Second-order chaotic projection synchronization method based on non-singular terminal sliding mode controller
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A non-singular terminal and controller technology, applied in synchronization devices, secure communication through chaotic signals, digital transmission systems, etc., can solve the problems of slow approach speed and no automatic adjustment.
Active Publication Date: 2018-11-16
NORTHEASTERN UNIV
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The parameters in the existing exponential reaching law are fixed, the
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specific Embodiment 1
[0062] The drive system and the response system are isomorphic systems, both of which are Duffing-Holmes chaotic systems. The state equation of the Duffing-Holmes chaotic system is
[0063]
[0064] in, When the parameter selection is a1=-1, a=0.25, b=0.3, ω=1.0, the system is in a chaotic state. Formula (1) is the driving system. The initial state of the drive system is set to x 1 (0)=-1,x 2 (0)=1
[0065] The controlled system with modeling uncertainties and external disturbance signals is expressed as
[0066]
[0067] in, The modeling uncertainty Δf(y) is set to Δf(y)=0.5y 1 , the external interference signal d(t) is set as d(t)=0.5sin(5t), and μ=b can be obtained 0 +b 1 |y 1 |, where b 0 =0.5,b 1 = 0.5. Formula (2) with modeling uncertainties and external disturbance signals is taken as the response system. The initial state of the response system is set to y 1 (0)=1.5,y 2 (0)=1.5.
[0068] The projection synchronization error system is formula (4...
specific Embodiment 2
[0078] Drive system and response system are heterogeneous systems. The driving system is a Duffing-Holmes chaotic system, and the response system is a van der Pol chaotic system. The state equation of the Duffing-Holmes chaotic system is
[0079]
[0080] in, When the parameter is selected as a 1 =-1, a=0.25, b=0.3, ω=1.0, the system is in a chaotic state. Formula (1) is used as the driving system. The initial state of the drive system is set to x 1 (0)=2,x 2 (0)=-2.
[0081] The state equation of the van der Pol chaotic system is
[0082]
[0083] Among them, f y (y,t)=-y 1 +B(1-y 1 2 )y 2 +Asin(ω 2 t). When the parameter selection is B=3, A=5, ω 2 =1.788, the system is in a chaotic state. The controlled system with modeling uncertainties and external disturbance signals is expressed as
[0084]
[0085] Among them, the modeling uncertainty Δf(y) is set to Δf(y)=0.8y 2 , the external interference signal d(t) is set as d(t)=0.7sin(3t), and μ=b can b...
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Abstract
The invention provides a second-order chaotic projection synchronization method based on a non-singular terminal sliding mode controller. The method includes the following steps: step 1, establishinga projection synchronization error system according to a state equation of a driving system and a response system; step 2, designing a nonlinear sliding mode surface and an adaptive exponential approach law; and step 3, designing a non-singular terminal sliding mode controller to control the projection synchronization error system, and forming a closed-loop control system, wherein the closed-loopcontrol system realizes the projection synchronization between the driving system and the response system. The adaptive exponential approach law is proposed, automatic adjustment can be performed according to errors, the convergence speed of the errors can be increased, and the approach rate can be accelerated; the nonlinear sliding mode surface is applied to the second-order chaotic projection synchronization, and the nonlinear sliding mode surface has a faster approach speed than a linear sliding mode surface, can converge in a finite time, can overcome singular problems, and can ensure theisomorphic or heterogeneous second-order chaotic projection synchronization in different initial states in the case of modeling uncertainty and external interference signals.
Description
technical field [0001] The invention belongs to the technical field of automatic control, and in particular relates to a second-order chaos projection synchronization method based on a non-singular terminal sliding mode controller. Background technique [0002] Chaotic system is a nonlinear dynamical system, which has the characteristics of overall stability and local instability, and exists widely in nature and human society. Chaotic systems are very sensitive to initial parameters, and have broad application prospects and important application values in secure communication and weak signal detection. Since Mainieri and Rehacek proposed the concept of projective synchronization, different types of chaotic synchronization phenomena have been unified. [0003] Sliding mode control has the advantages of simple algorithm, good robustness and high reliability to external disturbances, and is often used in the synchronization and control of chaotic systems. Because the tradit...
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