Turnpike Conditions in Infinite Dimensional Optimal Control

✍ Scribed by Alexander J. Zaslavski

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 578
• Series: Springer Optimization and Its Applications 148
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
Introduction (Alexander J. Zaslavski)....Pages 1-24
Discrete-Time Autonomous Problems (Alexander J. Zaslavski)....Pages 25-130
Discrete-Time Nonautonomous Problems on the Half-Axis (Alexander J. Zaslavski)....Pages 131-195
Discrete-Time Nonautonomous Problems on Axis (Alexander J. Zaslavski)....Pages 197-267
Continuous-Time Autonomous Problems (Alexander J. Zaslavski)....Pages 269-384
Continuous-Time Nonautonomous Problems on the Half-Axis (Alexander J. Zaslavski)....Pages 385-478
Continuous-Time Nonautonomous Problems on Axis (Alexander J. Zaslavski)....Pages 479-562
Back Matter ....Pages 563-570

✦ Subjects

Mathematics; Calculus of Variations and Optimal Control; Optimization; Partial Differential Equations; Functional Analysis; Group Theory and Generalizations