Approximate synchronization of uncertain complex delayed networks with non-identical nodes. (English) Zbl 1410.34228
Summary: In this article, a delayed complex network model with non-identical nodes is established, where the mismatched uncertain parameters are involved in each node. The concept of approximate synchronization is proposed. A linear feedback controller is designed and a sufficient condition for boundedness of the synchronous error is presented in terms of linear matrix inequalities. A pseudoconvex optimization problem for minimizing the upper bound of the synchronous error is proposed. Furthermore, an iterative algorithm involving convex problem is designed to solve this pseudoconvex optimization problem and obtain the globally optimal solution, by which the approximate synchronization is achieved. At last, two numerical examples are given to show the effectiveness of the proposed criterion.
MSC:
| 34K25 | Asymptotic theory of functional-differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 34K35 | Control problems for functional-differential equations |
Keywords:
complex network; approximate synchronization; time delay; uncertainty; linear matrix inequality; pseudoconvex optimizationReferences:
| [1] | Avriel M., Nonlinear Programming: Analysis and Methods (1976) |
| [2] | DOI: 10.1126/science.286.5439.509 · Zbl 1226.05223 · doi:10.1126/science.286.5439.509 |
| [3] | DOI: 10.1080/00207160701704580 · Zbl 1142.93361 · doi:10.1080/00207160701704580 |
| [4] | DOI: 10.1140/epjb/e2009-00078-6 · doi:10.1140/epjb/e2009-00078-6 |
| [5] | DOI: 10.1016/j.neunet.2009.06.009 · Zbl 1338.93097 · doi:10.1016/j.neunet.2009.06.009 |
| [6] | DOI: 10.1007/978-94-017-1965-0 · doi:10.1007/978-94-017-1965-0 |
| [7] | DOI: 10.1109/TCSI.2004.835655 · Zbl 1374.94915 · doi:10.1109/TCSI.2004.835655 |
| [8] | DOI: 10.1088/1751-8113/41/38/385103 · Zbl 1145.93012 · doi:10.1088/1751-8113/41/38/385103 |
| [9] | DOI: 10.1142/S0219493710003108 · Zbl 1209.34089 · doi:10.1142/S0219493710003108 |
| [10] | DOI: 10.1016/j.camwa.2011.05.033 · Zbl 1228.93044 · doi:10.1016/j.camwa.2011.05.033 |
| [11] | DOI: 10.1080/00207721.2010.517865 · Zbl 1259.93088 · doi:10.1080/00207721.2010.517865 |
| [12] | DOI: 10.1016/j.automatica.2010.04.005 · Zbl 1194.93090 · doi:10.1016/j.automatica.2010.04.005 |
| [13] | DOI: 10.1080/00207160701670310 · Zbl 1183.34116 · doi:10.1080/00207160701670310 |
| [14] | DOI: 10.1016/j.chaos.2009.03.024 · Zbl 1198.93182 · doi:10.1016/j.chaos.2009.03.024 |
| [15] | DOI: 10.1016/j.automatica.2008.05.006 · Zbl 1153.93329 · doi:10.1016/j.automatica.2008.05.006 |
| [16] | DOI: 10.1080/00207160410001708779 · Zbl 1090.68006 · doi:10.1080/00207160410001708779 |
| [17] | DOI: 10.1109/TNN.2010.2090669 · doi:10.1109/TNN.2010.2090669 |
| [18] | DOI: 10.1109/TCSI.2009.2024971 · doi:10.1109/TCSI.2009.2024971 |
| [19] | DOI: 10.1016/j.physleta.2009.11.032 · Zbl 1234.05218 · doi:10.1016/j.physleta.2009.11.032 |
| [20] | DOI: 10.1103/PhysRevLett.100.114101 · doi:10.1103/PhysRevLett.100.114101 |
| [21] | DOI: 10.1007/s11071-011-0093-4 · Zbl 1242.93009 · doi:10.1007/s11071-011-0093-4 |
| [22] | DOI: 10.1038/30918 · Zbl 1368.05139 · doi:10.1038/30918 |
| [23] | DOI: 10.1016/j.automatica.2006.11.014 · Zbl 1330.93180 · doi:10.1016/j.automatica.2006.11.014 |
| [24] | DOI: 10.1080/00207179608921866 · Zbl 0841.93014 · doi:10.1080/00207179608921866 |
| [25] | DOI: 10.1016/j.automatica.2008.07.016 · Zbl 1158.93308 · doi:10.1016/j.automatica.2008.07.016 |
| [26] | DOI: 10.1002/rnc.1339 · Zbl 1160.93342 · doi:10.1002/rnc.1339 |
| [27] | DOI: 10.1016/j.chaos.2009.03.158 · Zbl 1198.93023 · doi:10.1016/j.chaos.2009.03.158 |
| [28] | DOI: 10.1016/j.amc.2010.05.037 · Zbl 1200.65103 · doi:10.1016/j.amc.2010.05.037 |
| [29] | Zhang Y., Int. J. Comput. Math. 88 (2) pp 249– (2011) |
| [30] | DOI: 10.1109/TAC.2006.872760 · Zbl 1366.93544 · doi:10.1109/TAC.2006.872760 |
| [31] | Zhou J., Nonlinear Anal. 5 (3) pp 513– (2011) |
| [32] | DOI: 10.1016/j.automatica.2011.09.012 · Zbl 1235.93214 · doi:10.1016/j.automatica.2011.09.012 |
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.
