Çok etmenli sistemlerde çoklu denge noktalarının sürekli zamanda analizi
Year 2016,
Volume: 22 Issue: 8, 666 - 670, 27.12.2016
Özlem Feyza Erkan
Mehmet Akar
Abstract
Bu
makalede, n etmenden oluşan ve etmenler arası iletişimi sabit/değişken olan
ağlar için çoklu denge noktaları içeren dağıtık onaylaşım problemi
incelenmiştir. Literatürde bulunan klasik onaylaşım problemi genişletilerek,
çoklu denge noktaları içeren sürekli zaman onaylaşım algoritması için kuramsal
sonuçlar elde edilmiştir. Yönsüz çizgelerle modellenmiş ağlarda algoritmanın
çoklu denge noktalı onaylaşımı sağlaması için gerek ve yeter koşullar
belirlenmiştir. Algoritmanın yakınsama analizi yapılırken spektral çizge kuramı
ve anahtarlamalı sistem kuramı kullanılmıştır. Kuramsal sonuçlar benzetim
çalışmaları ile doğrulanmıştır.
References
- Jadbabaie A, Lin J, Morse A S. “Coordination of groups of mobile autonomous agents using nearest neighbor rules”. IEEE Transactions Automatic Control, 48(6), 988–1001, 2003.
- Olfati-Saber R, Murray R M. “Consensus problems in networks of agents with switching topology and time- delays”. IEEE Transactions on Automatic Control, 49(9), 1520-1533, 2004.
- Ren W, Beard R W. “Consensus seeking in multiagent systems under dynamically changing interaction topologies”. IEEE Transactions on Automatic Control, 50(5), 655-66, 2005.
- Moreau L. “Stability of multiagent systems with time-dependent communication links”. IEEE Transactions on Automatic Control, 50(2), 169-182, 2005.
- Cao M, Morse A S, Anderson B D. “Agreeing asynchronously”. IEEE Transactions on Automatic Control, 53(8), 1826-1838, 2008.
- Cihan O, Akar M. “Effect of nonuniform varying delay on the rate of convergence in averaging-based consensus”. Turkish Journal of Electrical Engineering and Computer Sciences, 23, 1069-1080, 2015.
- Akar M, Shorten R. “On the Existence of Common Lyapunov Functions for Consensus Algorithms Based on Averaging”. Turkish Journal of Electrical Engineering and Computer Sciences, 19(3), 2011.
- Akar M, Shorten R. “Distributed probabilistic synchronization algorithms for communication networks”. IEEE Transactions on Automatic Control, 53, 389-393, 2008.
- Fax J A, Murray R M. “Information Flow and Cooperative Control of Vehicle Formations”. IEEE Transactions on Automatic Control, 49(9), 1465-1476, 2004.
- Lawton J, Beard R, Young B. “A Decentralized Approach to Formation Maneuvers”. IEEE Transactions on Robotics and Automation, 19(6), 933-941, 2003.
- Lin Z, Francis B, Maggiore M. “Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles”. IEEE Transactions on Automatic Control, 50(1), 121-127, 2005.
- Yu J, Wang L. “Group consensus of multi-agent systems with directed information exchange”. International Journal of Systems Science, 43(2), 334-348, 2012.
- Tan C, Liu G, Duan G. “Group consensus of networked multi-agent systems with directed topology”. 18th IFAC World Congress, Milano, Italy, 28 August-02 September 2011.
- Xia W, Cao M. “Clustering in diffusively coupled networks”. Automatica, 47(11), 2395-2405, 2011.
- Qin J, Yu C. “Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition”. Automatica, 49(9), 2898-2905, 2013.
Continuous-time analysis of multi-agent systems with multiple consensus equilibria
Year 2016,
Volume: 22 Issue: 8, 666 - 670, 27.12.2016
Özlem Feyza Erkan
Mehmet Akar
Abstract
In
this paper, we examine the multi-equilibrium consensus problem for a network of
n agents having fixed or time-varying communication links. We introduce
necessary and sufficient conditions on networks modeled with undirected graphs
such that multi-equilibrium consensus states are achieved, thus extending the
classical convergence results in the literature. Spectral graph theory and
switched systems theory are used to analyze the continuous-time algorithm.
Theoretical results are verified by simulation studies.
References
- Jadbabaie A, Lin J, Morse A S. “Coordination of groups of mobile autonomous agents using nearest neighbor rules”. IEEE Transactions Automatic Control, 48(6), 988–1001, 2003.
- Olfati-Saber R, Murray R M. “Consensus problems in networks of agents with switching topology and time- delays”. IEEE Transactions on Automatic Control, 49(9), 1520-1533, 2004.
- Ren W, Beard R W. “Consensus seeking in multiagent systems under dynamically changing interaction topologies”. IEEE Transactions on Automatic Control, 50(5), 655-66, 2005.
- Moreau L. “Stability of multiagent systems with time-dependent communication links”. IEEE Transactions on Automatic Control, 50(2), 169-182, 2005.
- Cao M, Morse A S, Anderson B D. “Agreeing asynchronously”. IEEE Transactions on Automatic Control, 53(8), 1826-1838, 2008.
- Cihan O, Akar M. “Effect of nonuniform varying delay on the rate of convergence in averaging-based consensus”. Turkish Journal of Electrical Engineering and Computer Sciences, 23, 1069-1080, 2015.
- Akar M, Shorten R. “On the Existence of Common Lyapunov Functions for Consensus Algorithms Based on Averaging”. Turkish Journal of Electrical Engineering and Computer Sciences, 19(3), 2011.
- Akar M, Shorten R. “Distributed probabilistic synchronization algorithms for communication networks”. IEEE Transactions on Automatic Control, 53, 389-393, 2008.
- Fax J A, Murray R M. “Information Flow and Cooperative Control of Vehicle Formations”. IEEE Transactions on Automatic Control, 49(9), 1465-1476, 2004.
- Lawton J, Beard R, Young B. “A Decentralized Approach to Formation Maneuvers”. IEEE Transactions on Robotics and Automation, 19(6), 933-941, 2003.
- Lin Z, Francis B, Maggiore M. “Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles”. IEEE Transactions on Automatic Control, 50(1), 121-127, 2005.
- Yu J, Wang L. “Group consensus of multi-agent systems with directed information exchange”. International Journal of Systems Science, 43(2), 334-348, 2012.
- Tan C, Liu G, Duan G. “Group consensus of networked multi-agent systems with directed topology”. 18th IFAC World Congress, Milano, Italy, 28 August-02 September 2011.
- Xia W, Cao M. “Clustering in diffusively coupled networks”. Automatica, 47(11), 2395-2405, 2011.
- Qin J, Yu C. “Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition”. Automatica, 49(9), 2898-2905, 2013.