Graph Interpretation of the Method of Orthogonal Projection for Regularization in Multiagent Systems

Agaev, Rafig; Khomutov, Dmitriy

doi:10.1109/mlsd52249.2021.9600239

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…In addition to describing physical diffusion processes in networks, similar models appear when simulating information processes, in particular the dynamics of opinions and reaching a consensus in multi-agent systems. At the present time, the classic DeGroot model [17] has many different modifications [18][19][20][21]. Homogeneous and non-homogeneous Markov chains are one of the main tools for describing multi-state systems, processes, and devices [22,23].…”

Section: Introductionmentioning

confidence: 99%

Some Properties of Stochastic Matrices and Non-Homogeneous Markov Chains Generated by Nonlinearities in the Resource Network Model

2022

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The resource network is a non-linear threshold model where vertices exchange resource in infinite discrete time. The model is represented by a directed weighted graph. At each time step, all vertices send their resources along all output edges following one of two rules. For each vertex, the threshold value for changing the operation rule is equal to the total weight of its outgoing edges. If all vertices have resources less than their thresholds, the network is completely described by a homogeneous Markov chain. If at least one of the vertices has a resource above the threshold, the network is described by a non-homogeneous Markov chain. The purpose of this article is to describe and investigate non-homogeneous Markov chains generated by the resource network model. It is proven that they are strongly ergodic. In addition, stochastic matrices of a special form were studied. A number of new properties were revealed for them. The results obtained were generalized to arbitrary stochastic matrices.

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Section: Introductionmentioning

confidence: 99%

Some Properties of Stochastic Matrices and Non-Homogeneous Markov Chains Generated by Nonlinearities in the Resource Network Model

2022

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On the Properties of Orthogonal Projection Method for Reaching Consensus

Agaev,

Khomutov

2023

Autom Remote Control

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O svoystvakh metoda ortogonal'noy proektsii v zadache o konsensuse

Agaev,

Khomutov

2023

Avtomatika i telemehanika

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The article is devoted to an asymptotic behavior of a multi-agent system with information links. We proved that the orthogonal projection method proposed for the regularization of the consensus protocol is characterized by a pseudoinverse matrix for the introduced auxiliary matrix for an arbitrary communication digraph of a multi-agent system. We cosidered the eigenprojection of the Laplacian matrix corresponding to the communication digraph, in which the influences on the fixed agent change proportionally. We obtained a number of results that are of independent importance and can be used in models of multi-agent systems with different protocols.

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Graph Interpretation of the Method of Orthogonal Projection for Regularization in Multiagent Systems

Cited by 3 publications

References 9 publications

Some Properties of Stochastic Matrices and Non-Homogeneous Markov Chains Generated by Nonlinearities in the Resource Network Model

Some Properties of Stochastic Matrices and Non-Homogeneous Markov Chains Generated by Nonlinearities in the Resource Network Model

On the Properties of Orthogonal Projection Method for Reaching Consensus

O svoystvakh metoda ortogonal'noy proektsii v zadache o konsensuse

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