Turnpike Theory of Continuous-Time Linear Optimal Control Problems

✍ Scribed by Alexander J. Zaslavski (auth.)

Publisher: Springer International Publishing
Year: 2015
Tongue: English
Leaves: 300
Series: Springer Optimization and Its Applications 104
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control and in applied functional analysis.

Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous convex smooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integrands.

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-19
Linear Control Systems with Periodic Convex Integrands....Pages 21-84
Linear Control Systems with Nonconvex Integrands....Pages 85-125
Stability Properties....Pages 127-162
Linear Control Systems with Discounting....Pages 163-190
Dynamic Zero-Sum Games with Linear Constraints....Pages 191-207
Genericity Results....Pages 209-231
Variational Problems with Extended-Valued Integrands....Pages 233-268
Dynamic Games with Extended-Valued Integrands....Pages 269-289
Back Matter....Pages 291-296

✦ Subjects

Calculus of Variations and Optimal Control; Optimization; Operations Research, Management Science; Game Theory, Economics, Social and Behav. Sciences

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