Synchronization for time-varying complex dynamical networks with different-dimensional nodes and non-dissipative coupling. (English) Zbl 1463.93234
Summary: This paper investigates synchronization for time-varying complex dynamical networks with different-dimensional nodes via decentralized control. The outer coupling configuration matrix (OCCM) in our network model, which represents the coupling strength and the topological structure, can be time-varying, non-dissipatively coupled, asymmetric and uncertain. In addition, the nonlinearly coupled inner state functions are admissible in the network model. The paper mainly focuses on the synthesis of decentralized controllers in two cases for uncertain coupling coefficients in OCCM, respectively. Firstly, the decentralized nonlinear state feedback controllers are synthesised based on the known coupling coefficients common bound. The proposed controllers can guarantee exponential synchronization of the networks. Then, an adaptive mechanism with only one parameter being adjusted online is introduced to synthesize the decentralized adaptive controllers according to the unknown coupling coefficients common bound so that the network realizes asymptotic synchronization. Finally, a numerical example is given to test the effectiveness of the theoretical results.
MSC:
| 93D99 | Stability of control systems |
| 93A14 | Decentralized systems |
| 93B70 | Networked control |
| 93B52 | Feedback control |
| 93C10 | Nonlinear systems in control theory |
| 93C40 | Adaptive control/observation systems |
Keywords:
complex dynamical network; synchronization; time-varying network; non-dissipatively coupled; different nodesReferences:
| [1] | Liu, T.; Dimirovski, G. M.; Zhao, J., Exponential synchronization of complex delayed dynamical networks with general topology, Phys A, 387, 643-652 (2008) |
| [2] | Zhang, L. L.; Wang, Y. H.; Wang, Q. Y.; Wang, Q. R.; Zhang, Y., Synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers, Int J Control, 86, 10, 1766-1776 (2013) · Zbl 1312.93015 |
| [3] | Lee, D. W.; Yoo, W. J.; Ji, D. H.; Park, J. H., Integral control for synchronization of complex dynamical networks with unknown non-identical nodes, Appl Math Comput, 224, 140-149 (2013) · Zbl 1336.93018 |
| [4] | Wang, Y. L.; Cao, J. D., Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems, Nonlinear Anal Real World Appl, 14, 842-851 (2013) · Zbl 1254.93013 |
| [5] | Liu, X. W.; Chen, T. P., Cluster synchronization in directed networks via intermittent pinning control, IEEE Trans Neural Networks, 22, 7, 1009-1020 (2011) |
| [6] | Zhao, J.; Hill, D. J.; Liu, T., Global bounded synchronization of general dynamical networks with nonidentical nodes, IEEE Trans Autom Control, 57, 10, 2656-2662 (2012) · Zbl 1369.93061 |
| [7] | Lee, T. H.; Park, J. H.; Ji, D. H.; Kwon, O. M.; Lee, S. M., Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control, Appl Math Comput, 218, 6469-6481 (2012) · Zbl 1238.93070 |
| [8] | Wong, W. K.; Li, H.; Leung, S. Y.S., Robust synchronization of fractional-order complex dynamical networks with parametric uncertainties, Commun Nonlinear Sci Numer Simul, 17, 12, 4877-4890 (2012) · Zbl 1261.93008 |
| [9] | Yu, W.; Chen, G.; Lü, J., On pinning synchronization of complex dynamical networks, Automatica, 45, 2, 429-435 (2009) · Zbl 1158.93308 |
| [10] | Checco, P.; Biey, M.; Kocarev, L., Synchronization in random networks with given expected degree sequences, Chaos, Solitons Fractals, 35, 3, 562-577 (2008) · Zbl 1138.93050 |
| [11] | Wang, Y. H.; Fan, Y. Q.; Wang, Q. Y.; Zhang, Y., Stabilization and synchronization of complex dynamical networks with different dynamics of nodes via decentralized controllers, IEEE Trans Circuits Syst Regul Pap, 59, 8, 1786-1795 (2012) · Zbl 1468.93139 |
| [12] | Ji, D. H.; Jeong, S. C.; Park, J. H.; Lee, S. M.; Won, S. C., Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling, Appl Math Comput, 218, 9, 4872-4880 (2012) · Zbl 1238.93053 |
| [13] | Ji, D. H.; Park, J. H.; Woo, W. J.; Won, S. C.; Lee, S. M., Synchronization criterion for Lur’e type complex dynamical networks with time-varying delay, Phys Lett A, 374, 10, 1218-1227 (2012) · Zbl 1236.05186 |
| [14] | Solís-Perales, G.; Ruiz-Velázquez, E.; Valle-Rodríguez, D., Synchronization in complex networks with distinct chaotic nodes, Commun Nonlinear Sci Numer Simul, 14, 6, 2528-2535 (2009) · Zbl 1221.34148 |
| [15] | Posadas-Castillo, C.; Cruz-hernández, C.; López-Gutiérrez, R. M., Experimental realization of synchronization in complex networks with Chua’s circuits like nodes, Chaos, Solitons Fractals, 40, 4, 1963-1975 (2009) |
| [16] | Lü, J. H.; Chen, G. R., A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Trans Autom Control, 50, 6, 841-846 (2005) · Zbl 1365.93406 |
| [17] | Wu, X. J.; Lu, H. T., Outer synchronization of uncertain general complex delayed networks with adaptive coupling, Neurocomputing, 82, 157-166 (2012) |
| [18] | Li, P.; Yi, Z., Synchronization analysis of delayed complex networks with time-varying couplings, Phys A, 387, 3729-3737 (2008) |
| [19] | Zheng, S., Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling, Nonlinear Dyn, 67, 2621-2630 (2012) · Zbl 1243.93042 |
| [20] | Belykh, I. V.; Belykh, V. N.; Hasler, M., Blinking model and synchronization in small-world networks with a time-varying coupling, Phys D, 195, 188-206 (2004) · Zbl 1098.82621 |
| [21] | Anzo, A.; Barajas-Ramírez, J. G., Synchronization in complex networks with structural evolution, J Franklin Inst, 351, 1, 358-372 (2014) · Zbl 1293.93145 |
| [22] | Wang, Q. Y.; Duan, Z. S.; Chen, G. R.; Feng, Z. S., Synchronization in a class of weighted complex networks with coupling delays, Phys A, 387, 5616-5622 (2008) |
| [23] | Fan, Y. Q.; Wang, Y. H.; Zhang, Y.; Wang, Q. R., The synchronization of complex dynamical networks with similar nodes and coupling time-delay, Appl Math Comput, 219, 6719-6728 (2013) · Zbl 1288.34064 |
| [24] | Grigoriev, R. O.; Cross, M. C.; Schuster, H. G., Pinning control of spatiotemporal chaos, Phys Rev Lett, 79, 15, 2795-2798 (1997) |
| [25] | Wang, Y. H.; Zhang, S. Y., Robust control for nonlinear similar composite systems with uncertain parameters, IEE Proc Control Theory Appl, 147, 80-86 (2000) |
| [26] | Slotine, J. E.; Li, W., Applied Nonlinear Control (2006), China Machine Press: China Machine Press Beijing, (simplified Chinese edition) |
| [27] | Hrg, D., Synchronization of two Hindmarsh-Rose neurons with unidirectional coupling, Neural Networks, 40, 73-79 (2013) · Zbl 1283.92017 |
| [28] | Nguyen, L. H.; Hong, K. S., Adaptive synchronization of two coupled chaotic Hindmarsh-Rose neurons by controlling the membrane potential of a slave neuron, Appl Math Modell, 37, 4, 2460-2468 (2013) · Zbl 1349.93224 |
| [30] | Moujahid, A.; d’Anjou, A.; Torrealdea, F. J.; Torrealdea, F., Efficient synchronization of structurally adaptive coupled Hindmarsh-Rose neurons, Chaos, Solitons Fractals, 44, 929-933 (2011) |
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