Global finite-time synchronization of different dimensional chaotic systems. (English) Zbl 1480.34072
Summary: This paper addresses the problem of global finite-time synchronization of two different dimensional chaotic systems. Firstly, the definition of global finite-time synchronization of different dimensional chaotic systems are introduced. Based on the finite-time stability methods, the controller is designed such that the chaotic systems are globally synchronized in a finite time. Then, some uncertain parameters are adopted in the chaotic systems, new control law and dynamical parameter estimation are proposed to guarantee that the global finite-time synchronization can be obtained. By considering a dynamical parameter designed in the controller, the adaptive updated controller is also designed to achieve the desired results. At last, the results of two different dimensional chaotic systems are also extended to two different dimensional networked chaotic systems. Finally, three numerical examples are given to verify the validity of the proposed methods.
MSC:
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 93A14 | Decentralized systems |
| 93C40 | Adaptive control/observation systems |
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