共查询到18条相似文献,搜索用时 78 毫秒
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本文通过设计一个新型的含分数阶滑模面的滑模控制器,应用主动控制原理和滑模控制原理,实现了一个新分数阶超混沌系统和分数阶超混沌Chen系统的投影同步.应用Lyapunov理论,分数阶系统稳定理论和分数阶非线性系统性质定理对该控制器的存在性和稳定性分别进行了分析,并得到了异结构分数阶超混沌系统达到投影同步的稳定性判据.数值仿真采用分数阶超混沌Chen 系统和一个新分数阶超混沌系统的投影同步,仿真结果验证了方法的有效性.
关键词:
分数阶滑模面滑模控制器
稳定性分析
分数阶超混沌系统
投影同步 相似文献
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基于Lyapunov稳定性理论和分数阶系统稳定理论以 及分数阶非线性系统性质,提出了一种用来判定分数阶混沌系统是 否稳定的新的判定定理,并把该理论运用于对分数阶混沌系统的控制与 同步,同时给出了数学证明过程,严格保证了该方法的正确性与一般适用性. 运用所提出的稳定性定理,实现了异结构分数阶混沌系统的投影同步. 对分数阶Lorenz混沌系统与分数阶Liu混沌系统实现了投影同步; 针对四维超混沌分数阶系统,也实现了异结构投影同步. 该稳定性定理避 免了求解分数阶平衡点以及Lyapunov指数的问题,从而可以方便地选 择出控制律,并且所得的控制器结构简单、适用范围广. 数值仿真的结果取得了预期的效果,进一步验证了这一稳定性定理的 正确性及普遍适用性. 相似文献
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基于分数阶系统稳定性理论,提出了用状态观测器来实现分数阶混沌系统完全状态投影同步的思想. 设计的状态观测器能够实现一类非线性分数阶系统的完全状态投影同步而不要求分数阶混沌系统是部分线性的,推广了投影同步的应用范围,且无需计算系统的条件Lyapunov指数. 另外,该方法理论严格,设计简单,能够达到任意比例因子的完全状态同步. 最后,利用该方法实现了分数阶Rssler系统的完全状态投影同步,数值仿真结果证实了它的有效性.
关键词:
分数阶
混沌系统
状态观测器
投影同步 相似文献
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以超混沌Chen系统和超混沌Lorenz系统为例,研究了慢时变参数超混沌系统的反同步问题.首先利用主动控制的思想,消去超混沌系统中的非线性部分,然后基于Lyapunov稳定性理论,合理地选取参数自适应控制律,很好的解决了时变参数的参数摄动问题,从而实现了两个超混沌系统的反同步.在此基础之上,又进一步研究了分数阶超混沌系统,使用滑模控制方法对其进行控制,理论上分析了该方法的可行性.数值模拟实验进一步验证了所提出方法的有效性.
关键词:
超混沌
分数阶
自适应
滑模 相似文献
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Margarita Rivero Juan J. Trujillo M. Pilar Velasco 《Central European Journal of Physics》2013,11(10):1246-1254
The objective of this paper is to show an approach to the fractional version of the Sturm-Liouville problem, by using different fractional operators that return to the ordinary operator for integer order. For each fractional operator we study some of the basic properties of the Sturm-Liouville theory. We analyze a particular example that evidences the applicability of the fractional Sturm-Liouville theory. 相似文献
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Vijay K. Yadav Vijay K. Shukla Subir Das Mayank Srivastava 《Chinese Journal of Physics (Taipei)》2018,56(2):696-707
In this article, the stability analysis, chaos control and the function projective synchronization between fractional order identical satellite systems have been studied. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate and incommensurate fractional order systems are discussed. Feedback control method is used to control the chaos in the considered fractional order satellite system. Using the fractional calculus theory and computer simulation, it is found that the chaotic behavior exists in the fractional order satellite system and the lowest order of derivative where the chaos exits is 2.82. Adams-Bashforth-Moulton method is applied during numerical simulations and the results obtain are displayed through graphs. 相似文献
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This paper studies the stability of the fractional order
unified chaotic system. On the unstable equilibrium points, the
``equivalent passivity' method is used to design the nonlinear
controller. With the definition of fractional derivatives and
integrals, the Lyapunov function is constructed by which it is
proved that the controlled fractional order system is stable. With
Laplace transform theory, the equivalent integer order state
equation from the fractional order nonlinear system is obtained, and the
system output can be solved. The simulation results validate the
effectiveness of the theory. 相似文献
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Mayank Srivastava Saurabh K. Agrawal Subir Das 《Central European Journal of Physics》2013,11(10):1504-1513
The article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization. 相似文献
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Shao-Kai Luo Yun Dai Ming-Jing Yang Xiao-Tian Zhang 《International Journal of Theoretical Physics》2018,57(4):1024-1038
In this paper, we present a basic theory of fractional dynamics, i.e., the fractional conformal invariance of Mei symmetry, and find a new kind of conserved quantity led by fractional conformal invariance. For a dynamical system that can be transformed into fractional generalized Hamiltonian representation, we introduce a more general kind of single-parameter fractional infinitesimal transformation of Lie group, the definition and determining equation of fractional conformal invariance are given. And then, we reveal the fractional conformal invariance of Mei symmetry, and the necessary and sufficient condition whether the fractional conformal invariance would be the fractional Mei symmetry is found. In particular, we present the basic theory of fractional conformal invariance of Mei symmetry and it is found that, using the new approach, we can find a new kind of conserved quantity; as a special case, we find that an autonomous fractional generalized Hamiltonian system possesses more conserved quantities. Also, as the new method’s applications, we, respectively, find the conserved quantities of a fractional general relativistic Buchduhl model and a fractional Duffing oscillator led by fractional conformal invariance of Mei symmetry. 相似文献
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Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller 下载免费PDF全文
In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme. 相似文献