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Theorems about Ergodicity and Class-Ergo...

Bolouki, Sadegh...

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Theorems about Ergodicity and Class-Ergodicity of Chains with Applications in Known Consensus Models by Bolouki, Sadegh ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	11-08-2023
Summary	In a multi-agent system, unconditional (multiple) consensus is the property of reaching to (multiple) consensus irrespective of the instant and values at which states are initialized. For linear algorithms, occurrence of unconditional (multiple) consensus turns out to be equivalent to (class-) ergodicity of the transition chain (A_n). For a wide class of chains, chains with so-called balanced asymmetry property, necessary and sufficient conditions for ergodicity and class-ergodicity are derived. The results are employed to analyze the limiting behavior of agents' states in the JLM model, the Krause model, and the Cucker-Smale model. In particular, unconditional single or multiple consensus occurs in all three models. Moreover, a necessary and sufficient condition for unconditional consensus in the JLM model and a sufficient condition for consensus in the Cucker-Smale model are obtained.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1204.6624

Citation

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AMA 11th EditionReferences

Bolouki, Sadegh. Theorems about Ergodicity and Class-Ergodicity of Chains with Applications in Known Consensus Models. Australian National University. August 11, 2023. Accessed October 01, 2025. https://online.provdatabase.com/cite/15884

APA 7th EditionReferences

Bolouki, Sadegh. (2023). Theorems about Ergodicity and Class-Ergodicity of Chains with Applications in Known Consensus Models. Australian National University. https://online.provdatabase.com/cite/15884

Chicago 17th EditionReferences

Bolouki, Sadegh. Theorems about Ergodicity and Class-Ergodicity of Chains with Applications in Known Consensus Models. Australian National University. 2023. https://online.provdatabase.com/cite/15884

HarvardReferences

Bolouki, Sadegh. (2023). Theorems about Ergodicity and Class-Ergodicity of Chains with Applications in Known Consensus Models. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/15884. (Accessed 01 October 2025).

Harvard AustraliaReferences

Bolouki, Sadegh, 2023, Theorems about Ergodicity and Class-Ergodicity of Chains with Applications in Known Consensus Models, Australian National University, viewed 01 October 2025, <https://online.provdatabase.com/cite/15884>

MLA 9th EditionWorks Cited

Bolouki, Sadegh. Theorems about Ergodicity and Class-Ergodicity of Chains with Applications in Known Consensus Models. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/15884.

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