Lozovanu Optimization and Multiobjective Control of Time-Discrete Systems

Dynamic Networks and Multilayered Structures
1. Auflage 2009
ISBN: 978-3-540-85025-0
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 285 Seiten

Richard Bellmann developed a theory of dynamic programming which is for many reasons still in the center of great interest. The authors present a new approach in the ?eld of the optimization and multi-objective control of time-discrete systems which is closely related to the work of Richard Bellmann. They develop their own concept and their extension to the optimization and multi-objective control of time-discrete systems as well as to dynamic networks and multilayered structures are very stimulating for further research. Di?erent perspectives of discrete control and optimal dynamic ?ow problems on networks are treated and characterized. Together with the algorithmic solutions a framework of multi-objective control problems is - rived. The conclusion with a real world example underlines the necessity and - portance of their theoretic framework. As they come back to the classical Bellmann concept of dynamic programming they stress and honor his basic concept without debase their own work. Multilayereddecisionprocessesaspartofthedesignandanalysisofcomplexsystems and networks will be essential in many ways and ?elds in the future.

Autoren/Hrsg.

Lozovanu, Dmitrii

Inhaltsverzeichnis

1;Foreword;5
2;Preface;6
3;Contents;9
4;1 Multi-Objective Control of Time-Discrete Systems and Dynamic Games on Networks;15
4.1;1.1 Problem Formulation;15
4.2;1.2 Multi-Objective Control of Time-Discrete Systems with Infinite Time Horizon;24
4.3;1.3 Alternate Players’ Control Condition and Nash Equilibria for Dynamic Games in Positional Form;25
4.4;1.4 Algorithms for Solving Single-Objective Control Problems on Networks;29
4.5;1.5 Multi-Objective Control and Non-Cooperative Games on Dynamic Networks;36
4.6;1.6 Main Results for Dynamic c-Games with Constant Costs of the Edges and Determining Optimal Stationary Strategies of the Players;40
4.7;1.7 Computational Complexity of the Problem of Determining Optimal Stationary Strategies in a Dynamic c-Game;59
4.8;1.8 Determining the Optimal Stationary Strategies for a Dynamic c-Game with Non-Constant Cost Functions on the Edges;59
4.9;1.9 Determining Nash Equilibria for Non-Stationary Dynamic c-Games;67
4.10;1.10 Application of the Dynamic c-Game for Studying and Solving Multi-Objective Control Problems;71
4.11;1.11 Multi-Objective Control and Cooperative Games on Dynamic Networks;72
4.12;1.12 Determining Pareto Solutions for Multi-Objective Control Problems on Networks;74
4.13;1.13 Determining Pareto Optima for Multi-Objective Control Problems;80
4.14;1.14 Determining a Stackelberg Solution for Hierarchical Control Problems;81
5;2 Max-Min Control Problems and Solving Zero-Sum Games on Networks;94
5.1;2.1 Discrete Control and Finite Antagonistic Dynamic Games;94
5.2;2.2 Max-Min Control Problem with Infinite Time Horizon;95
5.3;2.3 Zero-Sum Games on Networks and a Polynomial Time Algorithm for Max-Min Paths Problems;96
5.4;2.4 A Polynomial Time Algorithm for Solving Acyclic;114
5.5;2.5 Cyclic Games: Algorithms for Finding the Value and the Optimal Strategies of the Players;118
5.6;2.6 Cyclic Games with Random States’ Transitions of the Dynamical System;130
5.7;2.7 A Nash Equilibria Condition for Cyclic Games with;131
5.8;2.8 Determining Pareto Optima for Cyclic Games with p Players;135
6;3 Extension and Generalization of Discrete Control Problems and Algorithmic Approaches for its Solving;137
6.1;3.1 Discrete Control Problems with Varying Time of States’ Transitions of the Dynamical System;137
6.2;3.2 The Control Problem on a Network with Transition-Time Functions on the Edges;145
6.3;3.3 Multi-Objective Control of Time-Discrete Systems with Varying Time of States’ Transitions;153
6.4;3.4 An Algorithm for Solving the Discrete Optimal Control Problem with Infinite Time Horizon and Varying Time of the States’ Transitions;162
6.5;3.5 A General Approach for Algorithmic Solutions of Discrete Optimal Control Problems and its Game-Theoretic Extension;166
6.6;3.6 Pareto-Nash Equilibria for Multi-Objective Games;183
7;4 Discrete Control and Optimal Dynamic Flow Problems on Networks;192
7.1;4.1 Single-Commodity Dynamic Flow Problems and the Time-Expanded Network Method for Their Solving;192
7.2;4.2 Multi-Commodity Dynamic Flow Problems and Algorithms for their Solving;225
7.3;4.3 The Game-Theoretic Approach for Dynamic Flow Problems on Networks;242
8;5 Applications and Related Topics;244
8.1;5.1 Analysis and Control of Time-Discrete Systems: Resource Planning - The TEM Model;244
8.2;5.2 Algorithmic Solutions for an Emission Reduction Game: The Kyoto Game;261
8.3;5.3 An Emission Reduction Process - The MILAN Model;280
9;Conclusion;286
10;References;287
11;Index;293