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This work presents recent mathematical methods in the area of
optimal control with a particular emphasis on the computational
aspects and applications. Optimal control theory concerns the
determination of control strategies for complex dynamical systems,
in order to optimize some measure of their performance. Started in
the 60's under the pressure of the "space race" between the US and
the former USSR, the field now has a far wider scope, and embraces
a variety of areas ranging from process control to traffic flow
optimization, renewable resources exploitation and management of
financial markets. These emerging applications require more and
more efficient numerical methods for their solution, a very
difficult task due the huge number of variables. The chapters of
this volume give an up-to-date presentation of several recent
methods in this area including fast dynamic programming algorithms,
model predictive control and max-plus techniques. This book is
addressed to researchers, graduate students and applied scientists
working in the area of control problems, differential games and
their applications.
This largely self-contained book provides a unified framework of
semi-Lagrangian strategy for the approximation of hyperbolic PDEs,
with a special focus on Hamilton-Jacobi equations. The authors
provide a rigorous discussion of the theory of viscosity solutions
and the concepts underlying the construction and analysis of
difference schemes; they then proceed to high-order semi-Lagrangian
schemes and their applications to problems in fluid dynamics, front
propagation, optimal control, and image processing. The
developments covered in the text and the references come from a
wide range of literature.
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