Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller
This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/452549 |
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| _version_ | 1832548816373415936 |
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| author | Zengyun Wang Lihong Huang Xuxin Yang Dingyang Lu |
| author_facet | Zengyun Wang Lihong Huang Xuxin Yang Dingyang Lu |
| author_sort | Zengyun Wang |
| collection | DOAJ |
| description | This paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu) in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller. |
| format | Article |
| id | doaj-art-56d5b5bce0c247e0a985169886ab1b73 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-56d5b5bce0c247e0a985169886ab1b732025-02-03T06:12:55ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/452549452549Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode ControllerZengyun Wang0Lihong Huang1Xuxin Yang2Dingyang Lu3Department of Mathematics, Hunan First Normal University, Changsha 410205, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaDepartment of Mathematics, Hunan First Normal University, Changsha 410205, ChinaDepartment of Mathematics, Hunan First Normal University, Changsha 410205, ChinaThis paper investigates the problem of synchronization for two different stochastic chaotic systems with unknown parameters and uncertain terms. The main work of this paper consists of the following aspects. Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. Secondly, we design an adaptive sliding mode controller to realize the asymptotical synchronization in mean squares. Thirdly, we design an adaptive sliding mode controller to realize the almost surely synchronization. Finally, the designed adaptive sliding mode controllers are used to achieve synchronization between two pairs of different stochastic chaos systems (Lorenz-Chen and Chen-Lu) in the presence of the uncertainties and unknown parameters. Numerical simulations are given to demonstrate the robustness and efficiency of the proposed robust adaptive sliding mode controller.http://dx.doi.org/10.1155/2013/452549 |
| spellingShingle | Zengyun Wang Lihong Huang Xuxin Yang Dingyang Lu Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller Abstract and Applied Analysis |
| title | Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller |
| title_full | Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller |
| title_fullStr | Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller |
| title_full_unstemmed | Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller |
| title_short | Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller |
| title_sort | adaptive synchronization for two different stochastic chaotic systems with unknown parameters via a sliding mode controller |
| url | http://dx.doi.org/10.1155/2013/452549 |
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