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k-dimensional agreement in multiagent systems
G. Bianchin, M. Vaquero, J. Cortés, E. Dall'Anese
IEEE Transactions on Automatic Control 69 (12) (2024), 8978-8985

Abstract

We study the problem of k-dimensional linear agreement, whereby a group of agents is interested in computing k independent weighted means of a global vector whose entries are known only by individual agents. This problem is motivated by applications in distributed computing and sensing, where agents seek to evaluate multiple independent functions at a common vector point by running a single distributed algorithm. We propose the use of linear network protocols for this task, and we show that linear dynamics can agree on quantities that are oblique projections of the global vector onto certain subspaces. Moreover, we provide algebraic necessary and sufficient conditions that characterize all agreement protocols that are consistent with a certain graph, we propose a design procedure for constructing such protocols, and we study what classes of graphs can achieve agreement on arbitrary weights. Overall, our results suggest that k-dimensional agreement requires the use of communication graphs with higher connectivity compared to standard consensus algorithms; more precisely, we relate the existence of Hamiltonian decompositions in a graph with the capability of that graph to sustain an agreement protocol. The applicability of the framework is illustrated via simulations for two problems in robotic formation and in distributed regression.

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