Turnpike Phenomenon in Metric Spaces

Author:   Alexander J. Zaslavski
Publisher:   Springer International Publishing AG
Edition:   1st ed. 2023
Volume:   201
ISBN:  

9783031272073


Pages:   362
Publication Date:   18 April 2023
Format:   Hardback
Availability:   Manufactured on demand   Availability explained
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Turnpike Phenomenon in Metric Spaces


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Overview

This book is devoted to the study of the turnpike phenomenon arising in optimal control theory. Special focus is placed on Turnpike results, in sufficient and necessary conditions for the turnpike phenomenon and in its stability under small perturbations of objective functions. The most important feature of this book is that it develops a large, general class of optimal control problems in metric space. Additional value is in the provision of solutions to a number of difficult and interesting problems in optimal control theory in metric spaces. Mathematicians working in optimal control, optimization, and experts in applications of optimal control to economics and engineering, will find this book particularly useful. All main results obtained in the book are new. The monograph contains nine chapters. Chapter 1 is an introduction. Chapter 2 discusses Banach space valued functions, set-valued mappings in infinite dimensional spaces, and related continuous-time dynamical systems. Some convergence results are obtained. In Chapter 3, a discrete-time dynamical system with a Lyapunov function in a metric space induced by a set-valued mapping, is studied. Chapter 4 is devoted to the study of a class of continuous-time dynamical systems, an analog of the class of discrete-time dynamical systems considered in Chapter 3. Chapter 5 develops a turnpike theory for a class of general dynamical systems in a metric space with a Lyapunov function. Chapter 6 contains a study of the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of half-axis in metric spaces, which are not necessarily compact. Chapter 7 contains preliminaries which are needed in order to study turnpike properties of infinite-dimensional optimal control problems. In Chapter 8, sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems on subintervals of the half-axis in metric spaces, is established. In Chapter 9, the examination continues of the turnpike phenomenon for the continuous-time optimal control problems on subintervals of half-axis in metric spaces discussed in Chapter 8.

Full Product Details

Author:   Alexander J. Zaslavski
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2023
Volume:   201
Weight:   0.723kg
ISBN:  

9783031272073


ISBN 10:   3031272072
Pages:   362
Publication Date:   18 April 2023
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Preface1. Introduction2. Differential inclusions3. Discrete-time dynamical systems4. Continuous-time dynamical systems5. General dynamical systems with a Lyapunov function6. Discrete-time nonautonomous problems on half-axis7. Infinite-dimensional control8. Continuous-time nonautonomous problems on half-axis9. Stability and genericity resultsReferencesIndex

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Author Information

Alexander J. Zaslavski, Department of Mathematics, Technion – Israel Institute of Technology, Rishon LeZion, Israel.

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