Continuous-time Proportional-Integral Distributed Optimization for Networked Systems
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Abstract
In this paper we explore the relationship between dual decomposition and the consensus-based
method for distributed optimization. The relationship is developed by examining the similarities
between the two approaches and their relationship to gradient-based constrained optimization.
By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient
method for optimization with one using a proportional control term and the other using an integral
control term to drive the system to the constraint set. Therefore, a significant contribution of this
paper is to combine these methods to develop a continuous-time proportional-integral distributed
optimization method. Furthermore, we establish convergence using Lyapunov stability techniques
and utilizing properties from the network structure of the multi-agent system.
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2014-07
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