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Introduction

In: Turnpike Theory of Continuous-Time Linear Optimal Control Problems

Author

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  • Alexander J. Zaslavski

    (The Technion - Israel Institute of Technology)

Abstract

The study of the existence and the structure of solutions of optimal control problems defined on infinite intervals and on sufficiently large intervals has recently been a rapidly growing area of research. See, for example, [2–4, 6–11, 13, 14, 16, 19, 20, 22, 25, 27, 32–34, 36, 37, 46–49, 51, 52] and the references mentioned therein. These problems arise in engineering [1, 23, 44, 56, 57], in models of economic growth [12, 13, 17, 22, 26, 31, 35, 39–41, 44, 45, 53, 55], in the game theory [18, 21, 43, 44, 50, 53, 54], in infinite discrete models of solid-state physics related to dislocations in one-dimensional crystals [5, 42], and in the theory of thermodynamical equilibrium for materials [15, 24, 28–30]. In this chapter we explain the turnpike phenomenon for a simple class of variational problems, discuss certain turnpike results obtained in our previous research, and describe the structure of the book.

Suggested Citation

  • Alexander J. Zaslavski, 2015. "Introduction," Springer Optimization and Its Applications, in: Turnpike Theory of Continuous-Time Linear Optimal Control Problems, edition 127, chapter 0, pages 1-19, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-19141-6_1
    DOI: 10.1007/978-3-319-19141-6_1
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