Duality and Approximation Methods for Cooperative Optimization and Control.

Duality and Approximation Methods for Cooperative Optimization and Control.

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Bibliographic Details
Online Access: Full text (MCPHS users only)
Main Author: Bürger, Mathias
Format: Electronic eBook
Language:English
Published: Berlin : Logos Verlag Berlin, 2014
Subjects:
Duality theory (Mathematics)
Local Note:ProQuest Ebook Central

MARC

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505 0 |a Intro; 1 Introduction; 1.1 Motivation and Focus; 1.2 Contributions and Organization; 2 Polyhedral Approximation Methods for Cooperative Optimization; 2.1 Introduction; 2.2 Distributed Algorithms in Peer-to-Peer Networks; 2.2.1 Communication Network Model; 2.2.2 Distributed Algorithms; 2.2.3 Complexity Notions; 2.3 The Cutting-Plane Consensus Algorithm; 2.3.1 General Problem Formulation; 2.3.2 Unique Solution Linear Programming; 2.3.3 The Algorithm Definition; 2.3.4 Technical Analysis; 2.4 Convex Inequality Constraints; 2.4.1 Problem Formulation; 2.4.2 Semidefinite Constraints. 
505 8 |a 2.4.3 Linear Constraints2.4.4 Application Example: Position Estimation in Wireless Sensor Networks; 2.5 Robust Optimization with Uncertain Constraints; 2.5.1 Problem Formulation; 2.5.2 Efficiently Solvable Problems; 2.5.3 Computational Study: Robust Linear Programming; 2.6 Conclusions; 3 Dual Cutting-Plane and Trajectory Exchange Optimization; 3.1 Introduction; 3.2 A Motivating Problem: Distributed Cooperative Model Predictive Control; 3.2.1 Problem Formulation; 3.2.2 Dual Semi-Infinite Problem Representation; 3.3 Revisiting the Richards and How Algorithm. 
505 8 |a 3.4 Distributed Nonlinear Dantzig-Wolfe Decomposition3.4.1 Distributed Constraint Generation; 3.4.2 Linear Programming Dual Interpretation; 3.4.3 CPC-based Trajectory Exchange Method; 3.5 Application Example: Distributed Microgrid Control; 3.6 Conclusions; 4 Duality and Network Theory in Cooperative Control; 4.1 Introduction; 4.2 Preliminaries; 4.2.1 Algebraic Graph Theory; 4.2.2 Network Theory; 4.2.3 Equilibrium Independent Passivity; 4.3 Duality in Passivity-based Cooperative Control; 4.3.1 The Plant Level; 4.3.2 The Control Level; 4.3.3 The Closed-Loop Perspective. 
505 8 |a 4.4 Application Example: Optimal Distribution Control4.5 Conclusions; 5 Clustering in Dynamical Networks; 5.1 Introduction; 5.2 Constrained Flows & Network Clustering; 5.2.1 A Primal/Dual and Saddle-Point Perspective; 5.2.2 Saddle-Point Problem and Network Clustering; 5.3 Clustering in Dynamical Networks; 5.3.1 A Dynamical Model for Clustering; 5.3.2 Clustering Analysis and Convergence; 5.3.3 Application Examples; 5.4 Hierarchical Clustering Using a Saddle-Point Analysis; 5.4.1 Combinatorial Conditions for Clustering; 5.4.2 A Hierarchical Clustering Algorithm. 
505 8 |a 5.4.3 Application Example: Structural Analysis of Power Networks5.5 Conclusions; 6 Conclusions and Outlook; 6.1 Conclusions; 6.2 Outlook; A Convex Analysis and Optimization Theory; B Dynamical Systems and Control Theory; C Graph Theory. 
520 8 |a Annotation  |b This thesis investigates the role of duality and the use of approximation methods in cooperative optimization and control. Concerning cooperative optimization, a general algorithm for convex optimization in networks with asynchronous communication is presented. Based on the idea of polyhedral approximations, a family of distributed algorithms is developed to solve a variety of distributed decision problems, ranging from semi-definite and robust optimization problems up to distributed model predictive control. Optimization theory, and in particular duality theory, are shown to be central elements also in cooperative control. This thesis establishes an intimate relation between passivity-based cooperative control and network optimization theory. The presented results provide a complete duality theory for passivity-based cooperative control and lead the way to novel analysis tools for complex dynamic phenomena. In this way, this thesis presents theoretical insights and algorithmic approaches for cooperative optimization and control, and emphasizes the role of convexity and duality in this field. 
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