IJMNTA  Vol.5 No.4 , December 2016
Super-Twisting Control of the Duffing-Holmes Chaotic System
Abstract: In this paper, a super twisting controller (STC) is designed to control the chaotic behavior of the Duffing-Holmes system in stabilization and tracking cases. Due to lack of availability of the performance evaluation of STC in controlling Duffing-Holmes system, this paper aims to test the performance of STC in controlling Duffing-Holmes system. In order to achieve this control design, a modification of the conventional super twisting algorithm is adapted. Numerical simulations showed that the modified STC had high performance and ability to ensure robustness with respect to bounded external disturbances.
Cite this paper: Abu Khadra, F. (2016) Super-Twisting Control of the Duffing-Holmes Chaotic System. International Journal of Modern Nonlinear Theory and Application, 5, 160-170. doi: 10.4236/ijmnta.2016.54016.

[1]   Sharma, A., Patidar, V., Purohit, G. and Sud, K.K. (2012) Effects on the Bifurcation and Chaos in Forced Duffing Oscillator Due to Nonlinear Damping. Communications in Nonlinear Science and Numerical Simulation, 17, 2254-2269.

[2]   Kyriazis, M. (1991) Applications of Chaos Theory to the Molecular Biology of Aging. Experimental Gerontology, 26, 569-572.

[3]   Petrov, V., Gaspar, V., Masere, J. and Showalter, K. (1993) Controlling Chaos in the Belousov-Zhabotinsky Reaction. Nature, 361, 240-243.

[4]   Gaspard, P. (1999) Microscopic Chaos and Chemical Reactions. Physica A: Statistical Mechanics and Its Applications, 263, 315-328.

[5]   Mondal, S. and Mahanta, C. (2014) Adaptive Second Order Terminal Sliding Mode Controller for Robotic Manipulators. Journal of the Franklin Institute, 351, 2356-2377.

[6]   Volos, C.K., Kyprianidis, I.M. and Stouboulos, I.N. (2013) Experimental Investigation on Coverage Performance of a Chaotic Autonomous Mobile Robot. Robotics and Autonomous Systems, 61, 1314-1322.

[7]   Yuan, G., Zhang, X. and Wang, Z. (2014) Generation and Synchronization of Feedback-Induced Chaos in Semiconductor Ring Lasers by Injection-Locking. Optik-International Journal for Light and Electron Optics, 125, 1950-1953.

[8]   Li, N., Pan, W., Yan, L., Luo, B. and Zou, X. (2014) Enhanced Chaos Synchronization and Communication in Cascade-Coupled Semiconductor Ring Lasers. Communications in Nonlinear Science and Numerical Simulation, 19, 1874-1883.

[9]   Huang, X., Zhao, Z., Wang, Z. and Li, Y. (2012) Chaos and Hyperchaos in Fractional-Order Cellular Neural Networks. Neurocomputing, 94, 13-21.

[10]   Kaslik, E. and Sivasundaram, S. (2012) Nonlinear Dynamics and Chaos in Fractional-Order Neural Networks. Neural Networks, 32, 245-256.

[11]   Lian, S. and Chen, X. (2011) Traceable Content Protection Based on Chaos and Neural Networks. Applied Soft Computing, 11, 4293-4301.

[12]   Njah, A.N., Ojo, K.S., Adebayo, G.A. and Obawole, A.O. (2010) Generalized Control and Synchronization of Chaos in RCL-Shunted Josephson Junction Using Back Stepping Design. Physica C: Superconductivity, 470, 558-564.

[13]   Tu, J., He, H. and Xiong, P. (2014) Adaptive Backstepping Synchronization between Chaotic Systems with Unknown Lipschitz Constant. Applied Mathematics and Computation, 236, 10-18.

[14]   Vaidyanathan, S. (2012) Adaptive Backstepping Controller and Synchronizer Design for Arneodo Chaotic System with Unknown Parameters. International Journal of Computer Science and Information Technology, 4, 145-159.

[15]   Zhang, J., Li, C., Zhang, H. and Yu, J. (2004) Chaos Synchronization Using Single Variable Feed-Back Based on Backstepping Method. Chaos, Solitons & Fractals, 21, 1183-1193.

[16]   Vaidyanathan, S. (2012) Sliding Mode Control Based Global Chaos Control of Liu-Liu-Liu-Su Chaotic System. International Journal of Control Theory and Applications, 5, 15-20.

[17]   Lin, T.-C., Lee, T.-Y. and Balas, V.E. (2011) Adaptive Fuzzy Sliding Mode Control for Synchro-Nization of Uncertain Fractional Order Chaotic Systems. Chaos, Solitons & Fractals, 44, 791-801.

[18]   Roopaei, M. and Jahromi, M.Z. (2008) Synchronization of Two Different Chaotic Systems Using Novel Adaptive Fuzzy Sliding Mode Control. Chaos, 18, Article ID: 033133.

[19]   Utkin, V.I. (1992) Slides Modes in Control and Optimization. Springer, Berlin.

[20]   Sun, H., Li, S. and Sun, C. (2013) Finite Time Integral Sliding Mode Control of Hypersonic Vehicles. Nonlinear Dynamics, 73, 229-244.

[21]   Lu, K. and Xia, Y. (2013) Adaptive Attitude Tracking Control for Rigid Spacecraft with Finite-Time Convergence. Automatica, 49, 3591-3599.

[22]   Qiao, Z., et al. (2013) New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor. IEEE Transactions on Industrial Electronics, 60, 710-719.

[23]   Moradi, H., Saffar-Avval, M. and Bakhtiari-Nejad, F. (2012) Sliding Mode Control of Drum Water Level in an Industrial Boiler Unit with Time Varying Parameters: A Comparison with H∞-Robust Control Approach. Journal of Process Control, 22, 1844-1855.

[24]   Levant, A. and Levantovsky, L.V. (1993) Sliding Order and Sliding Accuracy in Sliding Mode Control. International Journal of Control, 58, 1247-1263.

[25]   Fridman, L. and Levant, A. (2002) Higher Order Sliding Modes. Sliding Mode Control in Engineering, 11, 53-102.

[26]   Moreno, J.A. and Osorio, M. (2012) Strict Lyapunov Functions for the Super-Twisting Algorithm. IEEE Transactions on Automatic Control, 57, 1035-1040.

[27]   Chen, G. and Yu, X. (Eds.) (2003) Chaos Control: Theory and Applications. Vol. 292, Springer, Berlin.

[28]   Defoort, M. and Djema?, M. (2012) A Lyapunov-Based Design of a Modified Super-Twisting Algorithm for the Heisenberg System. IMA Journal of Mathematical Control and Information, Online.