Stabilization of time-varying and disturbed complex dynamical networks with different-dimensional nodes and uncertain nonlinearities. (English) Zbl 1386.93261
Summary: This paper investigates the stabilization problem for time-varying and disturbed complex dynamical networks (CDNs) with different-dimensional nodes and uncertain nonlinearities. To be consistent with the properties of real-world networks, both the disturbances of our networks and the nonlinear structures of the nodes permit are completely unknown but bounded. Furthermore, the norm bounds of the uncertain nonlinearities and disturbances (NBUND) are applied to design the stabilization controllers. When the NBUND are known in advance, some decentralized state feedback controllers are proposed to stabilize our networks. And when they are unknown, adaptive decentralized stabilization schemes are brought forward for our network models. The effectiveness and feasibility of our theoretical results are verified by two simulation examples.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93A15 | Large-scale systems |
| 93C10 | Nonlinear systems in control theory |
| 93C41 | Control/observation systems with incomplete information |
Keywords:
complex dynamical networks; stabilization; uncertain nonlinearities and disturbances; time-varying; different dimensionsReferences:
| [1] | Zhang, L. L., L. H.Huang, and Z. W.Cai, “Finite‐time stabilization control for discontinuous time‐delayed networks: New switching design,” Neural Netw., Vol. 75, pp. 84-96 (2016). · Zbl 1415.93192 |
| [2] | Yuan, W. J., X. S.Luo, P. Q.Jiang, B. H.Wang, and J. Q.Fang, “Stability of a complex dynamical network model,” Physica A, Vol. 374, pp. 478-82 (2007). |
| [3] | Duan, Z. S., J. Z.Wang, G. R.Chen, and L.Huang, “Stability analysis and decentralized control of a class of complex dynamical networks,” Automatica, Vol. 44, pp. 1028-35 (2008). · Zbl 1283.93017 |
| [4] | Wang, Y. H., Y. Q.Fan, Q. Y.Wang, and Y.Zhang, “Stabilization and synchronization of complex dynamical networks with similar nodes via decentralized controllers,” IEEE Trans. Circuits Syst.‐I: Regul. Pap., Vol. 59, pp. 1786-95 (2012). · Zbl 1468.93139 |
| [5] | Lu, J., and D. W. C.Ho, “Stabilization of complex dynamical networks with noise disturbance under performance constraint,” Nonlinear Anal.‐Real World Appl., Vol. 12, pp. 1974-84 (2011). · Zbl 1246.37100 |
| [6] | Qiu, X., L.Yu, and D.Zhang, “Stabilization of supply networks with transportation delay and switching topology,” Neurocomputing, Vol. 155, pp. 247-52 (2015). |
| [7] | Cai, Z., L.Huang, M.Zhu, and D.Wang, “Finite‐time stabilization control of memristor‐based neural networks,” Nonlinear Anal.‐Hybrid Syst., Vol. 20, pp. 37-54 (2016). · Zbl 1336.93135 |
| [8] | Lu, W., X.Li, and Z.Rong, “Global stabilization of complex networks with digraph topologies via a local pinning algorithm,” Automatica, Vol. 46, pp. 116-21 (2010). · Zbl 1214.93090 |
| [9] | Xu, X., G.Zong, and L.Hou, “Passivity‐based stabilization and passive synchronization of complex nonlinear networks,” Neurocomputing, Vol. 175, pp. 101-9 (2016). |
| [10] | Moradi, H., and V. J.Majd, “Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach,” Math. Biosci., Vol. 275, pp. 10-7 (2016). · Zbl 1338.92042 |
| [11] | Li, S., J.Zhang, and W.Tang, “Robust H_∞ output feedback control for uncertain complex delayed dynamical networks,” Comput. Math. Applicat., Vol. 62, pp. 497-505 (2011). · Zbl 1228.93044 |
| [12] | Al‐mahbashi, G., M. S. M.Noorani, S. A.Bakar, and S.Vahedi, “Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance,” Neurocomputing, Vol. 207, pp. 645-52 (2016). |
| [13] | Lee, D. W., W. J.Yoo, D. H.Ji, and J. H.Park, “Integral control for synchronization of complex dynamical networks with unknown non‐identical nodes,” Appl. Math. Comput., Vol. 224, pp. 140-9 (2013). · Zbl 1336.93018 |
| [14] | Wang, L., G.Wei, and W.Li, “Probability‐dependent H_∞ synchronization control for dynamical networks with randomly varying nonlinearities,” Neurocomputing, Vol. 133, pp. 369-76 (2014). |
| [15] | Li, H. L., Y. L.Jiang, Z.Wang, L.Zhang, and Z.Teng, “Parameter identification and adaptive‐impulsive synchronization of uncertain complex networks with nonidentical topological structures,” Optik, Vol. 126, pp. 5771-6 (2015). |
| [16] | Streif, S., K. K. K.Kim, P.Rumschinski, M.Kishida, D. E.Shen, R.Findeisen, and R. D.Braatz, “Robustness analysis, prediction, and estimation for uncertain biochemical networks: An overview,” J. Process Control, Vol. 42, pp. 14-34 (2016). |
| [17] | Wen, G. H., W. W.Yu, G. Q.Hu, J. D.Cao, and X. H.Yu, “Pinning synchronization of directed networks with switching topologies: A multiple Lyapunov functions approach,” IEEE Trans. Neural Netw. Learn. Syst., Vol. 26, No. 12, pp. 3239-50 (2015). |
| [18] | Wen, G. H., W. W.Yu, M. Z. Q.Chen, X. H.Yu, and G. R.Chen, “H_∞ pinning synchronization of directed networks with aperiodic sampled‐data communications,” IEEE Trans. Circuits Syst.‐I: Regul. Pap., Vol. 61, No. 11, pp. 3245-55 (2014). |
| [19] | Zhao, J., D. J.Hill, and T.Liu, “Stability of dynamical networks with non‐identical nodes: A multiple V‐Lyapunov function method,” Automatica, Vol. 47, pp. 2615-25 (2011). · Zbl 1235.93214 |
| [20] | Wang, Q. Y., G. R.Chen, Q. S.Lu, and F.Hao, “Novel criteria of synchronization stability in complex networks with coupling delays,” Physica A, Vol. 378, pp. 527-36 (2007). |
| [21] | Zhang, L. L., Y. H.Wang, and Y. Y.Huang, “Synchronization for non‐dissipatively coupled time‐varying complex dynamical networks with delayed coupling nodes,” Nonlinear Dyn., Vol. 82, No. 3, pp. 1581-93 (2015). · Zbl 1348.34099 |
| [22] | Zhang, L. L., Y. H.Wang, and Q.Wang, “Synchronization for time‐varying complex dynamical networks with different‐dimensional nodes and non‐dissipative coupling,” Commun. in Nonlinear Sci. Numer. Simul., Vol. 24, pp. 64-74 (2015). · Zbl 1463.93234 |
| [23] | Zhang, L. L., Y. H.Wang, Y. Y.Huang, and X. S.Chen, “Delay‐dependent synchronization for non‐diffusively coupled time‐varying complex dynamical networks,” Appl. Math. Comput., Vol. 259, pp. 510-22 (2015). · Zbl 1390.93096 |
| [24] | Zhang, L. L., Y. H.Wang, Q. R.Wang, and S. Y.Zhang, “Synchronization for time‐delayed coupling complex dynamical networks with different dimensional nodes via decentralized dynamic compensation controllers,” Asian J. Control, Vol. 17, No. 2, pp. 664-74 (2015). · Zbl 1332.93037 |
| [25] | Wu, Z., X.Xu, G.Chen, and X.Fu, “Generalized matrix projective synchronization of general colored networks with different‐dimensional node dynamics,” J. Franklin Inst.‐Eng. Appl. Math., Vol. 351, pp. 4584-95 (2014). · Zbl 1395.93453 |
| [26] | DeLellis, P., M.Bernardo, T.E.Gorochowski, and G.Russo, “Synchronization and control of complex networks via contraction, adaptation and evolution,” IEEE Circuits Syst. Mag.: Complex Networks Application in Circuits and Syst., Third Quarter, pp. 64-82 (2010). |
| [27] | Li, C. S., and J.Zhao, “Geometrical dissipativity‐based output synchronization of discrete dynamical networks with non‐identical nodes,” Asian J. Control, Vol. 18, No. 3, pp. 1147-52 (2016). · Zbl 1348.93012 |
| [28] | Wen, G. H., Y.Zhao, Z. S.Duan, W. W.Yu, and G. R.Chen, “Containment of higher‐order multi‐leader multi‐agent systems: A dynamic output approach,” IEEE Trans. Autom. Control, Vol. 61, No. 4, pp. 1135-40 (2016). · Zbl 1359.93178 |
| [29] | Zhao, Y., Z. S.Duan, G. H.Wen, and G. R.Chen, “Distributed finite‐time tracking of multiple non‐identical second‐order nonlinear systems with settling time estimation,” Automatica, Vol. 64, No. 2, pp. 86-93 (2016). · Zbl 1329.93017 |
| [30] | Zhao, Y., Y. F.Liu, Z. S.Duan, and G. H.Wen, “Distributed average computation for multiple time‐varying signals with output measurements,” Int. J. Robust Nonlinear Control, Vol. 26, No. 13, pp. 2899-915 (2016). · Zbl 1346.93049 |
| [31] | Noroozi, N., M.Roopaer, and M. Z.Jahromi, “Adaptive fuzzy sliding mode control scheme for uncertain systems,” Commun. Nonlinear Sci. Numer. Simul., Vol. 14, pp. 3978-92 (2009). · Zbl 1221.93155 |
| [32] | Chen, L., G. R.Chen, and Y. W.Lee, “Fuzzy modeling and adaptive control of uncertain chaotic systems,” Inf. Sci., Vol. 121, pp. 27-37 (1999). · Zbl 0941.93539 |
| [33] | Khalil, H. K., Nonlinear Systems, Prentice‐Hall, Englewood Cliffs, NJ (2002). · Zbl 1003.34002 |
| [34] | Liu, Y. F., Y.Zhao, and G. R.Chen, “Finite‐time formation tracking control for multiple vehicles: A motion planning approach,” Int. J. Robust Nonlinear Control, Vol. 26, No. 14, pp. 3130-49 (2016). · Zbl 1346.93028 |
| [35] | Zhao, Y., Y. F.Liu, Z. K.Li, and Z. S.Duan, “Distributed average tracking for multiple signals generated by linear dynamical systems: An edge‐based framework,” Automatica, Vol. 75, pp. 158-66 (2017). · Zbl 1351.93065 |
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