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Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems 2014 ed. [Minkštas viršelis]

  • Formatas: Paperback / softback, 109 pages, aukštis x plotis: 235x155 mm, weight: 1942 g, X, 109 p., 1 Paperback / softback
  • Serija: SpringerBriefs in Optimization
  • Išleidimo metai: 01-Sep-2014
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319080334
  • ISBN-13: 9783319080338
Kitos knygos pagal šią temą:
Stability of the Turnpike Phenomenon in Discrete-Time Optimal Control Problems 2014 ed.Didesnis paveikslėlis
  • Formatas: Paperback / softback, 109 pages, aukštis x plotis: 235x155 mm, weight: 1942 g, X, 109 p., 1 Paperback / softback
  • Serija: SpringerBriefs in Optimization
  • Išleidimo metai: 01-Sep-2014
  • Leidėjas: Springer International Publishing AG
  • ISBN-10: 3319080334
  • ISBN-13: 9783319080338
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783319080338.html
Raktažodžiai:
The structure of approximate solutions of autonomous discrete-time optimal control problems and individual turnpike results for optimal control problems without convexity (concavity) assumptions are examined in this book. In particular, the book focuses on the properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals; these results apply to the so-called turnpike property of the optimal control problems. By encompassing the so-called turnpike property the approximate solutions of the problems are determined primarily by the objective function and are fundamentally independent of the choice of interval and endpoint conditions, except in regions close to the endpoints. This book also explores the turnpike phenomenon for two large classes of autonomous optimal control problems. It is illustrated that the turnpike phenomenon is stable for an optimal control problem if the corresponding infinite horizon optimal control

problem possesses an asymptotic turnpike property. If an optimal control problem belonging to the first class possesses the turnpike property, then the turnpike is a singleton (unit set). The stability of the turnpike property under small perturbations of an objective function and of a constraint map is established. For the second class of problems where the turnpike phenomenon is not necessarily a singleton the stability of the turnpike property under small perturbations of an objective function is established. Containing solutions of difficult problems in optimal control and presenting new approaches, techniques and methods this book is of interest for mathematicians working in optimal control and the calculus of variations. It also can be useful in preparation courses for graduate students.

1.Introduction.- 2. Optimal control problems with singleton-turnpikes.- 3. Optimal control problems with discounting.- 4. Optimal control problems with nonsingleton-turnpikes.- References.

Recenzijos

The book is intended for graduate students and researchers specialized in the areas of control, optimization and game theories, and their applications. The book is well organized. The presentation is clear and logical. The proofs of the stated results are rigorous. I believe that the book is an excellent addition to the existing literature on the turnpike theory and its applications and that it has the potential for stimulating further research in the area. (V. G. Gatsgori, Mathematical Reviews, October, 2015)

The book is a continuation of several papers and also a previous book by the author devoted to the study of the structure of approximate solutions of nonconvex (nonconcave) discrete-time optimal control problems. The book could be addressed to postgraduate students as well as to control engineers and researches. (Bozhidar Cheshankov, zbMATH, Vol. 1305, 2015)

1 Introduction
1(8)
1.1 The Turnpike Phenomenon
1(2)
1.2 Discrete-Time Problems
3(3)
1.3 Examples
6(3)
2 Optimal Control Problems with Singleton Turnpikes
9(38)
2.1 Preliminaries and Stability Results
9(5)
2.2 Extensions
14(2)
2.3 Three Lemmata
16(4)
2.4 Auxiliary Results
20(14)
2.5 Proofs of Theorems 2.2 and 2.3
34(3)
2.6 Proofs of Theorems 2.4 and 2.5
37(3)
2.7 Proof of Theorem 2.6
40(3)
2.8 Proof of Theorems 2.7 and 2.8
43(4)
3 Optimal Control Problems with Discounting
47(18)
3.1 Stability of the Turnpike Phenomenon
47(3)
3.2 Auxiliary Results
50(7)
3.3 Proofs of Theorems 3.2 and 3.3
57(4)
3.4 Proof of Theorem 3.4
61(4)
4 Optimal Control Problems with Nonsingleton Turnpikes
65(40)
4.1 Discrete-Time Optimal Control Systems
65(2)
4.2 The Turnpike Property
67(3)
4.3 Preliminaries
70(6)
4.4 Auxiliary Results
76(20)
4.5 Proof of Theorem 4.5
96(9)
References 105(4)
Index 109