Design of Proportional-Integral Sliding Mode Controllers for Hyperchaotic Systems in the Presence of Uncertainty, Disturbance and Nonlinear Control Inputs
Subject Areas : electrical and computer engineering
A.
Abooee
1
(University of Science and Technology)
M. R.
Jahed Motlagh
2
Z.
Rahmani
3
Keywords: Sliding surfaces vector hyperchaotic system reaching condition nonlinear control inputs,
Abstract :
In this paper, robust controllers for a new hyperchaotic system are investigated in the presence of uncertainty, disturbance and nonlinear control inputs. The controllers are designed by considering two major goals: first to stabilize the hyperchaotic system in the presence of uncertainties, disturbance and nonlinear control inputs; and second, to guarantee the prescribed disturbance attenuation, considering the defined performance index for it. Sliding mode control by defining three proportional integral switching surfaces is used to reach mentioned goals. Numerical simulations are used to exhibit the feasibility and performance of the proposed method.
[1] O. E. Rössler, "An equation for hyperchaos," Physics Letters A, vol. 71, no. 2, pp. 155-157, Apr. 1979.
[2] Y. Li, W. Tang, and G. Chen, "Hyperchaos evolved from the generalized lorenz equation," Int. J. of Circuit Theory and Applications, vol. 33, no. 4, pp. 235-251, Jul 2005.
[3] T. Gao, G. Chen, Z. Chen, and S. Chen, "The generation and circuit implementation of a new hyperchaos upon Lorenz system," Physics Letters A, vol. 361, no. 1, pp. 78-86, Jan. 2007.
[4] C. Wang, X. Zhang, Y. Zheng, and Y. Li, "A new modified hyperchoatic Lü system," Physica A: Statistical Mechanics and Its Applications, vol. 371, no. 2, pp. 260-272, Nov. 2006.
[5] Y. Li, W. Tang, and G. Chen, "Generating hyperchaos via state feedback control," Int. J. of Bifurcation and Chaos, vol. 15, no. 10, pp. 3367-3375, Oct. 2005.
[6] T. Gao, Z. Chen, Z. Yuan, and G. Chen, "A hyperchaos generated from chen’s system," Int. J. of Modern Physics C, vol. 17, no. 4, pp. 471-478, Jul. 2006.
[7] Z. Chen, Y. Yuang, G. Qi, and Z. Yuan, "A novel hyperchaos system only with one equilibrium," Physics Letters A, vol. 360, no. 6, pp. 696-701, Jan. 2007.
[8] W. Wu, Z. Chen, and Z. Yuan, "The evolution of a novel four -dimensional autonomous system: among 3 - torus, limit cycle, 2 -torus, chaos, and hyperchaos," Chaos, Solitons, and Fractals, vol. 39, no. 5,pp. 2340-2356, Mar. 2009.
[9] Y. Li, G. Chen, and W. Tang, "Controlling a unified chaotic system to hyperchaotic," IEEE Trans. Circuit System II, vol. 52, no. 4, pp. 204-207, Apr. 2005.
[10] ع. ابويي، م. ر. جاهد مطلق و ز. رحماني چراتي، "ارائه يک سيستم آشوبناک بعد بالاي جديد همراه با يک نقطه تعادل و پايدارسازي آن با استفاده از فيدبک حالت خطي،" مجله کنترل، جلد 3، شماره 1، صص. 46-37، بهار 1388.
[11] G. Perez and H. Cerdeira, "Extracting messages masked by chaos," Physical Review Letters, vol. 74, no. 1, pp.1970-1973, Mar. 1995.
[12] L. Pecora, "Hyperchaos harnessed," Physics World, vol. 9, no. 1, pp. 17-18, May. 1996.
[13] A. Genys, A. Tamasevicius, and A. Bazailiauskas, "Hyperchaos in coupled colpitts oscillators," Chaos, Solitons, and Fractals, vol. 17, no. 2, pp. 349-353, Jul. 2003.
[14] S. Cincotti and S. Stefano, "Complex dynamical behaviors in two non - linearly coupled chua's circuits," Chaos, Solitons, and Fractals, vol. 21, no. 3, pp. 633-641, Jul. 2004.
[15] J. P. Goedgebuer, L. Larger, and H. Porle, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Physical Review Letters, vol. 80, no. 10, pp. 2249-2252, Mar. 1998.
[16] J. A. Laoye, U. E. Vincent, and S. O. Kareem, "Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller," Chaos, Solitons, and Fractals, vol. 39, no. 1, pp. 356-362, Jan. 2009.
[17] F. Q. Dou, J. A. Sun, W. S. Duan, and K. P. Lü, "Controlling hyperchaos in the new hyperchaotic system," Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 552-559, Feb. 2009.
[18] Y. Y. Hou, T. L. Liao, and J. J. Yan, "H∞ synchronization of chaotic systems using output feedback control design," Physica A: Statistical Mechanics and its Applications, vol. 379, no. 1, pp. 81-89, Jun. 2007.
[19] W. Jiang, G. G. Qiao, and D. Bin, "H∞ variable universe adaptive fuzzy control for chaotic system," Chaos, Solitons, and Fractals, vol. 24, no. 4, pp. 1075-1086, May 2005.
[20] H. Guo, S. Lin, and J. Liu, "A radial basis function sliding mode controller for chaotic Lorenz system," Physics Letters A, vol. 351, no. 4, pp. 257-261, Mar. 2006.
[21] H. T. Yau and C. L. Chen, "Chattering-free fuzzy sliding - mode control strategy for uncertain chaotic systems," Chaos, Solitons, and Fractals, vol. 30, no. 3, pp. 709-718, Nov. 2006.
[22] M. J. Jang, C. L. Chen, and C. K. Chen, "Sliding mode control of hyperchaos in Rössler systems," Chaos, Solitons, and Fractals, vol. 14, no. 9, pp. 1465-1476, Dec. 2002.
[23] T. Y. Chiang and M. L. Hung, "Sliding mode control for uncertain unified chaotic systems with input nonlinearity," Chaos, Solitons, and Fractals, vol. 34, no. 3, pp. 437-442, Oct. 2007.
[24] H. Wang, Z. Z. Han, Q. Y. Xie, and W. Zhang, "Sliding mode control for chaotic systems based on LMI," Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1410-1417, Apr. 2009.
[25] T. L. Liao, J. J. Yan, and Y. Y. Hou, "Robust chaos suppression for the family of nonlinear chaotic systems with noise perturbation," Nonlinear Analysis: Theory, Methods, and Applications, vol. 69, no. 1, pp. 14-23, Jul. 2008.
[26] S. Dadras, H. R. Momeni, and V. J. Majd, "Sliding mode control for uncertain new chaotic dynamical system," Chaos, Solitons, and Fractals, vol. 41, no. 4, pp. 1857-1862, Aug. 2009.
[27] J. J. Yan, "H∞ controlling hyperchaos of the Rössler system with input nonlinearity," Chaos, Solitons, and Fractals, vol. 21, no. 2, pp. 283-293, Jul. 2004.