Design of the linear controller of a class of time-delay chaos
Chaos control has become one of the hottest issues in the current control field. According to the nonlinear dynamic characteristics of chaotic system and the stability principle of delay system, this paper discusses the control and synchronization of the time-delay chaotic system. It intends to research the time-delay chaotic system with a new method and design a feasible linear controller to realize the time-delay chaos control and synchronization of the Lorenz system. At the same time, this algorithm can not only control the chaotic system with the unknown time delays effectively, but also be extended to a class of time-delay chaos with different time delays. Finally, the numerical simulation results verify the effectiveness of the proposed control algorithm.
KeywordsThe Lorenz system Chaos synchronization Lyapunov–Razumikhin function Time delay Linear controller
This research is supported by the National Nature Science Foundation of China (No. 61603211), and Zhejiang Province Basic Public Welfare Research Project (LGG18E050003).
- 3.Science, C.S.B.Z.Y.C.X.M.L.C.J.S.S.o.M., Physics, P., University, X.: Xiangtan: construction of grid multi-scroll chaotic attractors and its circuit implementation with polynomial and step function. Acta Physica Sinica 60(2), 020149–020507 (2011)Google Scholar
- 4.Lin, Z., Guyeux, C., Yu, S., Wang, Q., Cai, S.: On the use of chaotic iterations to design keyed hash function. Cluster Comput. (2), 1–15 (2017)Google Scholar
- 5.Gupta, B.B.: [CFP] Special issue on recent advances in computational intelligence paradigms for privacy preserving security for clouds services. Cluster Comput. (2016)Google Scholar
- 6.Guo, Y.K., Wang, Z.H.: Synchronization of unified chaotic system based on 3 d improve the algorithm of color image encryption algorithm. Autom. Instrum. (2014)Google Scholar
- 9.SolÍsdaun, J.: Global CLF stabilization of systems with point-dissipative free dynamics via admissible controls: chaos control of a Chua’s system. Int. J. Bifurc. Chaos 23(11) (2013)Google Scholar
- 10.Gao, K.: A synchronization controller for the unified chaotic system and its application in secure communication. In: International Conference on Consumer Electronics, Communications and Networks 2011, pp. 4700–4703Google Scholar
- 11.Jin, X.U., Yan, J.I., Cui, B.T.: Synchronization and anti-synchronization of time-delay chaotic system and its application to secure communication. J. Comput. Appl. 30(9), 2413–2416 (2010)Google Scholar
- 15.An-Shan, L.U., Yi-Min, L.U.: The study on a new modified liu chaotic system analysis and circuit experiments study. J. Jiangxi Normal Univ. (2014)Google Scholar
- 16.Sun, K.H.: Circuit design and implementation of Lorenz chaotic system with one parameter. Acta Phys. Sin. 59(12), 527–533 (2010)Google Scholar