State Reconstruction for Complex Dynamical Networks with Noises

Abstract

The state reconstruction problem is addressed for complex dynamical networks coupled with states and outputs respectively, in a noisy transmission channel. By using Lyapunov stability theory and H performance, two schemes of state reconstruction are proposed for the complex dynamical networks with the nodes coupled by states and outputs respectively, and the estimation errors are convergent to zeros with H performance index. A numerical simulation demonstrates the effectiveness of the proposed observers.

Share and Cite:

C. Fan and G. Jiang, "State Reconstruction for Complex Dynamical Networks with Noises," International Journal of Modern Nonlinear Theory and Application, Vol. 1 No. 1, 2012, pp. 1-5. doi: 10.4236/ijmnta.2012.11001.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] S. H. Strogatz, “Exploring Complex Networks,” Nature, Vol. 410, No. 8, 2001, pp. 268-276. doi:10.1038/35065725
[2] E. De Silva and M. P. H. Stumpf, “Complex Networks and Simple Models in Biology,” Journal of the Royal Society Interface, Vol. 2, No. 5, 2005, pp. 419-430. doi:10.1098/rsif.2005.0067
[3] T. A. S. Pardo, L. Antiqueira, M. D. G. Nunes, O. N. Oliveira and L. D. F. Costa, “Using Complex Networks for Language Processing: The Case of Summary Evaluation,” 2006 International Conference on Communications, Circuits and Systems Proceedings, Guilin, 25-28 June 2006, pp. 2678-2682. doi:10.1109/ICCCAS.2006.285222
[4] S. J. Harrison and J. R. Dickinson, “A Metabolomic Analysis of Yeast Deletion Mutants Reveals Complex Networks of Control,” Yeast, Vol. 20, No. S1, 2003, pp. S220- S220.
[5] M. Chen and Tsinghua Univ, “Chaos Synchronization in Complex Networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 55, No. 5, 2008, pp. 1335- 1346. doi:10.1109/TCSI.2008.916436
[6] X. F. Wang and G. Chen, “Synchronization in Scale Free Dynamical Networks: Robustness and Fragility,” IEEE Transaction on Circuits Systems I: Fundamental Theory and Applications, Vol. 49, No. 1, 2002, pp. 54-62. doi:10.1109/81.974874
[7] X. Li and G. Chen, “Synchronization and Desynchronization of Complex Dynamical Networks: An Engineering Viewpoint,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 50, No. 11, 2003, pp. 1381-1390. doi:10.1109/TCSI.2003.818611
[8] R. Carli, A. Chiuso, L. Schenato and S. Zampieri, “Optimal Synchronization for Networks of Noisy Double Integrators,” IEEE Transactions on Automatic Control, Vol. 56, No. 5, 2011, pp. 1146-1152. doi:10.1109/TAC.2011.2107051
[9] G. Wang, J. Cao and J. Lu, “Outer Synchronization between Two Nonidentical Networks with Circumstance Noise,” Physica A: Statistical and Its Applications, Vol. 389, No. 7, 2010, pp. 1480-1488. doi:10.1016/j.physa.2009.12.014
[10] C.-X. Fan, G.-P. Jiang and F.-H. Jiang, “Synchronization between Two Complex Dynamical Networks Using Scalar Signals under Pinning Control,” IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 57, No. 11, 2010, pp. 2991-2998. doi:10.1109/TCSI.2010.2048774
[11] X. Q. Wu, W. X. Zheng and J. Zhou, “Generalized Outer Synchronization between Complex Dynamical Networks,” Chaos, Vol. 19, No. 1, 2009, p. 013109. doi:10.1063/1.3072787
[12] G.-P. Jiang, W. K.-S. Tang and G. Chen, “A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 53, No. 12, 2006, pp. 2739-2745. doi:10.1109/TCSI.2006.883876
[13] R. M. Gutierrez-Ríos, J. A. Freyre-Gonzalez, O. Resendis, J. Collado-Vides, M. Saier and G. Gosset, “Identification of Regulatory Network Topological Units Coordinating the Genome-Wide Transcriptional Response to Glucose in Escherichia coli,” BMC Microbiology, Vol. 7, No. 53, 2007. doi:10.1186/1471-2180-7-53
[14] W. K. S. Tang and L. Kocarev, “Identification and Monitoring of Biological Neural Network,” IEEE International Symposium on Circuits and Systems, New Orleans, 27-30 May 2007, pp. 2646-2649. doi:10.1109/ISCAS.2007.377957
[15] J. Zhou and J.-A. Lu, “Topology Identification of Weighted Complex Dynamical Networks,” Physica A: Statistical Mechanics and Its Applications, Vol. 386, No. 1, 2007, pp. 481-491. doi:10.1016/j.physa.2007.07.050
[16] H. Liu, G.-P. Jiang and C.-X. Fan, “State-Observer-Based Approach for Identification and Monitoring of Complex Dynamical Networks,” 2008 IEEE Asia Pacific Conference on Circuits and Systems (Apccas 2008), Macao, 30 November-3 December 2008, pp. 1212-1215. doi:10.1109/APCCAS.2008.4746244
[17] H. Liu, J. N. Lu and J. H. Lu, “Topology Identification of an Uncertain General Complex Dynamical Network,” Proceedings of 2008 IEEE International Symposium on Circuits and Systems, Seattle, 18-21 May 2008, pp. 109-112. doi:10.1109/ISCAS.2008.4541366
[18] X. Wu, “Synchronization-Based Topology Identification of Weighted General Complex Dynamical Networks with Time-Varying Coupling Delay,” Physica A: A-Statistical Mechanics and Its Applications, Vol. 387, No. 4, 2008, pp. 997-1008. doi:10.1016/j.physa.2007.10.030
[19] W. Guo, S. Chen and W. Sun, “Topology Identification of the Complex Networks with Non-Delayed and Delayed Coupling,” Physics Letters A, Vol. 373, No. 41, 2009, pp. 3724-3729. doi:10.1016/j.physleta.2009.08.054
[20] H. Liu, J.-A. Lu, J. Lü and D. J. Hill, “Structure Identification of Uncertain General Complex Dynamical Networks with Time Delay,” Automatica, Vol. 45, No. 8, 2009, pp. 1799-1807. doi:10.1016/j.automatica.2009.03.022
[21] G.-P Jiang, W. X. Zheng, W. K.-S. Tang and G. Chen, “Integral-Observer-Based Chaos Synchronization,” IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 53, No. 2, 2006, pp. 110-114. doi:10.1109/TCSII.2005.857087
[22] Y. Liu, Z. Wang, J. Liang and X. Liu, “Synchronization and State Estimation for Discrete-Time Complex Networks with Distributed Delays,” IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, Vol. 38, No. 5, 2008, pp. 1314-1324. doi:10.1109/TSMCB.2008.925745
[23] K. K. Busawon and P. Kaboreb, “Disturbance Attenuation Using Proportional Integral Observers,” International Journal of Control, Vol. 74, No. 6, 2001, pp. 618-627. doi:10.1080/00207170010025249

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.