NDLI: Continuous-time distributed optimization of homogenous dynamics

Content Provider	IEEE Xplore Digital Library
Author	Guodong Shi Proutiere, A. Johansson, K.H.
Copyright Year	2013
Description	Author affiliation: ACCESS Linnaeus Centre, R. Inst. of Technol., Stockholm, Sweden (Guodong Shi; Proutiere, A.; Johansson, K.H.)
Abstract	This paper makes an attempt to explore the fundamental properties of distributed methods for minimizing a sum of objective functions with each component only known to a particular node, given a certain level of node knowledge and computation capacity. The information each node receives from its neighbors can be any nonlinear function of its neighbors' states as long as the function takes value zero within the local consensus manifold. Each node also observes the gradient of its own objective function at its current state. The update dynamics of each node is a first-order integrator. The admissible control input of each node is homogeneous, given by a binary function with each variable corresponding to the neighboring term and the gradient term, respectively. The function determining the control law is assumed to be injective when the first variable is fixed to zero. It is proven that there exists a control rule which guarantees global optimal consensus if and only if the solution sets of the local objectives admit a nonempty intersection set for fixed strongly connected graphs. Then we show that for any tolerated error, we can find a simple control rule that guarantees global optimal consensus within this error for fixed, bidirectional, and connected graphs under mild conditions. For time-varying graphs, we show that optimal consensus can always be achieved by a simple control rule as long as the graph is uniformly jointly strongly connected and the nonempty intersection condition holds. The results illustrate that nonempty intersection for the local optimal solution sets is a critical condition for distributed optimization using consensus processing to connect the information over the nodes.
Sponsorship	IEEE Cont. Syst. Soc.
Starting Page	520
Ending Page	527
File Size	663884
Page Count	8
File Format	PDF
e-ISBN	9781479934102
DOI	10.1109/Allerton.2013.6736569
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-10-02
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Manifolds Distributed optimization Dynamical Systems Optimal consensus Linear programming Convex functions Trajectory Optimization Manganese Multi-agent systems
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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