Complex network dynamics of multiscroll chaotic attractors and their output-feedback pinning synchronization. (English) Zbl 1497.37118
Summary: The saturated function series have been successfully used to generate multiscroll chaotic attractors. In this paper, we revisit multiscroll chaotic attractors via saturated function series. We find that with a small constant drift acting on the saturated function, the number of scrolls will greatly decrease. This phenomenon brings extra difficulty in pinning synchronization of networked multiscroll chaotic attractors. A new output-feedback pinning controller is designed based on the unknown-input distributed observer to estimate the synchronization error, which has the advantage of saving the communication cost as the transmission of the observer information is not needed.
MSC:
| 37N35 | Dynamical systems in control |
| 34H10 | Chaos control for problems involving ordinary differential equations |
| 34H05 | Control problems involving ordinary differential equations |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 93D25 | Input-output approaches in control theory |
Keywords:
multiscroll chaotic attractor; complex network dynamics; output-feedback pinning synchronization; appointed-time unknown-input distributed observer; time-varying transformationReferences:
| [1] | Agha, R., Rehan, M., Ahn, C., Mustafa, G. & Ahmad, S. [2019] “ Adaptive distributed consensus control of one-sided Lipschitz nonlinear multiagents,” IEEE Trans. Syst. Man Cybern. Syst.49, 568-578. |
| [2] | Arena, P., Baglio, S., Fortuna, L. & Manganaro, G. [1996] “ Generation of n-double scrolls via cellular neural networks,” Int. J. Circuit Th. Appl.24, 241-252. |
| [3] | Chen, G. & Dong, X. [1998] From Chaos to Order: Methodologies, Perspectives and Applications (World Scientific, Singapore). · Zbl 0908.93005 |
| [4] | Chu, H., Gao, L., Yue, D. & Dou, C. [2020] “ Consensus of Lipschitz nonlinear multiagent systems with input delay via observer-based truncated prediction feedback,” IEEE Trans. Syst. Man Cybern. Syst.50, 3784-3794. |
| [5] | Chua, L. O., Komuro, M. & Matsumoto, T. [1986] “ The double scroll family,” IEEE Trans. Circuits Syst.33, 1072-1118. · Zbl 0634.58015 |
| [6] | Fu, J., Wen, G., Yu, W., Huang, T. & Cao, J. [2018] “Exponential consensus of multiagent systems with Lipschitz nonlinearities using sampled-data information,” IEEE Trans. Circ. Syst.-I: Reg. Papers65, 4363-4375. |
| [7] | He, X., Hao, Y. & Wang, Q. [2019] “ Leaderless finite-time consensus for second-order Lipschitz nonlinear multi-agent systems with settling time estimation,” Physica A514, 280-289. · Zbl 07562373 |
| [8] | Hua, C., You, X. & Guan, X. [2017] “ Adaptive leader-following consensus for second-order time-varying nonlinear multiagent systems,” IEEE Trans. Cybern.47, 1532-1539. |
| [9] | Li, Z., Liu, X., Fu, M. & Xie, L. [2012] “ Global \(h_\infty\) consensus of multi-agent systems with Lipschitz nonlinear dynamics,” IET Contr. Th. A6, 2041-2048. |
| [10] | Li, Z., Ren, W., Liu, X. & Fu, M. [2013] “ Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols,” IEEE Trans. Autom. Contr.58, 1786-1791. · Zbl 1369.93032 |
| [11] | Lorenz, E. N. [1963] “ Nonperiodic flow,” J. Atmos. Sci.20, 130-141. · Zbl 1417.37129 |
| [12] | Lü, J., Lu, J. & Chen, S. [2002] Chaotic Time Series Analysis and Its Applications(in Chinese) (Wuhan University Press, Wuhan, China). |
| [13] | Lü, J., Yu, X. & Chen, G. [2003] “ Generating chaotic attractors with multiple merged basins of attraction: A switching piecewise-linear control approach,” IEEE Trans. Circuits Syst.-I50, 198-207. · Zbl 1368.37041 |
| [14] | Lü, J., Chen, G., Yu, X. & Leung, H. [2004] “ Design and analysis of multiscroll chaotic attractors from saturated function series,” IEEE Trans. Circ. Syst.-I51, 2476-2490. · Zbl 1371.37060 |
| [15] | Lü, J. & Chen, G. [2006] “ Generating multiscroll chaotic attractors: Theories, methods and applications,” Int. J. Bifurcation and Chaos16, 775-858. · Zbl 1097.94038 |
| [16] | Lü, J., Yu, S., Leung, H. & Chen, G. [2006] “ Experimental verification of multidirectional multiscroll chaotic attractors,” IEEE Trans. Circ. Syst.-I53, 149-165. |
| [17] | Lv, Y., Li, Z. & Duan, Z. [2016] “ Distributed adaptive consensus protocols for multiple Lur’e systems over directed graphs,” IET Contr. Th. A10, 443-450. |
| [18] | Lv, Y., Wen, G. & Huang, T. [2020] “ Adaptive protocol design for distributed tracking with relative output information: A distributed fixed-time observer approach,” IEEE Trans. Contr. Netw. Syst.7, 118-128. · Zbl 1516.93136 |
| [19] | Pin, G., Yang, G., Serrani, A. & Parisini, T. [2020] “ Fixed-time observer design for LTI systems by time-varying coordinate transformation,” 59th IEEE Conf. Dec. Control (CDC), pp. 6040-6045. |
| [20] | Rehan, M., Jameel, A. & Ahn, C. [2018] “ Distributed consensus control of one-sided Lipschitz nonlinear multiagent systems,” IEEE Trans. Syst. Man Cybern. Syst.48, 1297-1308. |
| [21] | Rehman, A., Rehan, M., Iqbal, N. & Ahn, C. [2020] “ LPV scheme for robust adaptive output feedback consensus of Lipschitz multiagents using Lipschitz nonlinear protocol,” IEEE Trans. Syst. Man Cybern. Syst., https://doi.org/10.1109/TSMC.2020.2964567. |
| [22] | Tang, K. S., Zhong, G. Q., Chen, G. & Man, K. F. [2001] “ Generation of n-scroll attractors via sine function,” IEEE Trans. Circuits Syst.-I48, 1369-1372. |
| [23] | Xu, F., Yu, P. & Liao, X. [2013] “ Synchronization and stabilization of multi-scroll integer and fractional order chaotic attractors generated using trigonometric functions,” Int. J. Bifurcation and Chaos23, 1350145-1-33. · Zbl 1275.34070 |
| [24] | Yalcin, M. E., Suykens, J. A. K. & Vandewalle, J. [2000] “ Hyperchaotic n-scroll attractors,” Proc. IEEE Workshop on Nonlinear Dynamics of Electronic Systems (NDES’00), May 18-20, Catania, Italy, , pp. 25-28. |
| [25] | Yalcin, M. E., Suykens, J. A. K., Vandewalle, J. & Ozoguz, S. [2002] “ Families of scroll grid attractors,” Int. J. Bifurcation and Chaos12, 23-41. · Zbl 1044.37029 |
| [26] | Yu, W., Chen, G., Cao, M. & Kurths, J. [2010] “ Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics,” IEEE Trans. Syst. Man Cybern. B40, 881-891. |
| [27] | Zhang, H., Lewis, F. & Qu, Z. [2012] “ Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs,” IEEE Trans. Autom. Control59, 3026-3041. |
| [28] | Zhang, Z., Zhang, L., Hao, F. & Wang, L. [2017] “ Leader-following consensus for linear and Lipschitz nonlinear multiagent systems with quantized communication,” IEEE Trans. Cybern.47, 1970-1982. |
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.
