Robustness of the Adaptive Bellman -Ford Algorithm: Global Stability and Ultimate Bounds

Self-stabilizing distance estimation algorithms are an important building block of many distributed systems, such as seen in the emerging field of aggregate computing. Their safe use in feedback systems or under persistent perturbations has not previously been formally analyzed. Self-stabilization o...

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Vydané v:IEEE transactions on automatic control Ročník 64; číslo 10; s. 4121 - 4136
Hlavní autori: Mo, Yuanqiu, Dasgupta, Soura, Beal, Jacob
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.10.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Adaptive algorithms
Aggregates
Aggregating computing
Algorithms
Asymptotic methods
Asymptotic properties
Asymptotic stability
Computer networks
Convergence
Error analysis
Feedback
Internet of things
Liapunov functions
Lyapunov function
Lyapunov methods
Perturbation methods
Robustness
stability
Stability analysis
ultimate boundedness
ISSN:0018-9286, 1558-2523
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Shrnutí:Self-stabilizing distance estimation algorithms are an important building block of many distributed systems, such as seen in the emerging field of aggregate computing. Their safe use in feedback systems or under persistent perturbations has not previously been formally analyzed. Self-stabilization only involves eventual convergence, and is not endowed with robustness properties associated with global uniform asymptotic stability and thus does not guarantee stability under perturbations or feedback. We formulate a Lyapunov function to analyze the Adaptive Bellman-Ford distance estimation algorithm and use it to prove global uniform asymptotic stability, a property which the classical Bellman-Ford algorithm lacks. Global uniform asymptotic stability assures a measure of robustness to structural perturbations, empirically observed by us in a previous work. We also show that the algorithm is ultimately bounded under bounded measurement error and device mobility and provide a tight bound on the ultimate bound and the time to attain it.
Bibliografia:ObjectType-Article-1
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2019.2904239