CN106709564A - Neuron system parameter estimation technique - Google Patents

Abstract

The invention discloses a neuron system parameter estimation technique. For a class of biological neuron systems, the model transformation of a general formula is carried out to obtain a standard form applicable to recursive least squares algorithm parameter estimation, through collecting input and output data, information needed by a recursive least squares algorithm is constructed, and finally a system parameter is estimated in an online way. The technique of the invention has the advantages of on-line estimation and simple realization and can be used as an important mean for estimating a general biological neuron system parameter.

Description

Neuron system parameter estimation technology

Background

At present, most of the control theory research of biological neuron systems is to establish analysis under the condition that system model parameters are known, but in practice, the system model parameters are not always accurately known, so that the estimation of the neuron system parameters becomes one of important research subjects. The least square algorithm is an important parameter estimation means, and up to now, scholars at home and abroad propose and develop a plurality of least square algorithms aiming at different requirements or application occasions, wherein the recursive least square algorithm is widely applied due to simple analysis and easy realization.

Research shows that the system can present a chaotic state by setting related parameters of the biological neuron system, and the chaotic phenomenon has potential application value in the fields of chemistry, information science, secret communication and the like, so that the research on parameter estimation of the chaotic biological neuron system has important significance. So far, although some parameter estimation methods of the chaotic biological neuron system exist, such as an adaptive synchronization algorithm, the algorithms are complex, large in calculation amount, and have certain limitations because the parameters need to be estimated by utilizing synchronization control. The invention provides a simple and convenient neuron system parameter estimation technology capable of realizing online estimation.

Disclosure of Invention

The invention aims to overcome the defects of complex structure, large calculated amount and the like of the conventional neuron system parameter estimation algorithm, and provides a novel neuron system parameter estimation technology by utilizing the advantages of online identification and simplicity and convenience in realization of a recursive least square method.

The technical scheme adopted by the invention comprises the following steps:

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

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 neuron and the jth neuron; omega_i(t)(i＝1，2，…And n) is the external noise of the ith neuron.

The biological neuron system is 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

Compared with the existing estimation algorithm, the method has the following advantages:

1. the invention can estimate the parameter on line, and is simple and convenient to realize;

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

3. the parameter estimate can quickly converge to the true parameter value.

Drawings

Fig. 1 is a flow chart of a parameter estimation technique based on the scheme of the invention.

Fig. 2 is a graph of an iterative process of parameter estimation based on the scheme of the present invention in an example.

Detailed Description

In order to better understand the technical scheme of the invention, the following detailed description of the embodiments is provided to illustrate specific embodiments by combining an application example, but not limited to the embodiments.

Example (b): the Hindmarsh-Rose neuron system is an important biological neuron system, and the mathematical model equation is as follows:

wherein x is₁，x₂，x₃Is a state variable; a, b, d and r are system parameters; i is the external stimulation current of the neuron, and in the embodiment, I is 4; omega_i(t) (i ═ 1, 2, 3) is a white noise sequence with zero mean and a variance of 0.01. When the Hindmarsh-Rose neuron system parameters are selected to be a-1, b-3, d-5 and r-0.006, the system is in a chaotic state. The purpose of this example is to identify the 4 parameters a, b,d，r。

the technical work flow of the invention is shown in fig. 1, and the specific implementation can be divided into the following steps:

step 1: and (5) model transformation. The Hindmarsh-Rose neuron model was converted to the standard form:

wherein θ ═ a b d r]^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_max200, t 0, the initial parameter is estimated asCovariance matrix of P (0) 10⁶I, wherein 1 ═ 1111]^TAnd I is an identity matrix.

(b) Collecting data (obtained by solving a neuron system equation by adopting a fourth-order Runge-Kutta method), and constructing an 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

Fig. 2 shows a parameter estimation iteration process curve. As can be seen, all parameter estimates converge to true values approximately after 100 iterations.

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