© 2013

Structure of Approximate Solutions of Optimal Control Problems


Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Alexander J. Zaslavski
    Pages 1-9
  3. Alexander J. Zaslavski
    Pages 11-75
  4. Alexander J. Zaslavski
    Pages 77-104
  5. Alexander J. Zaslavski
    Pages 105-124
  6. Back Matter
    Pages 125-127

About this book


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.


Agreeable trajectory-control pair approximate solution good trajectory-control pair turnpike property

Authors and affiliations

  1. 1.Department of MathematicsTechnion- Israel Institute of TechnologyHaifaIsrael

Bibliographic information


From the reviews:

“The author is interested in properties of approximate solutions which are independent of the interval, for all sufficiently large intervals. The results in this book are focused on the so-called turnpike property of the optimal control problems. … The book should be of interest to researchers in mathematical economics and/or in optimal control theory and the calculus of variations.” (Marian Mureşan, Mathematical Reviews, March, 2014)