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Stability of the turnpike phenomenon in discrete-time optimal control problems

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 whi...

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Autor principal: Zaslavski, Alexander J
Lenguaje:eng
Publicado: Springer 2014
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-08034-5
http://cds.cern.ch/record/1952388
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author Zaslavski, Alexander J
author_facet Zaslavski, Alexander J
author_sort Zaslavski, Alexander J
collection CERN
description 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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spelling cern-19523882021-04-21T20:52:22Zdoi:10.1007/978-3-319-08034-5http://cds.cern.ch/record/1952388engZaslavski, Alexander JStability of the turnpike phenomenon in discrete-time optimal control problemsMathematical Physics and MathematicsThe 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.Springeroai:cds.cern.ch:19523882014
spellingShingle Mathematical Physics and Mathematics
Zaslavski, Alexander J
Stability of the turnpike phenomenon in discrete-time optimal control problems
title Stability of the turnpike phenomenon in discrete-time optimal control problems
title_full Stability of the turnpike phenomenon in discrete-time optimal control problems
title_fullStr Stability of the turnpike phenomenon in discrete-time optimal control problems
title_full_unstemmed Stability of the turnpike phenomenon in discrete-time optimal control problems
title_short Stability of the turnpike phenomenon in discrete-time optimal control problems
title_sort stability of the turnpike phenomenon in discrete-time optimal control problems
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-08034-5
http://cds.cern.ch/record/1952388
work_keys_str_mv AT zaslavskialexanderj stabilityoftheturnpikephenomenonindiscretetimeoptimalcontrolproblems