CN106709564A - Neuron system parameter estimation technique - Google Patents

Abstract

The invention discloses a neuron system parameter estimation technique. For a class of biological neuron system, the model transformation of its general formula is obtained to obtain a standard form suitable for parameter estimation of the recursive least squares algorithm. By collecting input and output data, the information required by the recursive least squares algorithm is constructed, and finally estimated online System parameters. The inventive technology has the advantages of online estimation and simple realization, and can be used as an important means for estimating the parameters of general biological neuron systems.

Description

A Parameter Estimation Technique for Neuron System

Background technique

At present, most of the control theory studies on biological neuron systems are based on the fact that the system model parameters are known, but in practice, the system model parameters are often not necessarily known accurately, so the parameter estimation of neuron systems has become one of the important research topics. one. The least squares algorithm is an important means of parameter estimation. So far, scholars at home and abroad have proposed and developed many least squares algorithms for different needs or applications. Among them, the recursive least squares algorithm is simple because of its analysis, Easy to implement and widely used.

Studies have shown that by setting the relevant parameters of the biological neuron system, the system will show a chaotic state, and the chaotic phenomenon has potential application value in the fields of chemistry, information science, secure communication, etc., so the parameter estimation of the chaotic biological neuron system is studied is of great significance. So far, although there are some parameter estimation methods for chaotic biological neuron systems, such as adaptive synchronization algorithms, these algorithms are complex, computationally intensive, and need to use synchronous control to estimate parameters, which has certain limitations. The invention will provide a simple and convenient neuron system parameter estimation technique that can be estimated online.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the existing neuron system parameter estimation algorithm, such as complex structure and large amount of calculation, and to propose a new type of neuron system parameter estimation technology by using the recursive least squares method, which can be identified online and realizes the advantages of simplicity and convenience. .

The technical solution adopted in the present invention comprises the following steps:

Step 1: Model transformation. A general biological neuron system can be described as:

Among them, x=[x ₁ (t), ..., x _n (t)] ^T is the state variable of the system; k _i (i=1, 2, ..., n) is the given input of the system; h _i (x) (i=1,2,...,n) is the nonlinear function of the i-th neuron system; p _ij (i=1,2,...,n,j=1,2,...,n) is the i-th neuron system The connection weight coefficient between the neuron and the _jth neuron; The activation function between neurons; ω _i (t) (i=1, 2,..., n) is the external noise of the i-th neuron.

Transform the above biological neuron system into the following estimated standard form:

in,

θ＝[p ₁₁ p ₁₂ ... p _1n p ₂₁ p ₂₂ ... p _2n ... p _n1 p _n2 ... p _nn ] ^T

Step 2: Parameter estimation. To estimate the parameter vector θ, the following recursive least squares algorithm is used:

(a) Parameter initialization. Let the parameter estimates be Take the maximum number of iterations as t _max , t=0, and estimate the initial parameters as The covariance matrix is P(0)=10 ⁶ I, where 1=[11...1] ^T , and I is the identity matrix.

(b) Collect data and construct output sequence Y(t) and measurable information

(c) Calculate the gain vector L(t) and covariance matrix P(t) according to the following formula:

(d) Update parameter estimates

(e) Let t:=t+1, if t<t _max , go to step (b) and continue the recursive calculation; otherwise, go to step 3.

Step 3: Stop the calculation and get the final estimated parameter values

Compared with the existing estimation algorithm, the present invention has the following advantages:

1. The present invention can estimate parameters online, and the realization is simple and convenient;

2. Under the interference of random noise, the neuron system parameters can still be accurately estimated;

3. Parameter estimates can quickly converge to real parameter values.

Description of drawings

Fig. 1 is a technical flowchart of parameter estimation based on the solution of the present invention.

Fig. 2 is a curve diagram of the iterative process of parameter estimation based on the solution of the present invention in the embodiment.

detailed description

In order to better understand the technical solution of the present invention, the implementation manner will be further described in detail below, and an application example will be used to illustrate the specific implementation manner, but not limited thereto.

Embodiment: Hindmarsh-Rose neuron system is a kind of important biological neuron system, and its mathematical model equation is as follows:

Wherein, x ₁ , x ₂ , x ₃ are state variables; a, b, d, r are system parameters; I is the external stimulation current of the neuron, and I=4 is taken in this embodiment; ω _i (t) (i=1, 2, 3) is a white noise sequence with zero mean and variance of 0.01. When the Hindmarsh-Rose neuron system parameters are selected as a=1, b=3, d=5, r=0.006, the system appears chaotic state. The purpose of this example is to identify the 4 parameters a, b, d, r of the system.

The technical workflow of the present invention is as shown in Figure 1, and the specific implementation method can be divided into the following steps:

Step 1: Model transformation. Transform the Hindmarsh-Rose neuron model into the following standard form:

where, θ=[abdr] ^T ,

Step 2: Parameter estimation. To estimate the parameter vector θ, the following recursive least squares algorithm is used:

(a) Parameter initialization. Let the parameter estimates be Take the maximum number of iterations as t _max =200, t=0, and estimate the initial parameters as The covariance matrix is P(0)=10 ⁶ I, where 1=[1 1 1 1] ^T , and I is the identity matrix.

(b) Collect data (here the fourth-order Runge-Kutta method is used to solve the neuron system equation), construct the output sequence Y(t) and the amount of measurable information

(c) Calculate the gain vector L(t) and covariance matrix P(t) according to the following formula:

(d) Update parameter estimates

(e) Let t:=t+1, if t<t _max , go to step (b) and continue the recursive calculation; otherwise, go to step 3.

Step 3: Stop the calculation and get the final estimated parameter values

Figure 2 shows the parameter estimation iterative process curves. It can be seen from the figure that after about 100 iterations, all parameter estimates converge to the true values approximately.

Claims (1)

1. A neuron system parameter estimation technology is characterized by comprising the following steps:

step 1: and (5) model transformation. A general biological neuronal system can be described as:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1\left(t\right)=h_1\left(x\right)+\underset{j=1}{\overset{m}{\&Sigma;}}{p}_{1j}{s}_{1j}\left(x\right)+k_1+{\mathrm{\&omega;}}_1\left(t\right)\\ {\stackrel{\&CenterDot;}{x}}_2\left(t\right)=h_2\left(x\right)+\underset{j=1}{\overset{m}{\&Sigma;}}{p}_{2j}{s}_{2j}\left(x\right)+k_2+{\mathrm{\&omega;}}_2\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\stackrel{\&CenterDot;}{x}}_n\left(t\right)=h_n\left(x\right)+\underset{j=1}{\overset{m}{\&Sigma;}}{p}_{nj}{s}_{nj}\left(x\right)+k_n+{\mathrm{\&omega;}}_n\left(t\right)\end{array}\right.---\left(1\right)$

wherein x is [ x ]₁(t)，…，x_n(t)]^TIs a state variable of the system; k is a radical of_i(i ═ 1, 2, …, n) gives the system inputs; h is_i(x) (i ═ 1, 2, …, n) is a nonlinear function of the ith neuronal system; p is a radical of_ij(i ═ 1, 2, …, n, j ═ 1, 2, …, n) is the connection weight coefficient between the ith neuron and the jth neuron; s_ij(x) (i-1, 2, …, n, j-1, 2, …, n) is the activation function between the ith and jth neurons；ω_i(t) (i ═ 1, 2, …, n) is the external noise of the ith neuron.

The above biological neuron system (1) was converted into the following estimation standard form:

wherein,

θ＝[p₁₁p₁₂… p_1np₂₁p₂₂… p_2n… p_n1p_n2… p_nn]^T

step 2: and (6) parameter estimation. To estimate the parameter vector θ, the following recursive least squares algorithm is used:

(a) and initializing parameters. Setting the parameter estimation value asTaking the maximum iteration number as t_maxT is 0, and the initial parameter is estimated asCovariance matrix of P (0) 10⁶I, wherein 1 ═ 11 … 1]^TAnd I is an identity matrix.

(b) Collecting data and constructing output sequence Y (t) and measurable information quantity

(c) The gain vector l (t) and the covariance matrix p (t) are calculated according to the following equations:

(d) updating parameter estimates

(e) Let t: t +1, if t < t_maxTurning to the step (b), and continuing to perform recursive calculation; otherwise, go to step 3.

And step 3: stopping calculation to obtain the final estimated parameter value