CN117077748B - Coupling synchronous control method and system for discrete memristor neural network - Google Patents
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Abstract
The invention belongs to the technical field of new generation information, and particularly relates to a coupling synchronous control method and system of a discrete memristor neural network, wherein the method comprises the following steps: step S1: establishing a discrete memristor neural network with random disturbance and mixed time lag; step S2: designing a pulse-based coupling synchronous controller according to the discrete memristor neural network with random disturbance and mixed time lag established in the step S1, and constructing a synchronous error system according to the designed coupling synchronous controller; step S3: and (3) selecting a corresponding Lyapunov function according to the synchronous error system constructed in the step (S2) and combining the coupling synchronous controller to realize coupling synchronization of the discrete memristor neural network. Step S4: and building a discrete memristor neural network model, carrying out numerical simulation by using the discrete memristor neural network model, and verifying the coupling synchronization effect between the discrete memristor neural networks. The invention has low control cost and high control precision.
Description
Technical Field
The invention relates to the technical field of new generation information, in particular to a coupling synchronous control method and system of a discrete memristor neural network.
Background
Neural network dynamics are widely used in system identification, optimization, signal processing, image classification, pattern recognition, and the like. Memristors, known as "missing fourth circuit elements", have received widespread attention in the field of electrical and electronic engineering for their unique memory capabilities, low power consumption, nanoscale, and other characteristics. Since the memristor can change its memory resistance according to its own historical current, researchers use the memristor as a synapse between neurons in a neural network model, replacing the traditional synapse structure consisting of transistors and capacitances. In recent years, memristor-based neural networks have been widely studied.
It is well known that random perturbations are unavoidable in the external environment in which neural networks operate. Meanwhile, due to network traffic congestion and limited transmission speed, mixed time lags often occur in complex dynamic networks. Random perturbations and mixed time lags can lead to poor synchronization performance of memristive neural networks. Among the dynamics of the neural network, the synchronization performance and the control problem thereof have been the focus of the study of the neural network. For multiple networks, synchronization is a collective behavior of the entire network system. It means that all subsystems have the same dynamic behavior through communication interactions with neighboring subsystems. To conserve network communication resources, the sensor only passes information to the neighboring nodes at certain instants. Therefore, in order to reduce the communication bandwidth of the network, the pulse control and the coupling control are combined, so that the waste of communication resources can be further reduced.
Disclosure of Invention
The invention aims to provide a coupling synchronous control method and a coupling synchronous control system for a discrete memristive neural network, which can realize the coupling synchronous control of a plurality of discrete memristive neural networks with random interference and mixed time lags.
The invention is realized by adopting the following technical scheme: a coupling synchronous control method of a discrete memristor neural network comprises the following steps:
step S1: establishing a discrete memristor neural network with random disturbance and mixed time lag, wherein a kinetic equation is as follows:
wherein k is a discrete time;representing the state variable of the ith discrete memristive neural network at time k, d=diag { D 1 ,d 2 ,…,d n The state feedback coefficient, |d j |<1；f(x i (k))＝[f 1 (x i1 (k)),f 2 (x i2 (k)),…,f n (x in (k))] T 、g(x i (k-τ(k)))＝[g 1 (x i1 (k-τ(k))),g 2 (x i2 (k-τ(k))),…,g n (x in (k-τ(k)))] T And h (x) i (s))＝[h 1 (x i1 (s)),h 2 (x i2 (s)),…,h n (x in (s))] T Representing a memristive neuron activation function; /> Representing an external input or bias to the system; τ (k) represents a time-varying lag over the bounded interval and satisfies τ m ≤τ(k)≤τ M ；σ(k,x i (k),x i (k- τ (k))) represents the random interference strength experienced by the system; omega (k) is defined in probability space +.>The one-dimensional Gaussian white noise sequence is satisfied +.>A(x i (k))＝[a sj (x ij (k))] n×n 、B(x i (k))＝[b sj (x ij (k))] n×n And C (x) i (k))＝[c sj (x ij (k))] n×n Respectively representing memristor connection weights and time lag weights, and satisfying:
wherein T is j >0 is a switching threshold;and->Is a constant; />Representing an n-dimensional euclidean space.
Step S2: and (3) designing a pulse-based coupling synchronous controller according to the discrete memristor neural network with random disturbance and mixed time lag established in the step (S1), and constructing a synchronous error system according to the designed coupling synchronous controller.
Step S3: and (3) selecting a corresponding Lyapunov function according to the synchronous error system constructed in the step (S2) and combining the coupling synchronous controller to realize coupling synchronization of the discrete memristor neural network.
Step S4: and building a neural network model, carrying out numerical simulation by using the neural network model, and verifying the coupling synchronization effect between the discrete memristor neural networks.
Preferably, the activation function f in step S1 i (·)、g i (. Cndot.) and h i (-) satisfy: wherein f i (·)、g i (. Cndot.) and h i (. Cndot.) is bounded and +.>And->Is a known parameter.
Preferably, the random interference strength σ (k, x 1 (k),x 2 (k) A) satisfies:wherein ρ is 1 ,ρ 2 >0。
Preferably, step S2 specifically includes the following steps:
step S21: according to the discrete memristor neural network with random disturbance and mixed time lag established in the step S1, a pulse-based coupling synchronous controller u is designed i (k) The method comprises the following steps:
in the formula, { k h } h≥1 Represents a discrete pulse time sequence and satisfies 0=k 0 <k 1 <k 2 <…<k h <…; k represents the coupling gain between memristive neurons; γ=diag { γ 1 ,γ 2 ,…,γ n }(γ i >0) Is a system internal coupling matrix; g is Is defined as: if there is a connection between nodes i and s (s+.i), g is >0, otherwise g is =0. Under the action of the coupling synchronous controller, the discrete memristor neural network with random disturbance and mixed time lag is subjected to state comparison at the pulse moment by usingTo represent updated state, i.e
Step S22: the coupling synchronous controller designed according to the step S21 sets the synchronous error as follows:
e ij (k)＝x i (k)-x j (k)。
step S23: according to the synchronization error set in the step S22, a synchronization error system based on coupling control is constructed as follows:
when k is not equal to k h In the time-course of which the first and second contact surfaces,
when k=k h In the time-course of which the first and second contact surfaces,
where j=1, i=2, 3, …, N. Let e (k) = [ e 21 (k)e 31 (k)…e N1 (k)] T . At this time, the synchronization error system can be written as follows:in (1) the->I n Representing n×n real identity matrices, +.> Represents the kronecker product of G and γ.
Preferably, the step S3 specifically includes the following steps:
step S31: the Lyapunov function expression is:
wherein,
step S32: according to the Lyapunov function, determining that the coupling gain K in the coupling synchronizer meets the following linear matrix inequality by utilizing the Lyapunov stability theory:
in the method, in the process of the invention,P 1 ,P 2 ,P 3 for three symmetrical positive definite matrices, the parameter beta is given>1,ζ∈(0,1),σ∈(ζ,1)，
The invention also provides a coupling synchronous control system of the discrete memristor neural network applied to the method. The control system includes: the construction module is used for constructing a discrete memristor neural network model with random disturbance and mixed time lag, constructing a pulse-based coupling synchronous controller according to the discrete memristor neural network model with random disturbance and mixed time lag, and constructing a synchronous error system according to the designed coupling synchronous controller; the coupling synchronization condition calculation module is used for selecting a corresponding Lyapunov function according to the constructed synchronization error system and combining the coupling synchronization controller to determine and calculate the coupling synchronization sufficient condition of the discrete memristor neural network; the setting module is used for setting parameters of the system and the controller according to the result of the coupling synchronization condition calculation module so as to realize the coupling synchronization of the discrete memristor neural network; and the verification module is used for building the discrete memristor neural network model, carrying out numerical simulation by using the discrete memristor neural network model, and verifying the coupling synchronization effect between the discrete memristor neural networks.
The invention provides a coupling synchronous control method and a system of a discrete memristor neural network, which have the following beneficial effects compared with the prior art:
1. in the invention, random disturbance and mixed time lag are particularly introduced, so that a more general discrete memristor neural network is formed, and the invention has wider application prospect.
2. In the present invention, a pulse-based coupling controller is designed, i.e. the coupling control only takes place at discrete pulse instants. The coupling control further reduces the communication bandwidth of the discrete memristive neural network, so that network communication resources can be saved while coupling synchronization is realized.
3. According to the invention, the synchronization conditions depending on random disturbance and mixed time lag are determined, and the discrete memristor neural network is controlled to realize collective coupling synchronization according to the synchronization conditions instead of master-slave synchronization with a single neural network, so that the method has more reference significance and research value.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
In the drawings:
FIG. 1 is a flow chart of a method for coupling synchronization control of a discrete memristive neural network of the present disclosure;
FIG. 2 is a schematic diagram of a state trace under coupling control in numerical simulation of the present invention;
FIG. 3 is a variable x without coupling control in the numerical simulation of the present invention i1 (k) Is a state trace of (1);
FIG. 4 is a variable x without coupling control in the numerical simulation of the present invention i2 (k) Is a state trace of (1);
FIG. 5 is a graph showing the variable x under coupling control in the numerical simulation according to the present invention i1 (k) Is a state trace of (1);
FIG. 6 is a graph showing the variable x under coupling control in the numerical simulation according to the present invention i2 (k) Is a state trace of (1);
FIG. 7 is a schematic diagram of a state trace of a synchronous error system in numerical simulation according to the present invention;
FIG. 8 is a block diagram of a coupled synchronous control system for a discrete memristor neural network in accordance with an embodiment of the present disclosure.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
Example 1
As shown in fig. 1, this embodiment provides a coupling synchronization control method of a discrete memristive neural network. The synchronous control method comprises the following steps:
step S1: establishing a discrete memristor neural network with random disturbance and mixed time lag, wherein a kinetic equation is as follows:
wherein k is a discrete time;representing the state variable of the ith discrete memristive neural network at time k, d=diag { D 1 ,d 2 ,…,d n The state feedback coefficient, |d j |<1；f(x i (k))＝[f 1 (x i1 (k)),f 2 (x i2 (k)),…,f n (x in (k))] T 、g(x i (k-τ(k)))＝[g 1 (x i1 (k-τ(k))),g 2 (x i2 (k-τ(k))),…,g n (x in (k-τ(k)))] T And h (x) i (s))＝[h 1 (x i1 (s)),h 2 (x i2 (s)),…,h n (x in (s))] T Representing a memristive neuron activation function; /> Representing an external input or bias to the system; τ (k) represents a time-varying lag over the bounded interval and satisfies τ m ≤τ(k)≤τ M ；σ(k,x i (k),x i (k- τ (k))) represents the random interference strength experienced by the system; omega (k) is defined in probability space +.>The one-dimensional Gaussian white noise sequence is satisfied +.>A(x i (k))＝[(a sj (x ij (k))] n×n 、B(x i (k))＝[b sj (x ij (k))] n×n And C (x) i (k))＝[c sj (x ij (k))] n×n Respectively representing memristor connection weights and time lag weights, and satisfying:
wherein T is j >0 is a switching threshold;and->Is a constant; />Representing an n-dimensional euclidean space.
Step S2: and (3) designing a pulse-based coupling synchronous controller according to the discrete memristor neural network with random disturbance and mixed time lag established in the step (S1), and constructing a synchronous error system according to the designed coupling synchronous controller.
Step S3: and (3) selecting a corresponding Lyapunov function according to the synchronous error system constructed in the step (S2) and combining the coupling synchronous controller to realize coupling synchronization of the discrete memristor neural network.
Step S4: and building a neural network model, carrying out numerical simulation by using the neural network model, and verifying the coupling synchronization effect between the discrete memristor neural networks.
In the present embodiment, the activation function f in step S1 i (·)、g i (. Cndot.) and h i (-) satisfy: wherein f i (·)、g i (. Cndot.) and h i (. Cndot.) is bounded and +.>And->Is a known parameter.
In the present embodiment, the random interference strength σ (k, x) of the system in step S1 1 (k),x 2 (k) A) satisfies:wherein ρ is 1 ,ρ 2 >0。
In this embodiment, the step S2 specifically includes the following steps:
step S21: according to the discrete memristor neural network with random disturbance and mixed time lag established in the step S1, a pulse-based coupling synchronous controller u is designed i (k) The method comprises the following steps:
in the formula, { k h } h≥1 Represents a discrete pulse time sequence and satisfies 0=k 0 <k 1 <k 2 <…<k h <…; k represents the coupling gain between memristive neurons; γ=diag { γ 1 ,γ 2 ,…,γ n }(γ i >0) Is a system internal coupling matrix; g is Is defined as: if there is a connection between nodes i and s (s+.i), g is >0, otherwise g is =0. Under the action of the coupling synchronous controller, the discrete memristor neural network with random disturbance and mixed time lag is subjected to state comparison at the pulse moment by usingTo represent updated state, i.e
Step S22: the coupling synchronous controller designed according to the step S21 sets the synchronous error as follows:
e ij (k)＝x i (k)-x j (k)。
step S23: according to the synchronization error set in the step S22, a synchronization error system based on coupling control is constructed as follows:
when k is not equal to k h In the time-course of which the first and second contact surfaces,
when k=k h In the time-course of which the first and second contact surfaces,
where j=1, i=2, 3, …, N. Let e (k) = [ e 21 (k)e 31 (k)…e N1 (k)] T . At this time, the synchronization error system can be written as follows:in (1) the->I n Representing n×n real identity matrices, +.> Represents the kronecker product of G and γ.
In this embodiment, the step S3 specifically includes the following steps:
step S31: the Lyapunov function expression is:
wherein,
step S32: according to the Lyapunov function, determining that the coupling gain K in the coupling synchronizer meets the following linear matrix inequality by utilizing the Lyapunov stability theory:
in the method, in the process of the invention,P 1 ,P 2 ,P 3 for three symmetrical positive definite matrices, the parameter beta is given>1,ζ∈(0,1),σ∈(ζ,1)，
It is worth noting that in the selection of the discrete memristor neural network model, according to the circuit characteristics of the memristor, random disturbance and mixed time lag are particularly introduced, a more general discrete memristor neural network model is established, and a pulse-based coupling synchronous control scheme is provided, namely, communication between the discrete memristor neural networks only needs to be carried out in discrete pulse time. The pulse-based coupling control scheme may save communication resources compared to the continuous control scheme.
Example two
The embodiment mainly comprises two parts of contents:
the effectiveness of the pulse-based coupling synchronization control scheme designed in the coupling synchronization control method of the discrete memristor neural network with random disturbance and mixed time lag in the first embodiment is theoretically proved.
And secondly, verifying whether the discrete memristor neural network with random disturbance and mixed time lag established in the first embodiment achieves coupling synchronization under a pulse-based coupling control scheme through numerical simulation.
(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 definition of synchronization and the quotation that will be adopted are given below.
Definition 1: if the systematic error condition satisfies lim k→∞ ||x i (k)-x j (k)||||＝0(i,j＝1,2,…,N),x i (k) If the initial value of (a) is any value, it is indicated that the discrete memristive neural network is synchronous.
Lemma 1: if f m (±T m )＝g m (±T m )＝h m (±T m ) =0, then there is:
wherein s, m=1, 2, …, n,
and (4) lemma 2: if it isIs a positive definite matrix, +.> Inequality->This is true.
And (3) lemma 3:is a positive definite matrix,/->Then the following is satisfied:2X T Y≤X T QX+Y T Q -1 Y。
the lyapunov function was constructed as:
V(k)＝V 1 (k)+V 2 (k)+V 3 (k)，
wherein,
first, when k+.k h-1 In the process, according to the lemma 1 and the synchronous error system, the following can be obtained:
the absolute value of the error state system is written in a compact matrix vector form:
thus according to V 1 (k) The expression of (2) and the above expression, can be obtained
Similarly, according to V 2 (k) Expression (2) and quotients 2) to give:
according to V 3 (k) The expression of (2) can be derived
Therefore, it is further available,
/>
wherein,
according to the method of the Shuerbu theory and the linear matrix inequality, the method can obtain
Thus, whenWhen (I)>
Second, whenIn this case, the method of synchronization error system and linear matrix inequality can be used
Likewise, whenWhen (I)>In the second step, let h=1, i.e. k e (0, k) 1 ]In the time-course of which the first and second contact surfaces,
thus, when k=k 1 In the time-course of which the first and second contact surfaces,second, any givenIs available in the form of
According toAnd a linear matrix inequality method, resulting,
third, according to the expression of V (k), when k=0,
in the method, in the process of the invention, to sum up, the drug is added with>In a further step the process is carried out,
thus, if and only if h→infinity, k→infinity,this meansFrom definition 1, it can be concluded that the discrete memristive neural network can achieve synchronization under coupling control.
2. Numerical simulation
In this embodiment, under the coupling control, 3 two-dimensional discrete memristor neural network systems with random disturbance and mixed delay are selected as follows:
the setting parameters are as follows:
d 1 ＝0.8,d 2 ＝0；
activation function f (x i (·))＝[tanh(|x i1 (·)|-0.15)tanh(-0.4|x i2 (·)|+0.08)] T ，g(x i (·))＝[tanh(|x i1 (·)|-0.15)tanh(-0.4|x i2 (·)|+0.08)] T ，h(x i (·))＝[tanh(|x i1 (·)|-0.15)tanh(-0.4|x i2 (·)|+0.08)] T ，τ(k)＝mod(k,3),τ M ＝2,d＝3,I(k)＝[0 0] T Obtaining the parameters
Set a fixed pulse interval k h+1 -k h ＝2,β＝5.8,ζ＝0.005,σ∈(0.005,0.029]，/>Interference intensity sigma (k, x) i (k),x i (k-τ(k)))＝0.2x i (k)+0.2x i (k- τ (k)) (i=1, 2, 3); initial initiationThe conditions were set as follows: x is x 1 (∈)＝[2.5 -0.8] T ,x 2 (∈)＝[-2.2 -2.5] T ,x 3 (∈)＝[-0.5-2.6] T (∈[-3,0))。
The result of solving the synchronization condition is as follows:
and under the set parameters, the discrete memristor neural network system and the pulse-based coupling synchronous controller carry out a numerical simulation experiment on the discrete memristor neural network system and the pulse-based coupling synchronous controller. Fig. 2 is a schematic diagram of a state trace under pulse control. FIG. 3 is a variable x without synchronous control i1 (k) Figure 4 is a variable x without synchronous control i2 (k) Is a state trace of (a). As can be seen from fig. 3 and 4, the discrete memristive neural network is unsynchronized without synchronous control. FIG. 5 shows the variable x under pulse-based coupling synchronization control i1 (k) Figure 6 is a state trace of a variable x under pulse-based coupled synchronization control i2 (k) Is a state trace of (a). From fig. 5 and 6, it can be seen that the variable x is under pulse-based coupling synchronization control 1 (k)、x 2 (k) And x 3 (k) Gradually overlap the state trajectories of (c). As shown in fig. 7, x is under pulse-based coupling synchronization control i (k) (i=2, 3) and x 1 (k) The synchronization error between them gradually converges to 0. Thus, as can be seen from FIGS. 3-7, the discrete memristive neural network is unsynchronized without synchronous control, while in the case of random disturbance and mixed time lags, coupled synchronization of the discrete memristive neural network can be achieved by pulse-based coupled synchronous control.
Example III
The embodiment mainly comprises the following contents:
based on the same inventive concept, the present embodiment provides a coupling synchronization control system of a discrete memristive neural network, and the principle of solving the problem is similar to that of the coupling synchronization control method of the discrete memristive neural network, and is not repeated. Referring to fig. 8, fig. 8 is a block diagram of a coupling synchronization control system of a discrete memristor neural network according to an embodiment of the present disclosure. The control system may specifically include:
the construction module 100 is used for constructing a discrete memristor neural network model 101 with random disturbance and mixed time lag, constructing a pulse-based coupling synchronous controller 102 according to the discrete memristor neural network model with random disturbance and mixed time lag, and constructing a synchronous error system 103 according to the designed coupling synchronous controller;
the coupling synchronization condition calculation module 200 is used for selecting a corresponding lyapunov function according to the constructed synchronization error system and combining the coupling synchronization controller to determine and calculate the coupling synchronization sufficient condition of the discrete memristor neural network;
the setting module 300 is used for setting parameters of the system and the controller according to the result of the coupling synchronization condition calculation module so as to realize the coupling synchronization of the discrete memristor neural network;
the verification module 400 is configured to build the discrete memristive neural network model and perform numerical simulation by using the discrete memristive neural network model, so as to verify the coupling synchronization effect between the discrete memristive neural networks.
Finally, it should be noted that the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited to the foregoing embodiments, but may be modified or substituted for some of the features described in 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 (3)
1. The coupling synchronous control method of the discrete memristor neural network is characterized by comprising the following steps of:
step S1: establishing a discrete memristor neural network with random disturbance and mixed time lag, wherein a kinetic equation is as follows:
wherein k is a discrete time;representing the state variable of the ith discrete memristive neural network at time k, d=diag { D 1 ,d 2 ,…,d n The state feedback coefficient, |d j |<1；f(x i (k))＝[f 1 (x i1 (k)),f 2 (x i2 (k)),…,f n (x in (k))] T 、g(x i (k-τ(k)))＝[g 1 (x i1 (k-τ(k))),g 2 (x i2 (k-τ(k))),…,g n (x in (k-τ(k)))] T And h (x) i (s))＝[h 1 (x i1 (s)),h 2 (x i2 (s)),…,h n (x in (s))] T Representing a memristive neuron activation function; /> Representing an external input or bias to the system; τ (k) represents a time-varying lag over the bounded interval and satisfies τ m ≤τ(k)≤τ M ；σ(k,x i (k),x i (k- τ (k))) represents the random interference strength experienced by the system; omega (k) is defined in probability space +.>The one-dimensional Gaussian white noise sequence is satisfied +.>A(x i (k))＝[a sj (x ij (k))] n×n 、B(x i (k))＝[b sj (x ij (k))] n×n And C (x) i (k))＝[c sj (x ij (k))] n×n Respectively representing memristor connection weights and time lag weights, and satisfying:
wherein T is j >0 is a switching threshold;and->Is a constant; />Representing an n-dimensional euclidean space;
step S2: designing a pulse-based coupling synchronous controller according to the discrete memristor neural network with random disturbance and mixed time lag established in the step S1, and constructing a synchronous error system according to the designed coupling synchronous controller;
step S3: selecting a corresponding Lyapunov function according to the synchronous error system constructed in the step S2 and combining the coupling synchronous controller to realize coupling synchronization of the discrete memristor neural network;
step S4: building a neural network model, carrying out numerical simulation by using the neural network model, and verifying the coupling synchronization effect between the discrete memristor neural networks;
the activation function f in step S1 i (·)、g i (. Cndot.) and h i (-) satisfy: wherein f i (·)、g i (. Cndot.) and h i (. Cndot.) is bounded, and x 1 ≠x 2 ，/>And->Is a known parameter;
the random interference strength sigma (k, x) of the system in step S1 1 (k),x 2 (k) A) satisfies:wherein ρ is 1 ,ρ 2 >0；
The step S2 specifically comprises the following steps:
step S21: according to the discrete memristor neural network with random disturbance and mixed time lag established in the step S1, a pulse-based coupling synchronous controller u is designed i (k) The method comprises the following steps:
in the formula, { k h } h≥1 Represents a discrete pulse time sequence and satisfies 0=k 0 <k 1 <k 2 <…<k h <…; k represents the coupling gain between memristive neurons; y = diag { gamma } 1 ,γ 2 ,…,γ n }(γ i >0) Is a system internal coupling matrix; g is Is defined as: if there is a connection between nodes i and s (s+.i), g is >0, otherwise g is =0; under the action of the coupling synchronous controller, the discrete memristor neural network with random disturbance and mixed time lag performs state update at pulse time by usingTo represent updated state, i.e
Step S22: the coupling synchronous controller designed according to the step S21 sets the synchronous error as follows:
e ij (k)＝x i (k)-x j (k)；
step S23: according to the synchronization error set in the step S22, a synchronization error system based on coupling control is constructed as follows:
when k is not equal to k h In the time-course of which the first and second contact surfaces,
when k=k h In the time-course of which the first and second contact surfaces,
where j=1, i=2, 3, …, N; let e (k) = [ e 21 (k) e 31 (k) … e N1 (k)] T The method comprises the steps of carrying out a first treatment on the surface of the At this time, the synchronization error system can be written as follows:in (1) the->I n Representing n×n real identity matrices, +.> Represents the Cronecker product of G and gamma.
2. The method for synchronously controlling the coupling of the discrete memristive neural network according to claim 1, wherein the step S3 specifically comprises the following steps:
step S31: the Lyapunov function expression is:
wherein,
step S32: according to the Lyapunov function, determining that the coupling gain K in the coupling synchronizer meets the following linear matrix inequality by utilizing the Lyapunov stability theory:
in the method, in the process of the invention,P 1 ,P 2 ,P 3 for three symmetrical positive definite matrices, the parameter beta is given>1,ζ∈(0,1),σ∈(ζ,1)，
3. A coupled synchronous control system for a discrete memristive neural network applied to the method of any one of claims 1-2, comprising:
the construction module is used for constructing a discrete memristor neural network model with random disturbance and mixed time lag, constructing a pulse-based coupling synchronous controller according to the discrete memristor neural network model with random disturbance and mixed time lag, and constructing a synchronous error system according to the designed coupling synchronous controller;
the coupling synchronization condition calculation module is used for selecting a corresponding Lyapunov function according to the constructed synchronization error system and combining the coupling synchronization controller to determine and calculate the coupling synchronization sufficient condition of the discrete memristor neural network;
the setting module is used for setting parameters of the system and the controller according to the result of the coupling synchronization condition calculation module so as to realize the coupling synchronization of the discrete memristor neural network;
and the verification module is used for building the discrete memristor neural network model, carrying out numerical simulation by using the discrete memristor neural network model, and verifying the coupling synchronization effect between the discrete memristor neural networks.
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