Chaos total state hybrid projection synchronization method based on active integral sliding mode

An integral sliding mode and full-state technology, which is applied in the direction of instruments, adaptive control, control/regulation systems, etc., can solve the problem that the synchronization error cannot converge to zero, and achieve weakened chattering, fast speed, and good robustness Effect

Inactive Publication Date: 2019-05-24
NORTHEASTERN UNIV
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  • Application Information

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Problems solved by technology

Active control methods are only suitable for chaotic systems with precise mathematical models. When there are modeling uncertainties and external interference signals in the response system, the synchronization error cannot converge to zero

Method used

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  • Chaos total state hybrid projection synchronization method based on active integral sliding mode
  • Chaos total state hybrid projection synchronization method based on active integral sliding mode
  • Chaos total state hybrid projection synchronization method based on active integral sliding mode

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specific Embodiment 1

[0090] Taking the 2-dimensional chaotic system as an example, the driving system is a Duffing chaotic system, and the response system is a van der Pol chaotic system with modeling uncertainties and external interference signals.

[0091] Step 1: The driving system is a Duffing chaotic system, and the response system is a van der Pol chaotic system with modeling uncertainties and external interference signals. According to the driving system and response system, a full-state hybrid projection synchronization error system is established.

[0092] The driving system is a 2-dimensional Duffing chaotic system, and the state equation is expressed as:

[0093]

[0094] where x 1 and x 2 is the state variable of the Duffing chaotic system, x=[x 1 ,x 2 ] T , t is time, f 1 (x, t) and f 2 (x,t) is a continuous function.

[0095] The response system is a 2-dimensional van der Pol chaotic system with modeling uncertainties and external disturbance signals, and the state equation...

specific Embodiment 2

[0123] Taking the 3D chaotic system as an example, the full-state hybrid projection synchronization control is carried out. The driving system is Chen chaos, and the response system is Lorenz chaos with modeling uncertainties and external disturbance signals.

[0124] Step 1: The driving system is a 3-dimensional Chen chaos, and the response system is a 3-dimensional Lorenz chaos with modeling uncertainties and external interference signals. According to the driving system and the response system, a full-state hybrid projection synchronization error system is established.

[0125] The driving system is a 3-dimensional Chen chaos, and the state equation is expressed as

[0126]

[0127] where x 1 , x 2 and x 3 is the state variable of Chen’s chaotic system, x=[x 1 ,x 2 ,x 3 ] T , t is time, f 1 (x,t), f 2 (x, t) and f 3 (x, t) is a continuous function.

[0128] The response system is Lorenz chaos with modeling uncertainties and external disturbance signals, and th...

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Abstract

The invention belongs to the technical field of chaotic trajectory tracking, particularly relates to a chaos total state hybrid projection synchronization method based on an active integral sliding mode. The method includes the steps: S1 building a total state hybrid projection synchronization error system equation according to a driving system equation and response system equation; S2 combining an active control method and an integral sliding mode control method to build an active integral sliding mode controller equation, and synchronously controlling the total state hybrid projection synchronization error system equation by active integral sliding mode controller equation. A driving system is an n-dimensional system, and a response system is an n-dimensional chaotic system with modelinguncertainty and external interference signals. According to the hybrid projection synchronization method, total state hybrid projection synchronization control of the driving system and the responsesystem can be achieved, a closed loop system is formed, and a total state hybrid projection synchronization error is gradually converged into zero.

Description

technical field [0001] The invention belongs to the technical field of chaotic trajectory, and in particular relates to a chaotic full-state hybrid projection synchronization method based on an active integral sliding mode. Background technique [0002] Chaos is extremely sensitive to initial conditions and is a ubiquitous phenomenon in nonlinear systems, widely existing in nature and human society. The key to the study of chaos theory lies in the control and utilization of the chaotic system. Chaos theory has very wide application value in many fields. The active control method has the advantages of simple design and fast convergence in the chaotic synchronization control. Active control methods are only suitable for chaotic systems with precise mathematical models. When there are modeling uncertainties and external disturbance signals in the response system, the synchronization error cannot converge to zero. In practical applications, the modeling uncertainty of the res...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G05B13/04
Inventor 赵海滨刘冲陆志国
Owner NORTHEASTERN UNIV
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