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Hamilton-Jacobi-Bellman Equations
Numerical Methods and Applications in Optimal Control
Dante Kalise, Karl Kunisch, Zhiping Rao, Dante Kalise, Karl Kunisch, Zhiping Rao
- 209 pages
- English
- ePUB (adapté aux mobiles)
- Disponible sur iOS et Android
Hamilton-Jacobi-Bellman Equations
Numerical Methods and Applications in Optimal Control
Dante Kalise, Karl Kunisch, Zhiping Rao, Dante Kalise, Karl Kunisch, Zhiping Rao
Ă propos de ce livre
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-AmpĂšre 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 HamiltonâJacobiâBellman equations
Improving policies for HamiltonâJacobiâBellman 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 HamiltonâJacobiâBellman equations based on diagonally implicit symplectic RungeâKutta methods
Numerical solution of the simple MongeâAmpere 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 HamiltonâJacobiâBellman equation within the European Union Emission Trading Scheme
Foire aux questions
Informations
1From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving HamiltonâJacobiâBellman equations
Table des matiĂšres
- Cover
- Title Page
- Copyright
- Preface
- Contents
- List of contributing authors
- 1 From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving HamiltonâJacobiâBellman equations
- 2 Improving policies for HamiltonâJacobiâBellman equations by postprocessing
- 3 Viability approach to simulation of an adaptive controller
- 4 Galerkin approximations for the optimal control of nonlinear delay differential equations
- 5 Efficient higher order time discretization schemes for HamiltonâJacobiâBellman equations based on diagonally implicit symplectic RungeâKutta methods
- 6 Numerical solution of the simple MongeâAmpĂšre equation with nonconvex Dirichlet data on nonconvex domains
- 7 On the notion of boundary conditions in comparison principles for viscosity solutions
- 8 Boundary mesh refinement for semi-Lagrangian schemes
- 9 A reduced basis method for the HamiltonâJacobiâBellman equation within the European Union Emission Trading Scheme
- Index
- Radon Series on Computational and Applied Mathematics