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This book presents cutting-edge contributions in the areas of
control theory and partial differential equations. Over the
decades, control theory has had deep and fruitful interactions with
the theory of partial differential equations (PDEs). Well-known
examples are the study of the generalized solutions of
Hamilton-Jacobi-Bellman equations arising in deterministic and
stochastic optimal control and the development of modern analytical
tools to study the controllability of infinite dimensional systems
governed by PDEs. In the present volume, leading experts provide an
up-to-date overview of the connections between these two vast
fields of mathematics. Topics addressed include regularity of the
value function associated to finite dimensional control systems,
controllability and observability for PDEs, and asymptotic analysis
of multiagent systems. The book will be of interest for both
researchers and graduate students working in these areas.
This book presents cutting-edge contributions in the areas of
control theory and partial differential equations. Over the
decades, control theory has had deep and fruitful interactions with
the theory of partial differential equations (PDEs). Well-known
examples are the study of the generalized solutions of
Hamilton-Jacobi-Bellman equations arising in deterministic and
stochastic optimal control and the development of modern analytical
tools to study the controllability of infinite dimensional systems
governed by PDEs. In the present volume, leading experts provide an
up-to-date overview of the connections between these two vast
fields of mathematics. Topics addressed include regularity of the
value function associated to finite dimensional control systems,
controllability and observability for PDEs, and asymptotic analysis
of multiagent systems. The book will be of interest for both
researchers and graduate students working in these areas.
The term "control theory" refers to the body of results -
theoretical, numerical and algorithmic - which have been developed
to influence the evolution of the state of a given system in order
to meet a prescribed performance criterion. Systems of interest to
control theory may be of very different natures. This monograph is
concerned with models that can be described by partial differential
equations of evolution. It contains five major contributions and is
connected to the CIME Course on Control of Partial Differential
Equations that took place in Cetraro (CS, Italy), July 19 - 23,
2010. Specifically, it covers the stabilization of evolution
equations, control of the Liouville equation, control in fluid
mechanics, control and numerics for the wave equation, and Carleman
estimates for elliptic and parabolic equations with application to
control. We are confident this work will provide an authoritative
reference work for all scientists who are interested in this field,
representing at the same time a friendly introduction to, and an
updated account of, some of the most active trends in current
research.
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