Discrete-time optimal control and games on large intervals. ([2017])
- Record Type:
- Book
- Title:
- Discrete-time optimal control and games on large intervals. ([2017])
- Main Title:
- Discrete-time optimal control and games on large intervals
- Further Information:
- Note: Alexander J. Zaslavski.
- Authors:
- Zaslavski, Alexander J
- Contents:
- Preface; Contents; 1 Introduction; 1.1 Convex Discrete-Time Problems; 1.2 The Turnpike Phenomenon; 1.3 Nonconcave (Nonconvex) Problems; 1.4 Examples; 1.5 Two-Player Zero-Sum Games; 2 Lagrange Problems; 2.1 Discrete-Time Optimal Control Systems; 2.2 The Turnpike Results; 2.3 Auxiliary Results for Theorem 2.5; 2.4 Proof of Theorem 2.5; 2.5 Proof of Theorem 2.6; 2.6 Overtaking Optimal Programs; 2.7 Auxiliary Results; 2.8 Structure of Solutions in the Regions Close to the Endpoints; 2.9 Proof of Theorems 2.15 and 2.16; 2.10 Proof of Proposition 2.25. 2.11 Proofs of Propositions 2.26, 2.27, and 2.312.12 A Basic Lemma for Theorem 2.32; 2.13 Proof of Theorem 2.32; 2.14 Proof of Theorem 2.33; 2.15 Proof of Proposition 2.34; 2.16 Proof of Theorem 2.35; 2.17 Structure of Solutions of the Problem (P1); 2.18 Proof of Theorem 2.43; 3 Bolza Problems; 3.1 The First Class of Bolza Problems; 3.2 Structure of Solutions of the Problem (P4) in the Regions Close to the Endpoints; 3.3 A Basic Lemma for Theorem 3.4; 3.4 Proof of Theorem 3.4; 3.5 Proof of Proposition 3.7; 3.6 Proof of Theorem 3.6; 3.7 Proof of Proposition 3.9. 3.8 The Second Class of Bolza Problems3.9 Proof of Theorem 3.14; 3.10 Auxiliary Results for Theorem 3.15; 3.11 Proof of Theorem 3.15; 3.12 Proof of Theorem 3.17; 3.13 Proof of Theorem 3.18; 4 Stability Results for Bolza Problems; 4.1 Preliminaries and Stability Results for Lagrange Problems; 4.2 Extensions; 4.3 Lagrange Problems with Discounting; 4.4 Turnpike Results forPreface; Contents; 1 Introduction; 1.1 Convex Discrete-Time Problems; 1.2 The Turnpike Phenomenon; 1.3 Nonconcave (Nonconvex) Problems; 1.4 Examples; 1.5 Two-Player Zero-Sum Games; 2 Lagrange Problems; 2.1 Discrete-Time Optimal Control Systems; 2.2 The Turnpike Results; 2.3 Auxiliary Results for Theorem 2.5; 2.4 Proof of Theorem 2.5; 2.5 Proof of Theorem 2.6; 2.6 Overtaking Optimal Programs; 2.7 Auxiliary Results; 2.8 Structure of Solutions in the Regions Close to the Endpoints; 2.9 Proof of Theorems 2.15 and 2.16; 2.10 Proof of Proposition 2.25. 2.11 Proofs of Propositions 2.26, 2.27, and 2.312.12 A Basic Lemma for Theorem 2.32; 2.13 Proof of Theorem 2.32; 2.14 Proof of Theorem 2.33; 2.15 Proof of Proposition 2.34; 2.16 Proof of Theorem 2.35; 2.17 Structure of Solutions of the Problem (P1); 2.18 Proof of Theorem 2.43; 3 Bolza Problems; 3.1 The First Class of Bolza Problems; 3.2 Structure of Solutions of the Problem (P4) in the Regions Close to the Endpoints; 3.3 A Basic Lemma for Theorem 3.4; 3.4 Proof of Theorem 3.4; 3.5 Proof of Proposition 3.7; 3.6 Proof of Theorem 3.6; 3.7 Proof of Proposition 3.9. 3.8 The Second Class of Bolza Problems3.9 Proof of Theorem 3.14; 3.10 Auxiliary Results for Theorem 3.15; 3.11 Proof of Theorem 3.15; 3.12 Proof of Theorem 3.17; 3.13 Proof of Theorem 3.18; 4 Stability Results for Bolza Problems; 4.1 Preliminaries and Stability Results for Lagrange Problems; 4.2 Extensions; 4.3 Lagrange Problems with Discounting; 4.4 Turnpike Results for Perturbed Problems (P4); 4.5 Proof of Theorem 4.13; 4.6 Proof of Theorem 4.14; 4.7 Turnpike Results for Perturbed Problems (P3); 4.8 Auxiliary Results; 4.9 Proof of Theorem 4.15; 4.10 Proof of Theorem 4.16. 4.11 Turnpike Results for Perturbed Problems (P5)4.12 Proof of Theorem 4.21; 4.13 Proof of Theorem 4.22; 4.14 Perturbed Problems (P4); 4.15 An Auxiliary Result for Problem (P4); 4.16 Structure of Solutions of Perturbed Problems (P4); 4.17 Perturbed Problems (P5); 4.18 An Auxiliary Result for Problem (P5); 4.19 Structure of Solutions of Perturbed Problems (P5); 4.20 Perturbed Problems (P5) with Discounting; 5 Unconstrained Games Without Convexity-Concavity Assumptions; 5.1 Preliminaries and Main Results; 5.2 Proof of Proposition 5.1; 5.3 Proof of Proposition 5.2; 5.4 Proof of Proposition 5.3. 5.5 Good Pairs of Sequences5.6 Proof of Proposition 5.6; 5.7 Proof of Proposition 5.7; 5.8 Auxiliary Results; 5.9 Proof of Theorem 5.8; 5.10 Proof of Theorem 5.9; 6 Constrained Games Without Convexity-Concavity Assumptions; 6.1 Preliminaries; 6.2 Main Results; 6.3 Proofs of Theorems 6.4 and 6.5; 6.4 Proof of Theorem 6.6; 6.5 Proof of Theorem 6.7; 6.6 Auxiliary Results; 6.7 Proofs of Theorems 6.8 and 6.9; 6.8 Proofs of Theorems 6.10 and 6.11; 6.9 Examples; 7 Nonautonomous Games with Convexity-Concavity Assumptions; 7.1 Preliminaries; 7.2 Proof of Theorem 7.4; 7.3 A Space of Objective Functions. … (more)
- Publisher Details:
- Cham, Switzerland : Springer
- Publication Date:
- 2017
- Copyright Date:
- 2017
- Extent:
- 1 online resource
- Subjects:
- 519.3
Mathematics
Two-person zero-sum games
Discrete-time systems
MATHEMATICS -- Applied
MATHEMATICS -- Probability & Statistics -- General
Discrete-time systems
Two-person zero-sum games
Science -- System Theory
Business & Economics -- Operations Research
Cybernetics & systems theory
Operational research
Mathematical optimization
Systems theory
Mathematics -- Calculus
Calculus of variations
Electronic books - Languages:
- English
- ISBNs:
- 9783319529325
3319529323 - Related ISBNs:
- 9783319529318
3319529315 - Notes:
- Note: Includes bibliographical references and index.
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