Abstract
This paper proposes a new finite-time controller that realizes multi-switching synchronization of chaotic systems with bounded disturbances using the drive and response system synchronization arrangement. The finite-time controller derives the synchronization error to zero within a specified time. The proposed controller consists of three basic terms; each of them accomplishes a distinct objective: (1) stability of the control loop, (2) smooth and fast convergence behavior of the synchronization error, and (3) disturbance rejection. This study also devises a methodology for designing the finite-time controller and describes a general approach that furnishes a systematic procedure for the analysis of the closed loop. The smooth behavior terminology introduced in (2) refers to the over-damped convergence of the synchronization error signals to zero and the synthesis of chattering-free control effort. The analysis, which assures the global stability of the closed loop, uses the second stability theorem of the Lyapunov, while the finite-time stability technique determines the finite-time convergence. This paper includes simulations of two numerical examples for the validation of the theoretical findings and discusses the comparative analysis. The proposed methodology is suitable to design controllers for a wide range of hyper(chaotic) systems. The contributions of the paper are: (1) describe an innovative generalize analytical methodology for the multi-switching combination synchronization of chaotic systems and (2) propose a novel controller design that insures the finite-time synchronization.
Similar content being viewed by others
References
Eroglu, D.; Lamb, J.S.W.; Pereira, T.: Synchronization of chaos and its applications. Contemp. Phys. 58(3), 207–243 (2017)
Qiu, J.; Sun, K.; Wang, T.; Gao, H.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzz. Syst. 27(11), 2152–2162 (2019)
Qiu, J.; Sun, K.; Rudas, I.J.; Gao, H.: Command filter-based adaptive NN control for mimo nonlinear systems with full-state constraints and actuator hysteresis. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2944761
Hu, D.; Hu, L.; Yan, Y.: Optimization methodology for control strategy of parallel hybrid electric vehicle based on chaos prediction. AIP Adv. 8, 115305 (2018). https://doi.org/10.1063/1.5055644
Sun, K.; Mou, S.; Qiu, J.; et al.: Adaptive fuzzy control for nontriangular structural stochastic switched nonlinear systems with full constraints. IEEE Trans. Fuzz. Syst. 27(8), 1587–1601 (2019)
Pecora, L.; Carroll, T.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)
He, G.; Fang, J.A.; Li, Z.; Wang, X.: Synchronization of coupled neural networks with time-varying delays. Arab. J. Sci. Eng. 40(12), 3759–3773 (2015)
Kheiri, H.; Naderi, B.: Dynamical behavior and synchronization of chaotic chemical reactors model. Iran. J. Math. Chem. 6(1), 81–92 (2015)
Kocamaz, U.E.; Cicek, S.; Uyaroglu, Y.: Secure communication with chaos and electronic circuit design using passivity based synchronization. J. Circ. Syst. Comput. 27(4), 1850057 (2018)
Lu, L.; Zhang, F.; Han, C.: Synchronization transmission of the target signal in the circuit network based on coupling technique. Physics A 535, 122412 (2019)
Khan, A.; Kumar, S.: Measuring chaos and synchronization of chaotic satellite systems using sliding mode control. Optim. Control Appl. Method 39(5), 1–13 (2018)
Liu, L.; Xie, G.; Li, R.: Synchronization stability analysis of medical cyber-physical cloud system considering multi-closed-loops. J. Circ. Syst. Comput. 28(12), 1950198 (2019)
Lu, L.; Wei, Q.: Parameter estimation and synchronization in the uncertain financial network. Physics A 535, 122418 (2019)
Cicek, E.; Dasdemir, J.: Output feedback synchronization of multiple robot systems under parametric uncertainties. Tran. Inst. Meas. Control 39(3), 277–287 (2017)
Aghababa, M.P.; Aghababa, H.P.: A novel finite-time sliding mode controller for synchronization of chaotic systems with input nonlinearity. Arab. J. Sci. Eng. 38(11), 3221–3232 (2013)
Yang, C.C.: Adaptive single input control for synchronization of a 4D Lorenz-Stenflo chaotic system. Arab. J. Arab. J. Sci. Eng. 39(3), 2413–2426 (2014)
Al-Azzawi, S.F.; Aziz, M.M.: Chaos synchronization of nonlinear dynamical systems via a novel analytical approach. Alex. Eng. J. 57(4), 3493–3500 (2018)
Ahmad, I.; Saaban, A.; Ibrahim, A.; Shahzad, M.; Naveed, N.: The synchronization of chaotic systems with different dimensions by a robust generalized active control. Optik 127(11), 4859–4871 (2016)
Chen, X.; Cao, J.; Park, J.; Huang, T.; Zong, G.; Qiu, J.: Finite-time complex function synchronization of multiple complex variable chaotic systems with network transmission and combination mode. J. Vib. Control 24(22), 1–11 (2018)
Li, D.; Cao, J.: Global finite-time output feedback synchronization for a class of high-order nonlinear systems. Nonlinear Dyn. 22(1–2), 1027–1037 (2015)
Yang, X.; Lu, J.: Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans. Auto Control 61(8), 2256–2261 (2016)
Bao, H.; Cao, J.: Finite-time generalized synchronization of non-identical delayed chaotic systems. Nonlinear Anal. Model. Control 21(3), 306–324 (2016)
Yang, X.; Song, X.; Liang, J.; He, H.: Finite-time synchronization of coupled discontinuous neural networks with mixed delays and non-identical perturbations. J. Franklin Inst. 352(10), 4382–4406 (2015)
Xi, X.; Mobayen, S.; Ren, H.; Jafari, S.: Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control. J. Vib. Control 24(7), 1–13 (2018)
Li, S.; Tian, Y.-P.: Finite time synchronization of chaotic systems. Chaos Solit. Fract. 15(2), 303–3110 (2003)
Wang, H.; Han, Z.; Xie, X.; Zhang, W.: Finite-time chaos synchronization of unified chaotic system with uncertain parameters. Commun. Non. Sci. Numer. Simul. 14(5), 2239–2247 (2009)
Yang, W.; Xia, X.; Dong, Y.; Zheng, S.: Finite-time synchronization between two different chaotic systems with uncertain parameters. Comput. Inform. Sci. 3(3), 174–179 (2010)
Cai, N.; Li, W.; Jing, Y.; Feng, Z.: Finite-time generalized synchronization of chaotic systems with different order. Nonlinear Dyn. 64(4), 385–393 (2011)
Kim, D.; Gillespie, R.; Chang, P.: Simple, robust control and synchronization of the Lorenz system. Nonlinear Dyn. 73(1–2), 971–980 (2013)
Chen, Q.; Ren, X.; Na, J.: Robust finite-time chaos synchronization of uncertain permanent synchronous motors. ISA Trans. 21(3), 262–269 (2015)
Shi, L.; Yang, X.; Li, Y.; Feng, Z.: Finite-time synchronization of non-identical chaotic systems with multiple time-varying delays and bounded perturbations. Nonlinear Dyn. 83(1–2), 75–87 (2016)
Chen, X.; Cao, J.; Park, J.; Huang, T.; Qiu, J.: Finite-time multi-switching synchronization behavior for multiple chaotic systems with network transmission mode. J. Franklin Inst. 355(5), 2892–2911 (2018)
Zhang, W.; Li, C.; He, X.; Li, H.: Finite-time synchronization of complex networks with non-identical nodes and impulsive disturbances. Mod. Phys. Lett. B 32(1), 1850002 (2018)
Li, Q.; Guo, J.; Sun, C.; Wu, Y.; Ding, Z.: Finite-time synchronization for a class of dynamical complex networks with non-identical nodes and uncertain disturbances. J. Syst. Sci. Comput. 32(3), 818–834 (2018)
Khan, A.; Budhraja, M.; Ibrahim, A.: Synchronization among different switches of four non-identical chaotic systems via adaptive control. Arab. J. Sci. Eng. 44(3), 2717–2728 (2019)
Ahmad, I.; Shafiq, M.; Alsawalha, M.M.: Globally exponential multiswitching-combination synchronization control of chaotic systems for secure communications. Chin. J. Phys. 56(3), 974–987 (2018)
Vincent, U.E.; Saseyi, A.O.; McClintock, P.E.: Multi-switching combination synchronization of chaotic systems. Nonlinear Dyn. 82(1–2), 845–854 (2015)
Zheng, S.: Multi-switching combination synchronization of three different chaotic oscillators via nonlinear control. Optik 127(21), 10247–10258 (2016)
Khan, A.; Khattar, D.; Prajapati, N.: Dual combination-combination multi switching synchronization of eight chaotic systems. Chin. J. Phys. 55(4), 1209–1218 (2017)
Ahmad, I.; Shafiq, M.; Shahzad, K.: Global finite-time multi switching synchronization of externally perturbed chaotic oscillators. J. Circ. Syst. Signal Process. 37(12), 5253–5278 (2018)
Bhat, S.; Bernstein, D.: Finite time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)
Khalil, H.K.: Non-Linear Systems. Prentice-Hall, New Jersey (2002)
Sun, J.; Shen, Y.; Zhang, G.; Xu, C.; Cui, G.: Combination–combination synchronization among four identical or different chaotic systems. Nonlinear Dyn. 73(3), 1211–1222 (2013)
Shimizu, T.; Morioka, N.: On the bifurcation of a symmetric limit cycle to an asymmetric one in a simple model. Phys. Lett. A 76(3–4), 201–204 (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ahmad, I., Shafiq, M. A Generalized Analytical Approach for the Synchronization of Multiple Chaotic Systems in the Finite Time. Arab J Sci Eng 45, 2297–2315 (2020). https://doi.org/10.1007/s13369-019-04304-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-019-04304-9