This paper presents the synchronization between the master and slave Lorenz chaotic systems by slide mode controller (SMC)-based technique. A proportional-integral (PI) switching surface is proposed to simplify the task of assigning the performance of the closed-loop error system in sliding mode. Then, extending the concept of equivalent control and using some basic electronic components, a secure communication system is constructed. Experimental results show the feasibility of synchronizing two Lorenz circuits via the proposed SMC.
Pecora, L.M.; Carroll, T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 1990, 64, 821–824.
[3]
Huang, C.K.; Tsay, S.C.; Wu, Y.R. Implementation of chaotic secure communication systems based on OPA circuits. Chaos Solitons Fractals 2005, 23, 589–600.
[4]
Alvarez, G.; Hernández, L.; Mu?oz, J.; Montoya, F.; Li, S.J. Security analysis of communication system based on the synchronization of different order chaotic systems. Phys. Lett. A. 2005, 345, 245–250.
[5]
Yau, H.T.; Kuo, C.L.; Yan, J.J. Fuzzy sliding mode control for a class of chaos synchronization with uncertainties. Int. J. Nonlin. Sci. Num. Simul. 2006, 7, 333–338.
[6]
Martinez-Guerra, R.; Yu, W. Chaotic synchronization and secure communication via sliding-mode observer. Int. J. Bifurcat. Chaos. 2008, 18, 235–243.
[7]
Hu, M.; Xu, Z. Adaptive feedback controller for projective synchronization. Nonlin. Anal. Real World Appl. 2008, 9, 1253–1260.
[8]
Liao, T.L.; Tsai, S.H. Adaptive synchronization of chaotic systems and its application to secure communications. Chaos Solitons Fractals 2000, 11, 1387–1396.
[9]
Li, Z.; Li, K.; Wen, C.; Soh, Y.C. A new chaotic secure communication system. IEEE Trans. Commun. 2003, 51, 1306–1312.
[10]
Li, Z.; Xu, D. A secure communication scheme using projective chaos synchronization. Chaos Solitons Fractals 2004, 477–481.
Zhou, J.; Huang, H.B.; Qi, G.X.; Yang, P.; Xie, X. Communication with spatial periodic chaos synchronization. Phys. Lett. A. 2005, 335, 191–196.
[13]
Wen, G.; Wang, Q.G.; Lin, C.; Han, X.; Li, G. Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays. Chaos Solitons Fractals 2006, 29, 1142–1146.
[14]
Hou, Y.Y.; Liau, B.Y.; Chen, H.C. Synchronization of unified chaotic systems using sliding mode controller. Math. Probl. Eng. 2012, doi:10.1155/2012/632712.
[15]
Tan, C.P.; Edwards, C. Sliding mode observers for detection and reconstruction of sensor faults. Automatica 2002, 38, 1815–1821.
[16]
Edwards, C.; Spurgeon, S.K.; Patton, R.J. Sliding mode observers for fault detection and isolation. Automatica 2000, 36, 541–548.