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Method for parameter identification of chaotic systems

A chaotic system and parameter identification technology, which is applied in the field of system identification and information security, can solve the problems of complex parameter control law and slow parameter convergence speed, and achieve the effect of simple identification method, fast parameter convergence speed, and improved parameter convergence rate

Active Publication Date: 2018-08-10
SHENYANG POLYTECHNIC UNIV
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Problems solved by technology

[0006] The purpose of the present invention is to overcome the chaotic parameter identification must meet the chaotic synchronization conditions, and the parameter control law is complex, the parameter convergence speed is slow, and to provide a chaotic parameter identification method without chaos synchronization, simple identification structure and fast convergence speed

Method used

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  • Method for parameter identification of chaotic systems
  • Method for parameter identification of chaotic systems
  • Method for parameter identification of chaotic systems

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Experimental program
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Embodiment

[0046] Example: Consider the following Lü chaotic system:

[0047]

[0048] In the formula, the parameters a and b are unknown, when a=1.5 and b=5, the trajectory of the system state variables is as follows figure 1 , figure 2 , image 3 and Figure 4 As shown, the time-domain waveform of the state variable is as Figure 5 , Figure 6 and Figure 7 As shown, it is known that the system state is chaotic at this time.

[0049] The specific implementation method is divided into the following steps:

[0050] Step 1: Consider the following system, Ax+Bf(x), x∈R n is the state vector, where R is a vector, A∈R n ×n is a known vector parameter, B∈R n is the unknown vector parameter,

[0051] Step 2: System parameter identification model transformation; Substituting the vector parameters into the system model, the chaotic system is obtained as formula (8);

[0052]

[0053] let z=a*x 3 , then there is Formula (8) can be arranged to get formula (9);

[0054]...

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Abstract

The invention provides a method for parameter identification of chaotic systems for a class of chaotic systems with unknown partial parameters. The method takes the driving response structure as the framework, adopts the objective function related to the synchronization error of some state variables, and uses the directional pattern search method to adaptively adjust an unknown parameter until theobjective function value reaches the minimum, that is, the estimation of the product of the unknown parameters is realized; and the amplitude ratios of the corresponding state variables of the driving and response systems are calculated, and the ratios and the estimated values of the product of the parameters are combined to estimate each parameter. Theoretical analysis and experimental simulations show that the proposed method can estimate the unknown parameters of the chaotic system well, the structure is simple, the convergence speed is fast, the error is small, and the method can be usedfor the decryption of chaotic secure communication.

Description

technical field [0001] The invention relates to the field of system identification and information security, in particular to an identification of some unknown parameters of a chaotic system. Background technique [0002] Due to its inherent properties such as sensitivity to initial conditions, aperiodicity, noise-like properties, and continuous wide spectrum, chaotic signals are highly unpredictable and naturally concealed, and are especially suitable as transmission carriers for secure communications. Because of the inherent property of chaotic signals, the control and synchronization of chaos has attracted more and more attention from researchers in recent years, and has been extensively studied. Most of the chaos control and applications are carried out when all the system parameters are known, but in practical applications, due to the complexity of the system or external interference, some parameters of the chaotic system are difficult to measure and determine, which is...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G05B13/04
CPCG05B13/042
Inventor 赵柏山张帆
Owner SHENYANG POLYTECHNIC UNIV
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