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Vol.2 , No. 6, Publication Date: Jan. 7, 2016, Page: 110-115
, and we designed control for each kind to perform control and synchronization of this system. However, in unknown parameters, we assume that Lyapunov function is always formed as<span> </span><span><img width="88" height="27" src="http://article.aascit.org/journal/909/9090791/image002.png" /></span>, where <span><img width="42" height="24" src="http://article.aascit.org/journal/909/9090791/image003.png" /></span> is the </span><span>identity</span><span> matrix. While we focused on selecting a suitable Lyapunov functions candidate that ensured asymptotically global stability in known parameters. Then, nonlinear control technique is better than adaptive and active nonlinear control because it deals with known and unknown parameters as well as to the design of more than control compared with the rest of the controls. Moreover, numerical simulations are offered to show the strength of the proposed theoretical results.</span>&picture=http://www.aascit.org/aascit/decorators/img/journal/909.jpg)
| [1] | Maysoon M. Aziz, Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq. |
| [2] | Saad F. AL-Azzawi, Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq. |
This paper is concerned with the problem of chaos control and synchronization for a novel 5-D hyperchaotic system, which is constructed by adding a feedback control to a 4-D hyperchaotic Lorenz system. Based on the Lyapunov stability theory and using nonlinear control technique with two different kinds of parameters (known and unknown parameters), and we designed control for each kind to perform control and synchronization of this system. However, in unknown parameters, we assume that Lyapunov function is always formed as 
, where 
is the identity matrix. While we focused on selecting a suitable Lyapunov functions candidate that ensured asymptotically global stability in known parameters. Then, nonlinear control technique is better than adaptive and active nonlinear control because it deals with known and unknown parameters as well as to the design of more than control compared with the rest of the controls. Moreover, numerical simulations are offered to show the strength of the proposed theoretical results.
Keywords
A Novel 5-D Hyperchaotic Lorenz System, Control, Synchronization, Lyapunov Stability Theory, Nonlinear Control Technique
Reference
| [01] | Ahmad I., Saaban A. B., Ibrahim A. B., Shahzad M., A Research on synchronization of two novel chaotic system based on nonlinear active control algorithm, Engineering, Technology & Applied Science Research, 5 (2015) 739-747. |
| [02] | AL-Azzawi S. F., Stability and bifurcation of pan chaotic system by using Routh-Hurwitz and Gardan method, Appl. Math. Comput. 219 (2012) 1144-1152. |
| [03] | Aziz M. M., AL-Azzawi S. F., Control and synchronization of a modified hyperchaotic Pan System via active and adaptive control techniques, Comput. Appl. Math. 1 (2015) 151-155. |
| [04] | Cai G., Tan Z., Chaos synchronize of a new chaotic system via nonlinear control, J. Uncertain Systems, 1 (2007) 235-240. |
| [05] | Changjin X., Peiluan L., Chaos control for a 4D hyperchaotic system, Applied Mechanics and Materials, 1 (2013) 84-87. |
| [06] | Chen HK., Global Chaos synchronization of new chaotic systems via nonlinear control, Chaos, Solitons and Fractals, 23 (2005) 1245-1251. |
| [07] | Pang S., Liu Y., A new hyperchaotic system from the Lu system and its control, J Compu. Appl. Math. 235(2011) 2775–2789. |
| [08] | Park J. H., Chaos synchronization of a chaotic system via nonlinear control, Chaos Solitons Fractals 25 (2005) 579-584. |
| [09] | Lu D., Wang A., Tian X., Control and synchronization of a new hyperchaotic system with unknown parameters, International Journal of Nonlinear Science. 6 (2008) 224-229. |
| [10] | Vaidyanatan S., Volos C., Pham VT., Hyperchaos, Adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation, Archives of Control Sciences. 24 (2014) 409 - 446. |
| [11] | Vaidyanatan S., Volos C., Pham VT., Analysis, Adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation, Archives of Control Sciences. 25 (2015) 135 - 158. |
| [12] | Xu J., Cai G., Zheng S., Adaptive synchronization for an uncertain new hyperchaos Lorenz system, International Journal of Nonlinear Science. 8 (2009) 117-123. |
| [13] | Yang Q. Chen C., A 5D hyperchaotic system with three positive Lyapunov exponents coined International Journal of Bifurcation and Chaos. 23 (2013) 13501091-135010923. |
| [14] | Zarei A., Complex dynamics in a 5-D hyper-chaotic attractor with four -wing, one equilibrium and multiple chaotic attractors. Nonlinear Dyn 5 (2013). |
| [15] | Zhu C., Control and synchronize a novel hyperchaotic system, Appl. Math. Comput. 216 (2010) 276-284. |
| [16] | Wang Y. Guan ZH., Wang H. O., Feedback and adaptive control for the synchronization of Chen system via a single variable. Physics Letters A 312 (2003) 34-40. |
