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An Adaptive Synchronization Method Based on Mittag-Leffler Stability

An adaptive and stable technology, applied in the direction of adaptive control, instrumentation, control/regulation system, etc., can solve the problems of lack of synchronous control methods, difficult to guarantee control accuracy, complex implementation process, etc., and achieve slow synchronous speed, strong general Adaptability, the realization of complex effects

Active Publication Date: 2022-07-29
ANSHUN UNIV
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Problems solved by technology

The implementation process of these two methods is complicated, the synchronization speed is slow, and the control accuracy is difficult to guarantee
For heterostructured fractional order chaotic systems with uncertain parameters, there is still a lack of a simple, fast and more universal synchronization control method

Method used

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  • An Adaptive Synchronization Method Based on Mittag-Leffler Stability
  • An Adaptive Synchronization Method Based on Mittag-Leffler Stability
  • An Adaptive Synchronization Method Based on Mittag-Leffler Stability

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Embodiment Construction

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] The adaptive synchronization method based on Mittag-Leffler stability of the present invention is specifically implemented according to the following steps:

[0058] Take the fractional order q=0.8, the system parameter a 1 =a 2 =1, then:

[0059] The adaptive synchronization method based on Mittag-Leffler stability is characterized in that, comprises the following steps:

[0060] Step (1) Description of adaptive synchronization chaotic problem.

[0061] The driving system is a fractional-order chaotic system with the following form:

[0062]

[0063] where x 1 , x 2 , x 3 and x 4 is a state variable, q is the fractional order, 0<q<1, and a is an unknown parameter.

[0064] The system (i) is numerically simulated by matlab software to verify that the system has chaotic behavior. The simulation algorithm adopts the pre...

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Abstract

The invention discloses an adaptive synchronization method based on Mittag-Leffler stability. The main steps are: (1) selecting two fractional-order chaotic systems with different structures and unknown parameters as the driving system and the response system; (2) using The state information of the chaotic drive system and the chaotic response system are different, and the fractional error system e is obtained 1 , e 2 , e 3 , e 4 ; (3) in fractional order error system e 1 , e 2 , e 3 , e 4 , respectively adding v 1 (t), v 2 (t), v 3 (t), v 4 (t) controller; (4) establish the adaptive law of estimated parameters, design v 1 (t), v 2 (t), v 3 (t), v 4 (t) Adaptive rate controller; (5) Construct the Lyapunov control function of the error system, and according to the Mittag-Leffler stability theory, determine the fractional-order error system e 1 , e 2 , e 3 , e 4 It is globally asymptotically stable and realizes the synchronization of two chaotic systems with unknown parameters. The invention solves the problem that the existing self-adaptive method for fractional-order chaotic system synchronization needs to find inequality substitution or construct complex sliding mode surface to realize synchronization control.

Description

technical field [0001] The invention relates to an adaptive synchronization method based on Mittag-Leffler stability, and belongs to the technical field of automatic control methods. Background technique [0002] It is found that fractional-order chaotic systems have higher nonlinear characteristics and extended power spectral density than integer-order chaotic systems, so they have broad application prospects in related scientific fields such as secure communication. Chaos synchronization control method is a key technology. [0003] The existing chaotic adaptive synchronization methods are mainly aimed at integer-order chaotic systems. The main reason is that the fractional-order synchronization error system is of fractional order, and the constructed Lyapunov function also needs to rely on complex fractional-order sliding mode control surfaces. "Adaptive sliding mode synchronization for a class of fractional-orderchaotic systems with disturbance" and the literature "Adapti...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G05B13/02
CPCG05B13/024
Inventor 刘立才杜传红陈美玉窦忠宇
Owner ANSHUN UNIV
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