Naseh M.R., Haeri M., “An Adaptive Approach to Synchronization of Two Chua's Circuits”, Proceedings of World Academy of Science, Engineering and Technology, 2005, 134–137 и телемех., 2005, № 3, 105–112 A. A. Ashimov, As. A. Ashimov, Yu. V. Borovskii, O. P. Volobueva, “Effective parametric control laws for market economy mechanisms”, Autom. Recently, a fractional-order vector controller is addressed to stabilize the unstable equilibriu.This publication is cited in the following articles: It is possible that traditional controller (integer-order controller) will be replaced by fractional-order controller in the future. Compared to the traditional controller (integer-order controller), the fractional-order controller has many advantages, such as less sensitivity to parameter variations and better disturbance rejection ratios. Moreover, control and synchronization of fractional-order chaotic systems have attracted much attention in the recent years. Many fractional-order chaotic systems have been presented, the fractional-order Chua’s chaotic circuit, the fractional-order Duffing chaotic system, the fractionalorder memristor-based chaotic system, the fractionalorder Lorenz chaotic system, the fractional-order Chen chaotic system, and so forth.
On the other hand, the chaotic or hyperchaos behaviors have been found in many fractional-order dynamical systems. ion among scientists in various fields.Many control schemes have been presented, such as feedback control, parametric perturbation control, adaptive control, and fuzzy control. (2016) Chaos in a Fractional-Order Single-Machine Infini.
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So far, almost all the studies of dynamics of power systems are concerned How to cite this paper: Liang, Z.H. Chaos causes electromechanical oscillations to behave randomly, which are harmful to the secure and stable operation of power systems, and even produce undesired negative consequences, such as angle divergence, voltage collapse and system splitting. Chaotic phenomena have been observed in power systems during the past few decades. Many chaotic systems, such as Lorenz system, Chua’s system, Duffing system, Rössler system, Chen system and so on, still remain chaotic when their equations become fractional. Fractional calculus provides a good instrument to describe the memory, hereditary, non-locality and self-similarity properties of various materials and processes. Introduction As a mathematical branch with a history of over 300 years, fractional calculus and its applications to physics and engineering have attracted increasing attentions in recent years. Keywords Power System, Fractional Calculus, Chaos, Backstepping Method 1. the validity of the proposed controller.