Structure of Approximate Solutions of Optimal Control Problems

verfasst von: Alexander J. Zaslavski

Verlag: Springer International Publishing

Buchreihe : SpringerBriefs in Optimization

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This title examines the structure of approximate solutions of optimal control problems considered on subintervals of a real line. Specifically at the properties of approximate solutions which are independent of the length of the interval. The results illustrated in this book look into the so-called turnpike property of optimal control problems. The author generalizes the results of the turnpike property by considering a class of optimal control problems which is identified with the corresponding complete metric space of objective functions. This establishes the turnpike property for any element in a set that is in a countable intersection which is open everywhere dense sets in the space of integrands; meaning that the turnpike property holds for most optimal control problems. Mathematicians working in optimal control and the calculus of variations and graduate students will find this book useful and valuable due to its presentation of solutions to a number of difficult problems in optimal control and presentation of new approaches, techniques and methods.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

In this chapter we discuss turnpike results for variational problems on large finite intervals and existence results for variational problems over an infinite horizon.

Alexander J. Zaslavski

Chapter 2. Turnpike Properties of Optimal Control Problems

Abstract

In this chapter we study a class of optimal control problems (with the same system of differential equations, the same functional constraints and the same boundary conditions) which is identified with the corresponding complete metric space of objective functions (integrands). The main results of this chapter establish the turnpike property for any element of a set which is a countable intersection of open everywhere dense sets in the space of integrands.

Alexander J. Zaslavski

Chapter 3. Infinite Horizon Problems

Abstract

In this chapter we study infinite horizon optimal control problems corresponding to the space of integrands introduced in Chap. 2. We establish the existence of overtaking optimal solutions and agreeable solutions for optimal control problems with integrands possessing the turnpike property.

Alexander J. Zaslavski

Chapter 4. Linear Control Systems

Abstract

In this chapter we apply the results of Chaps 2 and 3 for a class of linear control problems which is of great importance in the control theory and engineering. For this class of problems we establish the existence of solutions over an infinite horizon and the turnpike property.

Alexander J. Zaslavski

Backmatter

Titel: Structure of Approximate Solutions of Optimal Control Problems
verfasst von: Alexander J. Zaslavski
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-01240-7
Print ISBN: 978-3-319-01239-1
DOI: https://doi.org/10.1007/978-3-319-01240-7