Decentralized State-Dependent Markov Chain Synthesis with an Application to Swarm Guidance

Fuente: arXiv
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Auteurs principaux: Uzun, Samet, Ure, Nazim Kemal, Acikmese, Behcet
Format: Preprint
Publié: 2020
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author Uzun, Samet
Ure, Nazim Kemal
Acikmese, Behcet
author_facet Uzun, Samet
Ure, Nazim Kemal
Acikmese, Behcet
contents This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical conditions, without relying on any connectivity assumptions regarding the dynamic network topology. Utilizing the proposed consensus protocol, we develop the DSMC algorithm, updating the Markov matrix based on the current state while ensuring the convergence conditions of the consensus protocol. This result establishes the desired steady-state distribution for the resulting Markov chain, ensuring exponential convergence from all initial distributions while adhering to transition constraints and minimizing state transitions. The DSMC's performance is demonstrated through a probabilistic swarm guidance example, which interprets the spatial distribution of a swarm comprising a large number of mobile agents as a probability distribution and utilizes the Markov chain to compute transition probabilities between states. Simulation results demonstrate faster convergence for the DSMC based algorithm when compared to the previous Markov chain based swarm guidance algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2012_02303
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Decentralized State-Dependent Markov Chain Synthesis with an Application to Swarm Guidance
Uzun, Samet
Ure, Nazim Kemal
Acikmese, Behcet
Optimization and Control
Multiagent Systems
Dynamical Systems
Probability
This paper introduces a decentralized state-dependent Markov chain synthesis (DSMC) algorithm for finite-state Markov chains. We present a state-dependent consensus protocol that achieves exponential convergence under mild technical conditions, without relying on any connectivity assumptions regarding the dynamic network topology. Utilizing the proposed consensus protocol, we develop the DSMC algorithm, updating the Markov matrix based on the current state while ensuring the convergence conditions of the consensus protocol. This result establishes the desired steady-state distribution for the resulting Markov chain, ensuring exponential convergence from all initial distributions while adhering to transition constraints and minimizing state transitions. The DSMC's performance is demonstrated through a probabilistic swarm guidance example, which interprets the spatial distribution of a swarm comprising a large number of mobile agents as a probability distribution and utilizes the Markov chain to compute transition probabilities between states. Simulation results demonstrate faster convergence for the DSMC based algorithm when compared to the previous Markov chain based swarm guidance algorithms.
title Decentralized State-Dependent Markov Chain Synthesis with an Application to Swarm Guidance
topic Optimization and Control
Multiagent Systems
Dynamical Systems
Probability
url https://arxiv.org/abs/2012.02303