i-manager Publications

Synchronization of Two Identical Circular Restricted Three Body Problem using a Robust Adaptive Sliding Mode Controller with Application to Secure Communications

0*, Mohammed Raziuddin**, Ahmed Mohiuddin Mohammed***

* Assistant Professor, Department of General Requirements, College of Applied Sciences, Nizwa, Oman.

** Research Scholar, Singhania University, Jhunjhunu, Rajasthan, India.

*** Department of Mathematics & Statistics, Sultan Qaboos University.

Periodicity:October - December'2017
DOI : https://doi.org/10.26634/jmat.6.4.13862

Abstract

In this paper, the authors have synchronized the two identical systems of Circular Restricted Three Body Problem evolving from different initial conditions using a Robust Adaptive Sliding Mode Controller. The two chaotic identical systems have been synchronized under the effects of uncertainties and external disturbances with unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are implemented to tackle the uncertainties, external disturbances, and unknown parameters. For the synchronization of the two identical systems under consideration, all simulations are being done using Mathematica. Furthermore, the secure communication scheme has also been demonstrated.

Keywords

CRTBP, Synchronization, RASMC.

How to Cite this Article?

Shahzad, M., Raziuddin, M., Mohammed, A.M. (2017). Synchronization of Two Identical Circular Restricted Three Body Problem using a Robust Adaptive Sliding Mode Controller with Application to Secure Communications. i-manager’s Journal on Mathematics, 6(4), 19-28. https://doi.org/10.26634/jmat.6.4.13862

References

[1]. Aghababa, M. P. & Akbari, M. E. (2012). A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances. Applied Mathematics and Computation, 218(9), 5757-5768.

[2]. Aghababa, M. P. & Heydari, A. (2012). Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities. Applied Mathematical Modelling, 36(4), 1639-1652.

[3]. Ahmad, I., Saaban, A. B., Ibrahim, A. B., & Shahzad, M. (2014). Global Chaos Identical and Nonidentical Synchronization of a New Chaotic System using Linear Active Control. Complexity, 21(1), 379-386.

[4]. Ahmadi, A. A. & Majd, V. J. (2009). Robust synchronization of a class of uncertain chaotic systems. Chaos, Soliton Fract, 42, 1092–1096.

[5]. Asheghan, M. M. & Beheshti, M. T. (2009). An LMI approach to robust synchronization of a class of chaotic systems with gain variations. Chaos, Solitons & Fractals, 42(2), 1106-1111.

[6]. Bu, S. & Wang, B. H. (2004). Improving the security of chaotic encryption by using a simple modulating method. Chaos, Solitons & Fractals, 19(4), 919-924.

[7]. Cai, N., Jing, Y., & Zhang, S. (2010). Modified projective synchronization of chaotic systems with disturbances via active sliding mode control. Communications in Nonlinear Science and Numerical Simulation, 15(6), 1613-1620.

[8]. Chen, C. S. (2009). Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems. Expert Systems with Applications, 36(9), 11827-11835.

[9]. Chen, H. H., Sheu, G. J., Lin, Y. L., & Chen, C. S. (2009). Chaos synchronization between two different chaotic systems via nonlinear feedback control. Nonlinear Analysis: Theory, Methods & Applications, 70(12), 4393-4401.

[10]. Chen, X. & Lu, J. (2007). Adaptive synchronization of different chaotic systems with fully unknown parameters. Physics Letters A, 364(2), 123-128.

[11]. El-Gohary, A. (2006). Optimal synchronization of Rössler system with complete uncertain parameters. Chaos, Solitons & Fractals, 27(2), 345-355.

[12]. Feki, M. (2009). Sliding mode control and synchronization of chaotic systems with parametric uncertainties. Chaos, Solitons & Fractals, 41(3), 1390-1400.

[13]. Hwang, E. J., Hyun, C. H., Kim, E., & Park, M. (2009). Fuzzy model based adaptive synchronization of uncertain chaotic systems: robust tracking control approach. Physics Letters A, 373(22), 1935-1939.

[14]. Jianwen, F., Ling, H., Chen, X., Austin, F., & Geng, W. (2010). Synchronizing the noise-perturbed Genesio chaotic system by sliding mode control. Communications in Nonlinear Science and Numerical Simulation, 15(9), 2546-2551.

[15]. Kebriaei, H. & Yazdanpanah, M. J. (2010). Robust adaptive synchronization of different uncertain chaotic systems subject to input nonlinearity. Communications in Nonlinear Science and Numerical Simulation, 15(2), 430-441.

[16]. Khan, A. & Shahzad, M. (2013). Synchronization of circular restricted three body problem with Lorenz hyper chaotic system using a robust adaptive sliding mode controller. Complexity, 18(6), 58-64.

[17]. Li, W. L. & Chang, K. M. (2009). Robust synchronization of drive–response chaotic systems via adaptive sliding mode control. Chaos, Solitons & Fractals, 39(5), 2086-2092.

[18]. Lin, C. M., Peng, Y. F., & Lin, M. H. (2009). CMAC-based adaptive backstepping synchronization of uncertain chaotic systems. Chaos, Solitons & Fractals, 42(2), 981-988.

[19]. Lu, J., Wu, X., Han, X., & Lü, J. (2004). Adaptive feedback synchronization of a unified chaotic system. Physics Letters A, 329(4), 327-333.

[20]. Ma, J., Zhang, A. H., Xia, Y. F., & Zhang, L. P. (2010). Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems. Applied Mathematics and Computation, 215(9), 3318-3326.

[21]. Njah, A. N. (2011). Synchronization via active control of parametrically and externally excited Φ6 Van der Pol and Duffing oscillators and application to secure communications. Journal of Vibration and Control, 17(4), 493-504.

[22]. Pourmahmood, M., Khanmohammadi, S., & Alizadeh, G. (2011). Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller. Communications in Nonlinear Science and Numerical Simulation, 16(7), 2853-2868.

[23]. Rafikov, M. & Balthazar, J. M. (2008). On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Communications in Nonlinear Science and Numerical Simulation, 13(7), 1246-1255.

[24]. Salarieh, H. & Shahrokhi, M. (2008). Adaptive synchronization of two different chaotic systems with time varying unknown parameters. Chaos, Solitons & Fractals, 37(1), 125-136.

[25]. Shahzad, M. (2015). The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study. Nonlinear Dynamics, 79(3), 2037- 2054.

[26]. Sun, Y. J. (2009). Chaos synchronization of uncertain Genesio–Tesi chaotic systems with deadzone nonlinearity. Physics Letters A, 373(36), 3273-3276.

[27]. Szebehely, V. (1967). Theory of Orbits. Academic Press.

[28]. Wang, C. & Ge, S. S. (2001). Adaptive synchronization of uncertain chaotic systems via backstepping design. Chaos, Solitons & Fractals, 12(7), 1199-1206.

[29]. Wang, F., & Liu, C. (2007). Synchronization of unified chaotic system based on passive control. Physica D: Nonlinear Phenomena, 225(1), 55-60.

[30]. Wang, H., Han, Z. Z., Xie, Q. Y., & Zhang, W. (2009). Finite-time chaos synchronization of unified chaotic system with uncertain parameters. Communications in Nonlinear Science and Numerical Simulation, 14(5), 2239-2247.

[31]. Xiang, W. & Huangpu, Y. (2010). Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties. Communications in Nonlinear Science and Numerical Simulation, 15(11), 3241-3247.

[32]. Yan, J. J., Hung, M. L., Chiang, T. Y., & Yang, Y. S. (2006). Robust synchronization of chaotic systems via adaptive sliding mode control. Physics Letters A, 356(3), 220-225.

[33]. Yang, T. (2004). A survey of chaotic secure communication systems. International Journal of Computational Cognition, 2(2), 81-130.

[34]. Yassen, M. T. (2005). Adaptive synchronization of two different uncertain chaotic systems. Physics Letters A, 337(4), 335- 341.

[35]. Yassen, M. T. (2007). Controlling, synchronization and tracking chaotic Liu system using active backstepping design. Physics Letters A, 360(4), 582-587.

[36]. Yau, H. T. & Shieh, C. S. (2008). Chaos synchronization using fuzzy logic controller. Nonlinear Analysis: Real World Applications, 9(4), 1800-1810.

[37]. Zhang, G., Liu, Z., & Zhang, J. (2008). Adaptive synchronization of a class of continuous chaotic systems with uncertain parameters. Physics Letters A, 372(4), 447-450.

[38]. Zhang, H. & Ma, X. K. (2004). Synchronization of uncertain chaotic systems with parameters perturbation via active control. Chaos, Solitons & Fractals, 21(1), 39-47.

If you have access to this article please login to view the article or kindly login to purchase the article

Single Article

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Online	15	15

ADD TO CART

Options for accessing this content:

If you would like institutional access to this content, please recommend the title to your librarian.
If you already have i-manager's user account: Login above and proceed to purchase the article.
New Users: Please register, then proceed to purchase the article.