

Numerical Methods and Applications in Optimal Control

Ed. by Kalise, Dante / Kunisch, Karl / Rao, Zhiping

With contrib. 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:Radon Series on Computational and Applied Mathematics 21

    119,95 € / $137.99 / £109.00*

    eBook (PDF)
    Publication Date:
    August 2018
    Copyright year:
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    • 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

    Aims and Scope

    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.

    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


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