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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Calculus of variations
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Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems (Paperback, 2014 ed.)
Loot Price: R1,814
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Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems (Paperback, 2014 ed.)
Series: SpringerBriefs in Optimization
Expected to ship within 10 - 15 working days
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The structure of approximate solutions of autonomous discrete-time
optimal control problems and individual turnpike results for
optimal control problems without convexity (concavity) assumptions
are examined in this book. In particular, the book focuses on the
properties of approximate solutions which are independent of the
length of the interval, for all sufficiently large intervals; these
results apply to the so-called turnpike property of the optimal
control problems. By encompassing the so-called turnpike property
the approximate solutions of the problems are determined primarily
by the objective function and are fundamentally independent of the
choice of interval and endpoint conditions, except in regions close
to the endpoints. This book also explores the turnpike phenomenon
for two large classes of autonomous optimal control problems. It is
illustrated that the turnpike phenomenon is stable for an optimal
control problem if the corresponding infinite horizon optimal
control problem possesses an asymptotic turnpike property. If an
optimal control problem belonging to the first class possesses the
turnpike property, then the turnpike is a singleton (unit set). The
stability of the turnpike property under small perturbations of an
objective function and of a constraint map is established. For the
second class of problems where the turnpike phenomenon is not
necessarily a singleton the stability of the turnpike property
under small perturbations of an objective function is established.
Containing solutions of difficult problems in optimal control and
presenting new approaches, techniques and methods this book is of
interest for mathematicians working in optimal control and the
calculus of variations. It also can be useful in preparation
courses for graduate students.
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