Optimal distributed linear averaging

A new optimal distributed linear averaging (ODLA) problem is presented in this paper. This problem is motivated by the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering. The aim of th...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 47; no. 12; pp. 2713 - 2719
Main Author: Hui, Qing
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.12.2011
Elsevier
Subjects:
Adaptative systems
Algorithms
Applied sciences
Autonomous
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Constraints
Control of networks
Control system analysis
Control theory. Systems
Cooperative control
Cost engineering
Distributed consensus
Equivalence
Exact sciences and technology
Graphs
Linear iteration
Minimization
Optimal control
Optimization
Software
Distributed consensus
Control of networks
Optimal control
Cooperative control
Linear iteration
Optimization
Averaging method
Necessary and sufficient condition
Adaptive control
Convex programming
Cooperation
Quadratic cost
Infinite horizon
Optimal control (mathematics)
Mathematical programming
Coordination
Optimal algorithm
Initial value problem
Minimization
Distributed system
Consensus
Constrained optimization
Multiagent system
Distributed algorithm
Discrete time
Distributed control
Quadratic functional
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:A new optimal distributed linear averaging (ODLA) problem is presented in this paper. This problem is motivated by the distributed averaging problem which arises in the context of distributed algorithms in computer science and coordination of groups of autonomous agents in engineering. The aim of the ODLA problem is to compute the average of the initial values at nodes of a graph through an optimal distributed algorithm in which the nodes in the graph can only communicate with their neighbors. Optimality is given by a minimization problem of a quadratic cost functional under infinite horizon. We show that this problem has a very close relationship with the notion of semistability. By developing new necessary and sufficient conditions for semistability of linear discrete-time systems, we convert the proposed ODLA problem into an equivalent, constrained optimization problem and then derive a solvable, fixed-structure convex optimization problem.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2011.09.001