- Previous Article
- NHM Home
- This Issue
-
Next Article
An easy-to-use algorithm for simulating traffic flow on networks: Theoretical study
Group pinning consensus under fixed and randomly switching topologies with acyclic partition
1. | Department of Mathematics, Tongji University, Shanghai 200092, China |
References:
[1] |
A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno and C. Zhou, Synchronization in complex networks, Phys. Rep., 469 (2008), 93-153.
doi: 10.1016/j.physrep.2008.09.002. |
[2] |
J. Bang-Jensen and G. Z. Gutin, Digraphs: Theory, Algorithm and Applications, 2nd Ed., Springer-Verlag, London, 2009.
doi: 10.1007/978-1-84800-998-1. |
[3] |
V. N. Belykh, I. V. Belykh and M. Hasler, Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems, Phys. Rev. E, 62 (2000), 6332-6345.
doi: 10.1103/PhysRevE.62.6332. |
[4] |
V. Borkar and P. P. Varaiya, Asymptotic agreement in distributed estimation, IEEE Trans. Automat. Control, 27 (1982), 650-655.
doi: 10.1109/TAC.1982.1102982. |
[5] |
T. Chen, X. Liu and W. Lu, Pinning complex networks by a single controller, IEEE Trans. Circuit Syst. I, 54 (2007), 1317-1326.
doi: 10.1109/TCSI.2007.895383. |
[6] |
O. Costa and M. Fragoso, A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances, SIAM J. Contr. Optim., 44 (2005), 1165-1191.
doi: 10.1137/S0363012903434753. |
[7] |
T. Dahms, J. Lehnert and E. Schöll, Cluster and group synchronization in delay-coupled networks, Phys. Rev. E, 86 (2012), 016202.
doi: 10.1103/PhysRevE.86.016202. |
[8] |
X. Feng and K. A. Loparo, Stability of linear Markovian jump systems, Proc. of the 29th IEEE Conf. Decision and Control, Honolulu, HI, (1990), 1408-1413.
doi: 10.1109/CDC.1990.203842. |
[9] |
Y. Z. Feng, J. Lu, S. Xu and Y. Zou, Couple-group consensus for multi-agent networks of agents with discrete-time second-order dynamcis, J. Franklin Institute, 350 (2013), 3277-3292.
doi: 10.1016/j.jfranklin.2013.07.004. |
[10] |
Y. Han, W. Lu and T. Chen, Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs, IEEE Trans. Neural Networks and Learning Syst., 24 (2013), 566-578. |
[11] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Autom. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[12] |
Z. Li, Z. Duan and G. Chen, Dynamic consensus of linear multi-agent systems, IET Control Theory Appl., 5 (2011), 19-28.
doi: 10.1049/iet-cta.2009.0466. |
[13] |
W. Lu, F. M. Atay and J. Jost, Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays, Netw. Heterog. Media, 6 (2011), 329-349.
doi: 10.3934/nhm.2011.6.329. |
[14] |
I. Matei and J. S. Baras, Convergence results for the linear consensus problem under Markovian random graphs, SIAM J. Control Optim., 51 (2013), 1574-1591.
doi: 10.1137/100816870. |
[15] |
G. Miao, S. Xu and Y. Zou, Necessary and sufficient conditions for mean square consensus under Markov switching topologies, Int. J. Syst. Sci., 44 (2013), 178-186.
doi: 10.1080/00207721.2011.598961. |
[16] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233.
doi: 10.1109/JPROC.2006.887293. |
[17] |
R. Olfati-Saber and R. M. Murray, Consensus problem in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 49 (2004), 1520-1533.
doi: 10.1109/TAC.2004.834113. |
[18] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[19] |
J. Qin and C. Yu, Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition, Automatica, 49 (2013), 2898-2905.
doi: 10.1016/j.automatica.2013.06.017. |
[20] |
W. Ren and R. W. Beard, Consensus seeking in multiagent systems under dynamically changing interation topologies, IEEE Trans. Autom. Control, 50 (2005), 655-661.
doi: 10.1109/TAC.2005.846556. |
[21] |
A. H. Roger and R. J. Charles, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
doi: 10.1017/CBO9780511810817. |
[22] |
E. Seneta, Non-negative Matrices and Markov Chains, Springer, New York, 2006. |
[23] |
Y. Shang, Multi-agent coordination in directed moving neighborhood random networks, Chin. Phys. B, 19 (2010), 070201. |
[24] |
Y. Shang, Finite-time consensus for multi-agent systems with fixed topologies, Int. J. Syst. Sci., 43 (2012), 499-506.
doi: 10.1080/00207721.2010.517857. |
[25] |
Y. Shang, $L^1$ group consensus of multi-agent systems with stochastic inputs under directed interaction topology, Int. J. Control, 86 (2013), 1-8.
doi: 10.1080/00207179.2012.715753. |
[26] |
Y. Shang, Continuous-time average consensus under dynamically changing topologies and multiple time-varying delays, Appl. Math. Comput., 244 (2014), 457-466.
doi: 10.1016/j.amc.2014.07.019. |
[27] |
Y. Shang, Group consensus of multi-agent systems in directed networks with noises and time delays, Int. J. Syst. Sci.
doi: 10.1080/00207721.2013.862582. |
[28] |
Y. Shang, Group consensus in generic linear multi-agent sytesms with inter-group non-identical inputs, Cogent Engineering, 1 (2014), 947761.
doi: 10.1080/23311916.2014.947761. |
[29] |
F. Sorrentino and E. Ott, Network synchronization of groups, Phys. Rev. E, 76 (2007), 056114.
doi: 10.1103/PhysRevE.76.056114. |
[30] |
R. Stanley, Acyclic orientations of graphs, Discrete Math., 5 (1973), 171-178.
doi: 10.1016/0012-365X(73)90108-8. |
[31] |
W. Sun, Y. Q. Bai, R. Jia, R. Xiong and J. Chen, Multi-group consensus via pinning control with non-linear heterogeneous agents, Proc. 8th Asian Control Conference, Taiwan, (2011), 323-328. |
[32] |
C. Tan, G.-P. Liu and G.-R. Duan, Couple-group consensus of multi-agent systems with directed and fixed topology, Proc. 30th Chinese Contr. Conf., Yantai, (2011), 6515-6520. |
[33] |
B. Touri and A. Nedić, On ergodicity, infinite flow, and consensus in random models, IEEE Trans. Autom. Control, 56 (2011), 1593-1605.
doi: 10.1109/TAC.2010.2091174. |
[34] |
J. N. Tsitsiklis, Problems in Decentralized Decision Making and Computation, Ph.D. Dissertation, Massachusetts Inst. Technol., Cambridge, MA, 1984. |
[35] |
F. Xiao and L. Wang, Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE Trans. Autom. Control, 53 (2008), 1804-1816.
doi: 10.1109/TAC.2008.929381. |
[36] |
K. You, Z. Li and L. Xie, Consensus condition for linear multi-agent systems over randomly switching topologies, Automatica, 49 (2013), 3125-3132.
doi: 10.1016/j.automatica.2013.07.024. |
[37] |
W. Yu, G. Chen and J. Lü, On pinning control synchronization of complex dynamical networks, Automatica, 45 (2009), 429-435.
doi: 10.1016/j.automatica.2008.07.016. |
[38] |
J. Yu and L. Wang, Group consensus of multi-agent sytems with undirected communication graphs, Proc. 7th Asian Control Conf., (2009), 105-110. |
[39] |
J. Yu and L. Wang, Group consensus in multi-agent systems with switching topologies and communication delays, Syst. Control Lett., 59 (2010), 340-348.
doi: 10.1016/j.sysconle.2010.03.009. |
show all references
References:
[1] |
A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno and C. Zhou, Synchronization in complex networks, Phys. Rep., 469 (2008), 93-153.
doi: 10.1016/j.physrep.2008.09.002. |
[2] |
J. Bang-Jensen and G. Z. Gutin, Digraphs: Theory, Algorithm and Applications, 2nd Ed., Springer-Verlag, London, 2009.
doi: 10.1007/978-1-84800-998-1. |
[3] |
V. N. Belykh, I. V. Belykh and M. Hasler, Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems, Phys. Rev. E, 62 (2000), 6332-6345.
doi: 10.1103/PhysRevE.62.6332. |
[4] |
V. Borkar and P. P. Varaiya, Asymptotic agreement in distributed estimation, IEEE Trans. Automat. Control, 27 (1982), 650-655.
doi: 10.1109/TAC.1982.1102982. |
[5] |
T. Chen, X. Liu and W. Lu, Pinning complex networks by a single controller, IEEE Trans. Circuit Syst. I, 54 (2007), 1317-1326.
doi: 10.1109/TCSI.2007.895383. |
[6] |
O. Costa and M. Fragoso, A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances, SIAM J. Contr. Optim., 44 (2005), 1165-1191.
doi: 10.1137/S0363012903434753. |
[7] |
T. Dahms, J. Lehnert and E. Schöll, Cluster and group synchronization in delay-coupled networks, Phys. Rev. E, 86 (2012), 016202.
doi: 10.1103/PhysRevE.86.016202. |
[8] |
X. Feng and K. A. Loparo, Stability of linear Markovian jump systems, Proc. of the 29th IEEE Conf. Decision and Control, Honolulu, HI, (1990), 1408-1413.
doi: 10.1109/CDC.1990.203842. |
[9] |
Y. Z. Feng, J. Lu, S. Xu and Y. Zou, Couple-group consensus for multi-agent networks of agents with discrete-time second-order dynamcis, J. Franklin Institute, 350 (2013), 3277-3292.
doi: 10.1016/j.jfranklin.2013.07.004. |
[10] |
Y. Han, W. Lu and T. Chen, Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs, IEEE Trans. Neural Networks and Learning Syst., 24 (2013), 566-578. |
[11] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Autom. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[12] |
Z. Li, Z. Duan and G. Chen, Dynamic consensus of linear multi-agent systems, IET Control Theory Appl., 5 (2011), 19-28.
doi: 10.1049/iet-cta.2009.0466. |
[13] |
W. Lu, F. M. Atay and J. Jost, Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays, Netw. Heterog. Media, 6 (2011), 329-349.
doi: 10.3934/nhm.2011.6.329. |
[14] |
I. Matei and J. S. Baras, Convergence results for the linear consensus problem under Markovian random graphs, SIAM J. Control Optim., 51 (2013), 1574-1591.
doi: 10.1137/100816870. |
[15] |
G. Miao, S. Xu and Y. Zou, Necessary and sufficient conditions for mean square consensus under Markov switching topologies, Int. J. Syst. Sci., 44 (2013), 178-186.
doi: 10.1080/00207721.2011.598961. |
[16] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233.
doi: 10.1109/JPROC.2006.887293. |
[17] |
R. Olfati-Saber and R. M. Murray, Consensus problem in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 49 (2004), 1520-1533.
doi: 10.1109/TAC.2004.834113. |
[18] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), 2109-2112.
doi: 10.1103/PhysRevLett.80.2109. |
[19] |
J. Qin and C. Yu, Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition, Automatica, 49 (2013), 2898-2905.
doi: 10.1016/j.automatica.2013.06.017. |
[20] |
W. Ren and R. W. Beard, Consensus seeking in multiagent systems under dynamically changing interation topologies, IEEE Trans. Autom. Control, 50 (2005), 655-661.
doi: 10.1109/TAC.2005.846556. |
[21] |
A. H. Roger and R. J. Charles, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
doi: 10.1017/CBO9780511810817. |
[22] |
E. Seneta, Non-negative Matrices and Markov Chains, Springer, New York, 2006. |
[23] |
Y. Shang, Multi-agent coordination in directed moving neighborhood random networks, Chin. Phys. B, 19 (2010), 070201. |
[24] |
Y. Shang, Finite-time consensus for multi-agent systems with fixed topologies, Int. J. Syst. Sci., 43 (2012), 499-506.
doi: 10.1080/00207721.2010.517857. |
[25] |
Y. Shang, $L^1$ group consensus of multi-agent systems with stochastic inputs under directed interaction topology, Int. J. Control, 86 (2013), 1-8.
doi: 10.1080/00207179.2012.715753. |
[26] |
Y. Shang, Continuous-time average consensus under dynamically changing topologies and multiple time-varying delays, Appl. Math. Comput., 244 (2014), 457-466.
doi: 10.1016/j.amc.2014.07.019. |
[27] |
Y. Shang, Group consensus of multi-agent systems in directed networks with noises and time delays, Int. J. Syst. Sci.
doi: 10.1080/00207721.2013.862582. |
[28] |
Y. Shang, Group consensus in generic linear multi-agent sytesms with inter-group non-identical inputs, Cogent Engineering, 1 (2014), 947761.
doi: 10.1080/23311916.2014.947761. |
[29] |
F. Sorrentino and E. Ott, Network synchronization of groups, Phys. Rev. E, 76 (2007), 056114.
doi: 10.1103/PhysRevE.76.056114. |
[30] |
R. Stanley, Acyclic orientations of graphs, Discrete Math., 5 (1973), 171-178.
doi: 10.1016/0012-365X(73)90108-8. |
[31] |
W. Sun, Y. Q. Bai, R. Jia, R. Xiong and J. Chen, Multi-group consensus via pinning control with non-linear heterogeneous agents, Proc. 8th Asian Control Conference, Taiwan, (2011), 323-328. |
[32] |
C. Tan, G.-P. Liu and G.-R. Duan, Couple-group consensus of multi-agent systems with directed and fixed topology, Proc. 30th Chinese Contr. Conf., Yantai, (2011), 6515-6520. |
[33] |
B. Touri and A. Nedić, On ergodicity, infinite flow, and consensus in random models, IEEE Trans. Autom. Control, 56 (2011), 1593-1605.
doi: 10.1109/TAC.2010.2091174. |
[34] |
J. N. Tsitsiklis, Problems in Decentralized Decision Making and Computation, Ph.D. Dissertation, Massachusetts Inst. Technol., Cambridge, MA, 1984. |
[35] |
F. Xiao and L. Wang, Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE Trans. Autom. Control, 53 (2008), 1804-1816.
doi: 10.1109/TAC.2008.929381. |
[36] |
K. You, Z. Li and L. Xie, Consensus condition for linear multi-agent systems over randomly switching topologies, Automatica, 49 (2013), 3125-3132.
doi: 10.1016/j.automatica.2013.07.024. |
[37] |
W. Yu, G. Chen and J. Lü, On pinning control synchronization of complex dynamical networks, Automatica, 45 (2009), 429-435.
doi: 10.1016/j.automatica.2008.07.016. |
[38] |
J. Yu and L. Wang, Group consensus of multi-agent sytems with undirected communication graphs, Proc. 7th Asian Control Conf., (2009), 105-110. |
[39] |
J. Yu and L. Wang, Group consensus in multi-agent systems with switching topologies and communication delays, Syst. Control Lett., 59 (2010), 340-348.
doi: 10.1016/j.sysconle.2010.03.009. |
[1] |
Wenlian Lu, Fatihcan M. Atay, Jürgen Jost. Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays. Networks and Heterogeneous Media, 2011, 6 (2) : 329-349. doi: 10.3934/nhm.2011.6.329 |
[2] |
Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3837-3849. doi: 10.3934/dcdss.2020444 |
[3] |
Christian Pötzsche, Stefan Siegmund, Fabian Wirth. A spectral characterization of exponential stability for linear time-invariant systems on time scales. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1223-1241. doi: 10.3934/dcds.2003.9.1223 |
[4] |
Elimhan N. Mahmudov. Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 353-371. doi: 10.3934/naco.2021010 |
[5] |
Yi Zhang, Yuyun Zhao, Tao Xu, Xin Liu. $p$th Moment absolute exponential stability of stochastic control system with Markovian switching. Journal of Industrial and Management Optimization, 2016, 12 (2) : 471-486. doi: 10.3934/jimo.2016.12.471 |
[6] |
Ali Gholami, Mauricio D. Sacchi. Time-invariant radon transform by generalized Fourier slice theorem. Inverse Problems and Imaging, 2017, 11 (3) : 501-519. doi: 10.3934/ipi.2017023 |
[7] |
Mario Roy, Mariusz Urbański. Random graph directed Markov systems. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 261-298. doi: 10.3934/dcds.2011.30.261 |
[8] |
Liu Hui, Lin Zhi, Waqas Ahmad. Network(graph) data research in the coordinate system. Mathematical Foundations of Computing, 2018, 1 (1) : 1-10. doi: 10.3934/mfc.2018001 |
[9] |
Carol C. Horvitz, Anthony L. Koop, Kelley D. Erickson. Time-invariant and stochastic disperser-structured matrix models: Invasion rates of fleshy-fruited exotic shrubs. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1639-1662. doi: 10.3934/dcdsb.2015.20.1639 |
[10] |
Mario Roy, Mariusz Urbański. Multifractal analysis for conformal graph directed Markov systems. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 627-650. doi: 10.3934/dcds.2009.25.627 |
[11] |
Sebastià Galmés. Markovian characterization of node lifetime in a time-driven wireless sensor network. Numerical Algebra, Control and Optimization, 2011, 1 (4) : 763-780. doi: 10.3934/naco.2011.1.763 |
[12] |
Victor Kozyakin. Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3537-3556. doi: 10.3934/dcdsb.2018277 |
[13] |
Hong Man, Yibin Yu, Yuebang He, Hui Huang. Design of one type of linear network prediction controller for multi-agent system. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 727-734. doi: 10.3934/dcdss.2019047 |
[14] |
Xi Zhu, Changjun Yu, Kok Lay Teo. A new switching time optimization technique for multi-switching systems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022067 |
[15] |
Xiaojin Huang, Hongfu Yang, Jianhua Huang. Consensus stability analysis for stochastic multi-agent systems with multiplicative measurement noises and Markovian switching topologies. Numerical Algebra, Control and Optimization, 2022, 12 (3) : 601-610. doi: 10.3934/naco.2021024 |
[16] |
Byungik Kahng, Miguel Mendes. The characterization of maximal invariant sets of non-linear discrete-time control dynamical systems. Conference Publications, 2013, 2013 (special) : 393-406. doi: 10.3934/proc.2013.2013.393 |
[17] |
Shulin Qin, Gengsheng Wang, Huaiqiang Yu. On switching properties of time optimal controls for linear ODEs. Mathematical Control and Related Fields, 2021, 11 (2) : 329-351. doi: 10.3934/mcrf.2020039 |
[18] |
Weijun Zhan, Qian Guo, Yuhao Cong. The truncated Milstein method for super-linear stochastic differential equations with Markovian switching. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3663-3682. doi: 10.3934/dcdsb.2021201 |
[19] |
Thomas I. Seidman. Optimal control of a diffusion/reaction/switching system. Evolution Equations and Control Theory, 2013, 2 (4) : 723-731. doi: 10.3934/eect.2013.2.723 |
[20] |
Kehan Si, Zhenda Xu, Ka Fai Cedric Yiu, Xun Li. Open-loop solvability for mean-field stochastic linear quadratic optimal control problems of Markov regime-switching system. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2415-2433. doi: 10.3934/jimo.2021074 |
2021 Impact Factor: 1.41
Tools
Metrics
Other articles
by authors
[Back to Top]