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Since the 1950s control theory has established itself as a major
mathematical discipline, particularly suitable for application in a
number of research fields, including advanced engineering design,
economics and the medical sciences. However, since its emergence,
there has been a need to rethink and extend fields such as calculus
of variations, differential geometry and nonsmooth analysis, which
are closely tied to research on applications. Today control theory
is a rich source of basic abstract problems arising from
applications, and provides an important frame of reference for
investigating purely mathematical issues. In many fields of
mathematics, the huge and growing scope of activity has been
accompanied by fragmentation into a multitude of narrow
specialties. However, outstanding advances are often the result of
the quest for unifying themes and a synthesis of different
approaches. Control theory and its applications are no exception.
Here, the interaction between analysis and geometry has played a
crucial role in the evolution of the field. This book collects some
recent results, highlighting geometrical and analytical aspects and
the possible connections between them. Applications provide the
background, in the classical spirit of mutual interplay between
abstract theory and problem-solving practice.
Since the 1950s control theory has established itself as a major
mathematical discipline, particularly suitable for application in a
number of research fields, including advanced engineering design,
economics and the medical sciences. However, since its emergence,
there has been a need to rethink and extend fields such as calculus
of variations, differential geometry and nonsmooth analysis, which
are closely tied to research on applications. Today control theory
is a rich source of basic abstract problems arising from
applications, and provides an important frame of reference for
investigating purely mathematical issues. In many fields of
mathematics, the huge and growing scope of activity has been
accompanied by fragmentation into a multitude of narrow
specialties. However, outstanding advances are often the result of
the quest for unifying themes and a synthesis of different
approaches. Control theory and its applications are no exception.
Here, the interaction between analysis and geometry has played a
crucial role in the evolution of the field. This book collects some
recent results, highlighting geometrical and analytical aspects and
the possible connections between them. Applications provide the
background, in the classical spirit of mutual interplay between
abstract theory and problem-solving practice.
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