CN116430715A - Finite time synchronous control method of time-varying time-delay memristor recurrent neural network - Google Patents
Finite time synchronous control method of time-varying time-delay memristor recurrent neural network Download PDFInfo
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Abstract
The invention belongs to the technical field of new generation information, and particularly relates to a finite time synchronization control method of a time-varying time-delay memristor recurrent neural network. The method comprises the following steps: step S1: establishing a time-varying time-delay memristor recurrent neural network driving system and a response system; step S2: setting synchronous errors of a driving system and a response system according to the time-varying time-delay memristor recurrent neural network driving system and the response system established in the step S1, and establishing a synchronous error system; step S3: and (2) designing a state feedback synchronous controller according to the synchronous error set in the step (S2), and acting the state feedback synchronous controller on the response system to enable the response system to be synchronous with the driving system for a limited time. The invention can realize the finite time synchronization of the time-varying time-delay memristor recurrent neural network.
Description
Technical Field
The invention relates to the technical field of new generation information, in particular to a finite time synchronization control method of a time-varying time-delay memristor recurrent neural network.
Background
Memristors are novel nano devices which are paid attention to in recent years, have wide application prospects in the technical field of new generation information, and are particularly applied to new generation information technologies such as low-power-consumption brain-like calculation, data storage, nonvolatile logic and the like. Memristors have the characteristics of high speed, low power consumption, information storage, information functions and the like, and are considered as a fourth circuit basic element after resistance, capacitance and inductance. In addition, memristors, unlike resistances, have a very important characteristic: it can memorize the amount of charge flowing through it, i.e. there is a hysteresis-like loop in the volt-ampere characteristic of the memristor. This characteristic is similar to the memory characteristics of biological neuron synapses, so memristors are often used to simulate synapses in artificial neural networks.
The recurrent neural network is an artificial neural network with a tree-shaped hierarchical structure and the network nodes recursively carry out input information according to the connection sequence, has memory, parameter sharing and complete graphics, and therefore has certain advantages in learning the nonlinear characteristics of the sequence. Therefore, the memristor is introduced into the recurrent neural network to study the dynamic behavior of the memristive recurrent neural network.
In practical applications, it is always desirable that the system achieve synchronization as soon as possible. The finite time control method is a frequently adopted effective control method, and the finite time control method proves better interference suppression performance, robustness and the like. Currently, there are many synchronization criteria including time-lapse neural networks, but the problem of limited time synchronization control of memristive recurrent neural networks including time-lapse is often not fully considered.
Disclosure of Invention
Therefore, the invention aims to provide a limited time synchronization control method of a time-varying time-delay memristor recurrent neural network, which can realize limited time synchronization of the time-varying time-delay memristor recurrent neural network.
The invention is realized by adopting the following scheme: a finite time synchronous control method of a time-varying time-delay memristor recurrent neural network comprises the following steps:
step S1: establishing a time-varying time-delay memristor recurrent neural network driving system and a response system;
step S2: setting synchronous errors of a driving system and a response system according to the time-varying time-delay memristor recurrent neural network driving system and the response system established in the step S1, and establishing a synchronous error system;
step S3: and (2) designing a state feedback synchronous controller according to the synchronous error set in the step (S2), and acting the state feedback synchronous controller on the response system to enable the response system to be synchronous with the driving system for a limited time.
Further, the step S1 specifically includes the following steps:
step S11: the established time-varying time-delay memristor recurrent neural network driving system is as follows:
step S12: the established time-varying time-delay memristor recurrent neural network response system is as follows:
in the driving system and the response system, p, q=1, 2, …, n; n represents the number of neurons in the driving system and the response system; the time t is more than or equal to 0; v p(t) and wp (t) representing the state variables of the p-th neuron of the drive system and response system, respectively, at time t; d, d p Is a self-feedback connection weight and satisfies d p ≥0；g q (v q(t)) and gq (w q (t)) represents an activation function in which the q-th neuron in the driving system and the response system, respectively, does not contain a time lag; h is a q (v q (t-δ qp (t))) and h q (w q (t-δ qp (t)) representing an activation function in which the q-th neuron in the drive system and the response system, respectively, comprises a time-varying time-lag; the activation function g q (v q (t))、g q (w q (t))、h q (v q (t-δ qp (t))) and h q (w q (t-δ qp (t))) is a monotonically non-decreasing function and satisfies g q (0)＝h q (0)＝0、
wherein />
Is a positive constant; for any real numbers a and b, the activation function satisfies |g q (a)-g q (b)|≤η q A-b and +.>
wherein ηq and />
Is a positive constant; delta qp (t) represents a time-varying time lag; j (J) p Is an external input; u (u) p Representing a state feedback synchronous controller; />
Respectively represent v p (t)、w p (t) a derivative of time t; a, a pq (v q (t))、g q (w q (t))、b pq (v q (t-δ qp (t)))、h q (w q (t-δ qp (t))) represents memristor connection weights, respectively satisfying:
wherein ,D- (g q (v q (t))-v p (t)) represents g q (v q (t))-v p (t) solving for dini Zuo Daoshu for time t; d (D) - (g q (w q (t))-w p (t)) represents g q (w q (t))-w p (t) solving for dini Zuo Daoshu for time t; d (D) - (h q (v q (t-δ qp (t)))-v p (t)) represents h q (v q (t-δ qp (t)))-v p (t) solving for dini Zuo Daoshu for time t; d (D) - (h q (w q (t-δ qp (t)))-w p (t)) represents h q (w q (t-δ qp (t)))-w p (t) solving for dini Zuo Daoshu for time t;
are all constant;
since the right side of the equal sign of the driving system and the response system is discontinuous, solutions of the driving system and the response system need to be considered in the Filipply ov sense, and then the driving system and the response system are respectively rewritten as follows by adopting a set value mapping and differential inclusion theory:
in the formula ,
co[a pq (v q (t))]、co[v q (t-δ qp (t))]、co[a pq (w q (t))]、co[w q (t-δ qp (t))]the following respectively satisfy:
wherein ,
further, the step S2 specifically includes the following steps:
step S21: according to the time-varying time-delay memristor recurrent neural network driving system and the response system established in the step S1, setting the synchronous error of the driving system and the response system as follows:
e p (t)＝v p (t)-w p (t)
step S22: according to the driving system, the response system and the synchronization error set in the step S21, a synchronization error system is established as follows:
wherein ,
representing the synchronization error e p (t) derivative with respect to time t.
Further, the step S3 specifically includes the following:
step S31: the design state feedback synchronous controller is as follows:
wherein p, q=1, 2, …, n; lambda (lambda) p 、θ p 、κ p 、γ p Gain for controller, where lambda p >0、θ p >0；v∈(0，1)；sign(e p (t)) is expressed as a synchronization error e p A sign function of (t); e, e q (t-δ qp (t))＝v q (t-δ qp (t))-w q (t-δ qp (t)); controller gain lambda p 、κ p 、γ p The following inequality is satisfied:
wherein ,
step S32: and the state feedback synchronous controller acts on the response system so that the response system is synchronous with the driving system for a limited time.
Further, according to the finite time synchronization control method of the time-varying time-delay memristor recurrent neural network, the response system is synchronized with the driving system in finite time, and the finite time range is as follows:
wherein e (0) = (e) 1 (0)，e 2 (0)，…，e n (0)) T ；θ＝min{θ 1 ，θ 2 ，…，θ n }；||e(0)|| 2 Is the 2-norm of e (0).
The invention provides a finite time synchronous control method of a time-varying time-delay memristor recurrent neural network, which has the beneficial effects that compared with the prior art, the method is as follows:
1. in the invention, a memristor is adopted to simulate synapses in the neural network, so that the memristor recurrent neural network is constructed.
2. In the invention, the influence of time-varying time lag on the neural network model is considered, so that the finite time synchronous control method of the time-varying time lag memristor recurrent neural network has wider application.
3. The invention realizes the finite time synchronous control method of the time-varying time-delay memristor recurrent neural network, and compared with an asymptotic synchronous control method, the synchronous control method is a more practical synchronous control method, because the asymptotic synchronous control method has infinite synchronous time in theory, and the finite time synchronous control method ensures that a response system is synchronous with a driving system in finite time.
Drawings
FIG. 1 is a flow chart of a finite time synchronization control method of a time-varying time-lapse memristive recurrent neural network of the present invention;
FIG. 2 is a diagram showing a variation trace of a synchronization error without a controller in embodiment 2 of the present invention;
FIG. 3 shows the driving system state v without the controller in embodiment 2 of the present invention 1 (t) and responsive System status w 1 A trace map of (t);
FIG. 4 shows the driving system state v without the controller in embodiment 2 of the present invention 2 (t) and responsive System status w 2 A trace map of (t);
FIG. 5 is a diagram showing a variation trace of synchronization error under the action of a state feedback synchronization controller in embodiment 2 of the present invention;
FIG. 6 shows a driving system state v under the action of a state feedback synchronous controller in embodiment 2 of the present invention 1 (t) and responsive System status w 1 A trace map of (t);
FIG. 7 shows a driving system state v under the action of a state feedback synchronous controller in embodiment 2 of the present invention 2 (t) and responsive System status w 2 Trace map of (t).
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Example 1:
as shown in fig. 1, the present embodiment provides a finite time synchronization control method of a time-varying time-lapse memristive recurrent neural network. The synchronous control method comprises the following steps:
step S1: establishing a time-varying time-delay memristor recurrent neural network driving system and a response system;
step S2: setting synchronous errors of a driving system and a response system according to the time-varying time-delay memristor recurrent neural network driving system and the response system established in the step S1, and establishing a synchronous error system;
step S3: and (2) designing a state feedback synchronous controller according to the synchronous error set in the step (S2), and acting the state feedback synchronous controller on the response system to enable the response system to be synchronous with the driving system for a limited time.
In this embodiment, step S1 specifically includes the following:
step S11: the established time-varying time-delay memristor recurrent neural network driving system is as follows:
step S12: the established time-varying time-delay memristor recurrent neural network response system is as follows:
in the driving system and the response system, p, q=1, 2, …, n; n represents the number of neurons in the driving system and the response system; the time t is more than or equal to 0; v p(t) and wp (t) representing the state variables of the p-th neuron of the drive system and response system, respectively, at time t; d, d p Is a self-feedback connection weight and satisfies d p ≥0；g q (v q(t)) and gq (w q (t)) represents an activation function in which the q-th neuron in the driving system and the response system, respectively, does not contain a time lag; h is a q (v q (t-δ qp (t))) and h q (w q (t-δ qp (t)) representing an activation function in which the q-th neuron in the drive system and the response system, respectively, comprises a time-varying time-lag; the activation function g q (v q (t))、g q (w q (t))、h q (v q (t-δ qp (t))) and h q (w q (t-δ qp (t))) is a monotonically non-decreasing function and satisfies g q (0)＝h q (0)＝0、
wherein />
Is a positive constant; for any real numbers a and b, the activation function satisfies |g q (a)-g q (b)|≤η q A-b and +.>
wherein ηq and />
Is a positive constant; delta qp (t) represents a time-varying time lag; j (J) p Is an external input; u (u) p Representing a state feedback synchronous controller; />
Respectively represent v p (t)、w p (t) a derivative of time t; a, a pq (v q (t))、g q (w q (t))、b pq (v q (t-δ qp (t)))、h q (w q (t-δ qp (t))) represents memristor connection weights, respectively satisfying:
wherein ,D- (g q (v q (t))-v p (t)) represents g q (v q (t))-v p (t) solving for dini Zuo Daoshu for time t; d (D) - (g q (w q (t))-w p (t)) represents g q (w q (t))-w p (t) solving for dini Zuo Daoshu for time t; d (D) - (h q (v q (t-δ qp (t)))-v p (t)) represents h q (v q (t-δ qp (t)))-v p (t) solving for dini Zuo Daoshu for time t; d (D) - (h q (w q (t-δ qp (t)))-w p (t)) represents h q (w q (t-δ qp (t)))-w p (t) solving for dini Zuo Daoshu for time t;
are all constant;
since the right side of the equal sign of the driving system and the response system is discontinuous, solutions of the driving system and the response system need to be considered in the Filipply ov sense, and then the driving system and the response system are respectively rewritten as follows by adopting a set value mapping and differential inclusion theory:
in the formula ,
co[a pq (v q (t))]、co[v q (t-δ qp (t))]、co[a pq (w q (t))]、co[w q (t-δ qp (t))]the following respectively satisfy:
wherein ,
in this embodiment, the step S2 specifically includes the following steps:
step S21: according to the time-varying time-delay memristor recurrent neural network driving system and the response system established in the step S1, setting the synchronous error of the driving system and the response system as follows:
e p (t)＝v p (t)-w p (t)
step S22: according to the driving system, the response system and the synchronization error set in the step S21, a synchronization error system is established as follows:
wherein ,
representing the synchronization error e p (t) derivative with respect to time t.
In this embodiment, the step S3 specifically includes the following steps:
step S31: the design state feedback synchronous controller is as follows:
wherein p, q=1, 2, …, n; lambda (lambda) p 、θ p 、κ p 、γ p Gain for controller, where lambda p >0、θ p >0；v∈(0，1)；sign(e p (t)) is expressed as a synchronization error e p A sign function of (t); e, e q (t-δ qp (t))＝v q (t-δ qp (t))-w q (t-δ qp (t)); controller gain lambda p 、κ p 、γ p The following inequality is satisfied:
wherein ,
step S32: and the state feedback synchronous controller acts on the response system so that the response system is synchronous with the driving system for a limited time.
In this embodiment, according to the finite time synchronization control method of the time-varying time-delay memristor recurrent neural network, the response system is synchronized with the driving system in a finite time, and the finite time ranges are as follows:
wherein e (0) = (e) 1 (0)，e 2 (0)，…，e n (0)) T ；θ＝min{θ 1 ，θ 2 ，…，θ n }；||e(0)|| 2 Is the 2-norm of e (0).
It is worth to say that, according to the characteristics of the memristor, the influence of time-varying time delay on the memristor recurrent neural network model is particularly considered, so that the limited time synchronization control method of the time-varying time delay memristor recurrent neural network has wider application. In the invention, the memristor is adopted to simulate the synapse in the neural network, and in the neural network, the synapse is responsible for information storage and calculation, so that the memristor has similar memory characteristics as the synapse, and can better simulate the synapse. The invention realizes the finite time synchronous control method of the time-varying time-delay memristor recurrent neural network, and compared with an asymptotic synchronous control method, the synchronous control method is a more practical synchronous control method, because the asymptotic synchronous control method has infinite synchronous time in theory, and the finite time synchronous control method ensures that a response system is synchronous with a driving system in finite time.
Example 2:
the embodiment mainly comprises two parts of contents:
one is to carry out theoretical demonstration on the effectiveness of a finite time synchronization control method of a time-varying time-lapse memristor recurrent neural network proposed in embodiment 1.
Secondly, the synchronous performance of the time-varying time-delay memristor recurrent neural network driving system and the response system in the embodiment 1 is simulated and verified by a numerical simulation method.
(neither theoretical demonstration nor simulation experiment is intended to limit the invention, in other embodiments, simulation experiments may be omitted, or other experimental schemes may be used to verify the performance of the neural network system.)
1. Proof of theory
The definitions and quotients that will be employed in the attestation process are given below:
definition 1: for the driving system and the response system of the invention, if there is a time T, for t+.t, there is e (T) =v (T) -w (T) = (0, …, 0) T And
then the response system is said to be time-synchronized to the drive system for a limited period of time, where e (t) = (e) 1 (t)，e 2 (t)，…，e n (t)) T ，v(t)＝(v 1 (t)，v 2 (t)，…，v n (t)) T ，w(t)＝(w 1 (t)，w 2 (t)，…，w n (t)) T 。
Lemma 1: for the synchronization error e (t) of the drive system and the response system, if there is a positive definite continuous function V (t, e (t)), the inequality is satisfied: d (D) + V (T, e (T)). Ltoreq. -beta (V (T, e (T))), then the drive system and response system achieve limited time synchronization, and the limited time T satisfies
Further, if β (V (t, e (t))) =fv ε (T, e (T)), the finite time T satisfies:
wherein, for any χ>0, have
e (0) represents an initial value of a synchronization error; d (D) + An identification representing a derivative of the function diy; f (F)>0、0<ε<1。
And (4) lemma 2: if z 1 、z 2 、…、z n Are all nonnegative numbers, a 2 >a 1 >0, the following inequality holds:
according to embodiment 1, the synchronization error system is as follows:
order the
The synchronization error system can be rewritten as:
then, the following relationship can be obtained according to the condition satisfied by the activation function:
e p (t)sign(e p (t))＝|e p (t)|
next, the lyapunov functional is constructed:
the established lyapunov functional is then solved for the dily derivative:
again because:
then D + V (t, e (t)) can be further obtained:
and because of the controller gain lambda p 、κ p 、γ p The following three inequalities are satisfied:
then it is further possible to obtain:
then according to lemma 2, since v+1 ε (1, 2), we can get:
thus, it is possible to further obtain:
wherein θ=min { θ 1 ，θ 2 ，…，θ n }；v∈(0，1)。
According to lemma 1, for any χ e (0, ++ infinity a) of the above-mentioned components, can obtain
It can thus be derived that the finite time T satisfies:
wherein e (0) = (e) 1 (0)，e 2 (0)，…，e n (0)) T ；||e(0)|| 2 Is the 2-norm of e (0).
Thus, as can be seen from definition 1 and quotation 1, the response system is synchronized with the driving system for a limited time and within a limited time range under the action of the state feedback synchronous controller
2. Numerical simulation
In this embodiment, taking a time-varying time-lapse memristive recurrent neural network system containing two neurons as an example, the driving system is determined as:
the response system corresponding to the driving system is as follows:
wherein t is more than or equal to 0; g q (v q (t))＝tanh(v q (t))、h q (v q (t-δ qp (t)))＝tanh(v q (t-δ qp (t)))、g q (w q (t))＝tanh(w q (t))、h q (w q (t-δ qp (t)))＝tanh(w q (t-δ qp (t)))；d 1 ＝1.2、d 2 =0.9; constant (constant)
δ qp (t)＝0.76-0.24cos(t)；J 1 ＝J 2 =0; p=1, 2; q=1, 2; memristor connection weights are selected as: />
According to the above parameter settings, and inequality
and />
The parameter value ranges of the available state feedback synchronous controller are respectively as follows: lambda (lambda) 1 >3.25、λ 2 >2.85、κ 1 >2.7、κ 2 >2.4、γ 1 >2.05、γ 2 >2.15, the state feedback synchronous controller parameter may take the value: lambda (lambda) 1 ＝3.3、λ 2 ＝2.9、κ 1 ＝2.8、κ 2 ＝2.5、γ 1 ＝2.1、γ 2 =2.2; other state feedback synchronous controller parameters take the value of theta 1 ＝θ 2 ＝1。
And the driving system, the response system and the state feedback synchronous controller carry out numerical simulation experiments on the driving system, the response system and the state feedback synchronous controller under the set parameters. The initial values of the drive system and the response system are set as follows: v 1 (0)＝2.3，v 2 (0)＝0.5，w 1 (0)＝-2.1，w 2 (0) = -1.1, the specific simulation experiment results are as follows: FIG. 2 is a graph of the variation of synchronization error without the action of a controller; FIG. 3 shows the state v of the drive system without the action of a controller 1 (t) and responsive System status w 1 A trace map of (t); fig. 4 shows the driving system state v without the action of the controller 2 (t) and responsive System status w 2 A trace map of (t); FIG. 5 is a graph of the variation trace of synchronization error under the action of a state feedback synchronization controller; FIG. 6 shows a state feedback synchronous controllerUnder action drive system state v 1 (t) and responsive System status w 1 A trace map of (t); FIG. 7 shows the driving system state v under the action of the state feedback synchronous controller 2 (t) and responsive System status w 2 A trace map of (t); 2-4 show that the driving system and the response system cannot realize synchronization under the action of the controller; the traces of fig. 6-7 demonstrate that the response system is synchronized with the drive system within a finite time under the action of the state feedback synchronization controller, and the synchronization performance is verified.
Finally, it should be noted that: the foregoing is merely a preferred example of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The finite time synchronous control method of the time-varying time-delay memristor recurrent neural network is characterized by comprising the following steps of:
step S1: establishing a time-varying time-delay memristor recurrent neural network driving system and a response system;
step S2: setting synchronous errors of a driving system and a response system according to the time-varying time-delay memristor recurrent neural network driving system and the response system established in the step S1, and establishing a synchronous error system;
step S3: and (2) designing a state feedback synchronous controller according to the synchronous error set in the step (S2), and acting the state feedback synchronous controller on the response system to enable the response system to be synchronous with the driving system for a limited time.
2. The finite time synchronization control method of a time-varying time-lapse memristor recurrent neural network according to claim 1, wherein step S1 specifically comprises the steps of:
step S11: the established time-varying time-delay memristor recurrent neural network driving system is as follows:
step S12: the established time-varying time-delay memristor recurrent neural network response system is as follows:
in the driving system and the response system, p, q=1, 2, …, n; n represents the number of neurons in the driving system and the response system; the time t is more than or equal to 0; v p(t) and wp (t) representing the state variables of the p-th neuron of the drive system and response system, respectively, at time t; d, d p Is a self-feedback connection weight and satisfies d p ≥0；g q (v q(t)) and gq (w q (t)) represents an activation function in which the q-th neuron in the driving system and the response system, respectively, does not contain a time lag; h is a q (v q (t-δ qp (t))) and h q (w q (t-δ qp (t)) representing an activation function in which the q-th neuron in the drive system and the response system, respectively, comprises a time-varying time-lag; the activation function g q (v q (t))、g q (w q (t))、h q (v q (t-δ qp (t))) and h q (w q (t-δ qp (t))) is a monotonically non-decreasing function and satisfies g q (0)＝h q (0)＝0、
wherein />
Is a positive constant; for any real numbers a and b, the activation function satisfies |g q (a)-g q (b)|≤η q A-b and +.>
wherein ηq and />
Is a positive constant; delta qp (t) represents a time-varying time lag; j (J) p Is an external input; u (u) p Representing a state feedback synchronous controller; />
Respectively represent v p (t)、w p (t) a derivative of time t; a, a pq (v q (t))、g q (w q (t))、b pq (v q (t-δ qp (t)))、h q (w q (t-δ qp (t))) represents memristor connection weights, respectively satisfying:
wherein ,D- (g q (v q (t))-v p (t)) represents g q (v q (t))-v p (t) solving for dini Zuo Daoshu for time t; d (D) - (g q (w q (t))-w p (t)) represents g q (w q (t))-w p (t) solving for dini Zuo Daoshu for time t; d (D) - (h q (v q (t-δ qp (t)))-v p (t)) represents h q (v q (t-δ qp (t)))-v p (t) solving for dini Zuo Daoshu for time t; d (D) - (h q (w q (t-δ qp (t)))-w p (t)) represents h q (w q (t-δ qp (t)))-w p (t) solving for dini Zuo Daoshu for time t;
are all constant;
since the right side of the equal sign of the driving system and the response system is discontinuous, solutions of the driving system and the response system need to be considered in the Filipply ov sense, and then the driving system and the response system are respectively rewritten as follows by adopting a set value mapping and differential inclusion theory:
in the formula ,
co[a pq (v q (t))]、co[v q (t-δ qp (t))]、co[a pq (w q (t))]、co[w q (t-δ qp (t))]the following respectively satisfy:
wherein ,
3. the finite time synchronization control method of a time-varying time-lapse memristor recurrent neural network according to claim 1, wherein step S2 specifically comprises the following steps:
step S21: according to the time-varying time-delay memristor recurrent neural network driving system and the response system established in the step S1, setting the synchronous error of the driving system and the response system as follows:
e p (t)＝v p (t)-w p (t)
step S22: according to the driving system, the response system and the synchronization error set in the step S21, a synchronization error system is established as follows:
wherein ,
representing the synchronization error e p (t) derivative with respect to time t.
4. The finite time synchronization control method of a time-varying time-lapse memristor recurrent neural network according to claim 1, wherein step S3 specifically comprises the following steps:
step S31: the design state feedback synchronous controller is as follows:
wherein p, q=1, 2, …, n; lambda (lambda) p 、θ p 、κ p 、γ p Gain for controller, where lambda p >0、θ p >0；v∈(0，1)；sign(e p (t)) is expressed as a synchronization error e p A sign function of (t); e, e q (t-δ qp (t))＝v q (t-δ qp (t))-w q (t-δ qp (t)); controller gain lambda p 、κ p 、γ p The following inequality is satisfied:
wherein ,
step S32: and the state feedback synchronous controller acts on the response system so that the response system is synchronous with the driving system for a limited time.
5. The method of finite time synchronization control of a time-varying time-lapse memristive recurrent neural network of claim 1, wherein the response system is synchronized to the drive system for a finite time, and the finite time ranges from:
wherein e (0) = (e) 1 (0)，e 2 (0)，…，e n (0)) T ；θ＝min{θ 1 ，θ 2 ，…，θ n }；||e(0)|| 2 Is the 2-norm of e (0).
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