Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems

Business & Finance, Management & Leadership, Operations Research, Nonfiction, Science & Nature, Mathematics, Calculus
Cover of the book Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems by Alexander J. Zaslavski, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Alexander J. Zaslavski ISBN: 9783319080345
Publisher: Springer International Publishing Publication: August 20, 2014
Imprint: Springer Language: English
Author: Alexander J. Zaslavski
ISBN: 9783319080345
Publisher: Springer International Publishing
Publication: August 20, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Reviews of Environmental Contamination and Toxicology Volume 235 by Alexander J. Zaslavski
Cover of the book Topics in Cryptology – CT-RSA 2017 by Alexander J. Zaslavski
Cover of the book Ex Vivo Engineering of the Tumor Microenvironment by Alexander J. Zaslavski
Cover of the book Modern Approaches to Discrete Curvature by Alexander J. Zaslavski
Cover of the book Bilingual Learners and Social Equity by Alexander J. Zaslavski
Cover of the book Technosex by Alexander J. Zaslavski
Cover of the book Corpus Linguistics and Statistics with R by Alexander J. Zaslavski
Cover of the book Cognitive Radio Oriented Wireless Networks by Alexander J. Zaslavski
Cover of the book Virtual Work and Shape Change in Solid Mechanics by Alexander J. Zaslavski
Cover of the book Rare and Exotic Orchids by Alexander J. Zaslavski
Cover of the book Precision Medicine, CRISPR, and Genome Engineering by Alexander J. Zaslavski
Cover of the book The Automated Design of Materials Far From Equilibrium by Alexander J. Zaslavski
Cover of the book Case-Based Reasoning Research and Development by Alexander J. Zaslavski
Cover of the book Yeast Membrane Transport by Alexander J. Zaslavski
Cover of the book Cognitive Theory and Documentary Film by Alexander J. Zaslavski
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy