×

Optimizing pinned nodes to maximize the convergence rate of multiagent systems with digraph topologies. (English) Zbl 1421.93002

Summary: This paper investigates how to choose pinned node set to maximize the convergence rate of multiagent systems under digraph topologies in cases of sufficiently small and large pinning strength. In the case of sufficiently small pinning strength, perturbation methods are employed to derive formulas in terms of asymptotics that indicate that the left eigenvector corresponding to eigenvalue zero of the Laplacian measures the importance of node in pinning control multiagent systems if the underlying network has a spanning tree, whereas for the network with no spanning trees, the left eigenvectors of the Laplacian matrix corresponding to eigenvalue zero can be used to select the optimal pinned node set. In the case of sufficiently large pinning strength, by the similar method, a metric based on the smallest real part of eigenvalues of the Laplacian submatrix corresponding to the unpinned nodes is used to measure the stabilizability of the pinned node set. Different algorithms that are applicable for different scenarios are develped. Several numerical simulations are given to verify theoretical results.

MSC:

93A14 Decentralized systems
93C15 Control/observation systems governed by ordinary differential equations
93C73 Perturbations in control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE Transactions on Automatic Control, 50, 2, 169-182 (2005) · Zbl 1365.93268 · doi:10.1109/TAC.2004.841888
[2] Porfiri, M.; Stilwell, D. J., Consensus seeking over random weighted directed graphs, IEEE Transactions on Automatic Control, 52, 9, 1767-1773 (2007) · Zbl 1366.93330 · doi:10.1109/TAC.2007.904603
[3] Hatano, Y.; Mesbahi, M., Agreement over random networks, IEEE Transactions on Automatic Control, 50, 11, 1867-1872 (2005) · Zbl 1365.94482 · doi:10.1109/TAC.2005.858670
[4] Olfati-Saber, R.; Fax, J. A.; Murray, R. M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233 (2007) · Zbl 1376.68138 · doi:10.1109/JPROC.2006.887293
[5] Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50, 5, 655-661 (2005) · Zbl 1365.93302 · doi:10.1109/TAC.2005.846556
[6] Lu, W.; Atay, F. M.; Jost, J., Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays, Networks and Heterogeneous Media, 6, 2, 329-349 (2011) · Zbl 1258.93008 · doi:10.3934/nhm.2011.6.329
[7] Liu, B.; Lu, W.; Chen, T., Consensus in networks of multiagents with switching topologies modeled as adapted stochastic processes, SIAM Journal on Control and Optimization, 49, 1, 227-253 (2011) · Zbl 1222.93232 · doi:10.1137/090745945
[8] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514 · doi:10.1109/TAC.2003.812781
[9] Fax, J. A.; Murray, R. M., Information flow and cooperative control of vehicle formations, IEEE Transactions on Automatic Control, 49, 9, 1465-1476 (2004) · Zbl 1365.90056 · doi:10.1109/TAC.2004.834433
[10] Lu, W.; Li, X.; Rong, Z., Global stabilization of complex networks with digraph topologies via a local pinning algorithm, Automatica, 46, 1, 116-121 (2010) · Zbl 1214.93090 · doi:10.1016/j.automatica.2009.10.006
[11] Chen, T.; Liu, X.; Lu, W., Pinning complex networks by a single controller, IEEE Transactions on Circuits and Systems I: Regular Papers, 54, 6, 1317-1326 (2007) · Zbl 1374.93297 · doi:10.1109/TCSI.2007.895383
[12] Fletcher, J. M.; Wennekers, T., From Structure to Activity: Using Centrality Measures to Predict Neuronal Activity, International Journal of Neural Systems, 28, 02, 1750013 (2018) · doi:10.1142/S0129065717500137
[13] Wang, X. F.; Chen, G., Pinning control of scale-free dynamical networks, Physica A: Statistical Mechanics and its Applications, 310, 3, 521-531 (2002) · Zbl 0995.90008 · doi:10.1016/S0378-4371(02)00772-0
[14] Li, X.; Wang, X.; Chen, G., Pinning a complex dynamical network to its equilibrium, IEEE Transactions on Circuits and Systems I: Regular Papers, 51, 10, 2074-2087 (2004) · Zbl 1374.94915 · doi:10.1109/TCSI.2004.835655
[15] Sorrentino, F., Effects of the network structural properties on its controllability, Chaos: An Interdisciplinary Journal of Nonlinear Science, 17, 3, 033101 (2007) · Zbl 1163.37367 · doi:10.1063/1.2743098
[16] Turci, L. F. R.; Macau, E. E. N., Performance of pinning-controlled synchronization, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 84, 1 (2011) · doi:10.1103/PhysRevE.84.011120
[17] Zou, Y.; Chen, G., Choosing effective controlled nodes for scale-free network synchronization, Physica A: Statistical Mechanics and its Applications, 388, 14, 2931-2940 (2009) · doi:10.1016/j.physa.2009.03.040
[18] Orouskhani, Y.; Jalili, M.; Yu, X., Optimizing Dynamical Network Structure for Pinning Control, Scientific Reports, 6, 1, article no. 24252 (2016) · doi:10.1038/srep24252
[19] Jalili, M.; Sichani, O. A.; Yu, X., Optimal pinning controllability of complex networks: dependence on network structure, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 91, 1 (2015) · doi:10.1103/PhysRevE.91.012803
[20] Amani, A. M.; Jalili, M.; Yu, X.; Stone, L., Finding the most influential nodes in pinning controllability of complex networks, IEEE Transactions on Circuits and Systems II: Express Briefs, 64, 6, 685-689 (2017) · doi:10.1109/TCSII.2016.2601565
[21] Su, H.; Wang, X., Pinning control for complete synchronization of complex dynamical networks, Pinning Control of Complex Networked Systems, 17-44 (2013), Berlin, Germany: Springer, Berlin, Germany · Zbl 1366.93002
[22] Horn, R. A.; Johnson, C. R., Matrix Analysis (1985), Cambridge, UK: Cambridge University Press, Cambridge, UK · Zbl 0576.15001 · doi:10.1017/CBO9780511810817
[23] Minc, H., Nonnegative Matrices (1988), New York, NY, USA: John Wiley & Sons, Inc., New York, NY, USA · Zbl 0638.15008
[24] Li, R.-C., Matrix perturbation theory, Handbook of Linear Algebra (2014), Boca Raton, FL, USA: CRC Press, Boca Raton, FL, USA
[25] Lu, W.; Atay, F. M., Local pinning of networks of multi-agent systems with transmission and pinning delays, IEEE Transactions on Automatic Control, 61, 9, 2657-2662 (2015) · Zbl 1359.34085 · doi:10.1109/TAC.2015.2508883
[26] Erkan, O. F.; Cihan, O.; Akar, M., Distributed consensus with multi-equilibria in directed networks, Proceedings of the 2017 American Control Conference, ACC 2017
[27] Chen, H.; Zhao, X.; Liu, F.; Xu, S.; Lu, W., Optimizing interconnections to maximize the spectral radius of interdependent networks, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 95, 3 (2017) · doi:10.1103/PhysRevE.95.032308
[28] Qin, A. K.; Huang, V. L.; Suganthan, P. N., Differential evolution algorithm with strategy adaptation for global numerical optimization, IEEE Transactions on Evolutionary Computation, 13, 2, 398-417 (2009) · doi:10.1109/TEVC.2008.927706
[29] Hwang, D.; Chavez, M.; Amann, A.; Boccaletti, S., Synchronization in Complex Networks with Age Ordering, Physical Review Letters, 94, 13 (2005) · doi:10.1103/PhysRevLett.94.138701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.