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This book highlights new developments in the wide and growing field
of partial differential equations (PDE)-constrained optimization.
Optimization problems where the dynamics evolve according to a
system of PDEs arise in science, engineering, and economic
applications and they can take the form of inverse problems,
optimal control problems or optimal design problems. This book
covers new theoretical, computational as well as implementation
aspects for PDE-constrained optimization problems under
uncertainty, in shape optimization, and in feedback control, and it
illustrates the new developments on representative problems from a
variety of applications.
Focusing on applications to science and engineering, this book
presents the results of the ITN-FP7 SADCO network's innovative
research in optimization and control in the following
interconnected topics: optimality conditions in optimal control,
dynamic programming approaches to optimal feedback synthesis and
reachability analysis, and computational developments in model
predictive control. The novelty of the book resides in the fact
that it has been developed by early career researchers, providing a
good balance between clarity and scientific rigor. Each chapter
features an introduction addressed to PhD students and some
original contributions aimed at specialist researchers. Requiring
only a graduate mathematical background, the book is
self-contained. It will be of particular interest to graduate and
advanced undergraduate students, industrial practitioners and to
senior scientists wishing to update their knowledge.
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-Ampere 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
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