Turnpike Conditions in Infinite Dimensional Optimal Control

  • Alexander J. Zaslavski

Part of the Springer Optimization and Its Applications book series (SOIA, volume 148)

Table of contents

  1. Front Matter
    Pages i-x
  2. Alexander J. Zaslavski
    Pages 1-24
  3. Alexander J. Zaslavski
    Pages 25-130
  4. Alexander J. Zaslavski
    Pages 131-195
  5. Alexander J. Zaslavski
    Pages 197-267
  6. Alexander J. Zaslavski
    Pages 269-384
  7. Alexander J. Zaslavski
    Pages 385-478
  8. Alexander J. Zaslavski
    Pages 479-562
  9. Back Matter
    Pages 563-570

About this book


This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces.  

The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces.  Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.​


infinite dimensional optimal control turnpike phenomenon discrete-time optimal control problems continuous-time infinite dimensional optimal control finite-dimensional variational optimal control problems applied functional analysis

Authors and affiliations

  • Alexander J. Zaslavski
    • 1
  1. 1.Department of MathematicsThe Technion – Israel Institute of TechnologyHaifaIsrael

Bibliographic information