CN112884136A - Bounded clustering projection synchronous regulation control method and system for coupled neural network - Google Patents

Bounded clustering projection synchronous regulation control method and system for coupled neural network Download PDF

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CN112884136A
CN112884136A CN202110429664.XA CN202110429664A CN112884136A CN 112884136 A CN112884136 A CN 112884136A CN 202110429664 A CN202110429664 A CN 202110429664A CN 112884136 A CN112884136 A CN 112884136A
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CN112884136B (en
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汤泽
蒋晨辉
王艳
纪志成
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Jiangnan University
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Abstract

The invention relates to a bounded clustering projection synchronous regulation control method and system of a coupled neural network. Establishing a coupling neural network with a plurality of clusters of nonlinearity, non-constant and mixed time-varying time lag, and setting a target neural network for each cluster; establishing an error coupling neural network according to the coupling neural network and a target neural network; designing a containment pulse feedback controller according to the error coupling neural network model, and selecting a corresponding function based on the containment pulse feedback controller so as to realize bounded clustering projection synchronization between a neural network and a target neural network in each cluster; and verifying the bounded clustering projection synchronization effect between the target neural network and the coupling neural network by building a network model and performing numerical simulation by using the network model. The invention has low control cost and high control precision.

Description

Bounded clustering projection synchronous regulation control method and system for coupled neural network
Technical Field
The invention relates to the technical field of complex network synchronous control, in particular to a bounded clustering projection synchronous regulation control method and system of a coupled neural network.
Background
In recent years, the wide application of complex networks in various fields makes the research of complex networks an interesting subject. The system behavior in the network is forced to be consistent by calibrating system parameters or applying external control inputs, a phenomenon known as synchronization. At present, clustering behaviors of chaotic systems are widely applied to work such as image processing, secret communication and the like, and a synchronization phenomenon becomes an indispensable part in complex network research. Up to now, different types of synchronization phenomena have been discussed, such as boundary synchronization, lag synchronization, cluster synchronization, phase synchronization, projection synchronization, etc.
Among the above synchronization methods, the projection synchronization method has important significance in practical application due to different proportionality coefficients of each node. For example, in the field of digital communications, multilevel communications enable faster communications through projective synchronization. Bounded synchronization is a special synchronization, generally caused by parameter mismatch, internal interference, external attack, etc., and the system only needs to have consistency within a certain range. Furthermore, cluster synchronization, a common synchronization phenomenon, describes synchronization phenomena occurring in each subgroup.
In general, many complex networks alone have difficulty achieving synchronization. To solve this problem, several effective methods of achieving synchronization have been proposed, including holdover control, pulse control, distributed control, intermittent control, and the like. The pulse control is used as an efficient and energy-saving synchronization strategy, effective control can be realized with low consumption, and the containment control can realize synchronization only by controlling a few nodes in the network. Therefore, the above two control methods can be used in combination.
The non-constant coupled neural network comprises neural networks with different internal structures, and can be divided into different clusters according to the different internal structures. In the scheme design process of industrial products, a neural network is often applied to an inference mechanism of a decision support system, and an optimal scheme is obtained according to an inference strategy generated by the neural network through sample information data. The problem of synchronization of coupled neural networks under non-constant and parameter mismatch conditions is rarely discussed, and due to the difference of the connection weight matrices of different neural networks, it is necessary to consider the parameter mismatch characteristics. Compared with containment control, the distributed control of the existing coupling neural network has higher cost, while a general clustering containment control strategy aims to eliminate the interaction among different clusters and control key nodes connecting a plurality of clusters, and the control strategy has lower efficiency, fewer applicable scenes and can not ensure the realization of effective control.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defects that the synchronous control for completing the non-constant coupled neural network control in the prior art is high in cost and cannot be effectively controlled. .
In order to solve the technical problem, the invention provides a bounded clustering projection synchronous regulation control method of a coupled neural network, which comprises the steps of establishing the coupled neural network with a plurality of clusters of non-linearity, non-constant and mixed time-varying time lag, and setting a target neural network for each cluster; establishing an error coupling neural network according to the coupling neural network and a target neural network; designing a containment pulse feedback controller according to the error coupling neural network model, and selecting a corresponding function based on the containment pulse feedback controller so as to realize bounded clustering projection synchronization between a neural network and a target neural network in each cluster; and verifying the bounded clustering projection synchronization effect between the target neural network and the coupling neural network by building a network model and performing numerical simulation by using the network model.
In one embodiment of the present invention, the model of the coupled neural network is:
Figure BDA0003030895850000021
wherein:
Figure BDA0003030895850000022
is the state vector of the node; n neural networks are divided into l clusters, N is more than or equal to l and is more than 0, and the ith neural network and the jth neural network define mu in the zth clusteri＝μjZ, otherwise, is mui≠μj；
Figure BDA0003030895850000023
Figure BDA0003030895850000024
Figure BDA0003030895850000025
Is the μiA connection weight matrix of the neural network in each cluster;
Figure BDA0003030895850000026
is the external input vector of the neuron; f. ofk(·)：Rn→RnAnd k is 1, 2, 3 denotes the activation function of the neuron, among them
Figure BDA0003030895850000027
Figure BDA0003030895850000028
Figure BDA0003030895850000031
Figure BDA0003030895850000032
Figure BDA0003030895850000033
Normal number sigma1，σ2Is the coupling strength of the coupled neural network; gamma, gamma represents an internal coupling matrix of the coupling neural network, and gamma is an identity matrix; tau is1(t)，τ2(t) and τ3(t) respectively represents system time-varying time lag, state coupling time-varying time lag and distributed coupling time-varying time lag, and tau is more than or equal to 01(t)≤τ1，0≤τ2(t)≤τ2，0≤τ3(t)≤τ3And defines the maximum time lag as τ ═ max { τ ═ max1(t)，τ2(t)，τ3(t)}；G＝(gij)m×mAnd D ═ D (D)ij)m×mIs an external coupling matrix based on a coupling neural network topological structure, and the matrixes G and D meet the dissipation condition, namely meet the dissipation condition
Figure BDA0003030895850000034
And
Figure BDA0003030895850000035
if there is a connection between the ith neural network and the jth neural network, then there is gij＝gji＞0(dij＝dji> 0), otherwise gij＝0(dij＝0)；uiAnd (t) is a controller.
In one embodiment of the present invention, the model of the target neural network is:
Figure BDA0003030895850000036
wherein:
Figure BDA0003030895850000037
is the state vector of the neural network,
Figure BDA0003030895850000038
is a connection weight matrix of the neural network, and exists
Figure BDA0003030895850000039
Figure BDA00030308958500000310
Figure BDA00030308958500000311
In one embodiment of the invention, a matrix measure μ is definedq(M)：
Figure BDA00030308958500000312
Wherein: i is an n-dimensional unit vector, | | · | | non-woven phosphorqQ is 1, 2, infinity, representing an induced norm for which there is a constraint:
Figure BDA00030308958500000313
wherein
Figure BDA00030308958500000314
Is a normal number.
In one embodiment of the present invention, the model of the error-coupled neural network is:
Figure BDA00030308958500000315
wherein:
Figure BDA00030308958500000316
Figure BDA00030308958500000317
Figure BDA0003030895850000041
Figure BDA0003030895850000042
Figure BDA0003030895850000043
Figure BDA0003030895850000044
Figure BDA0003030895850000045
Figure BDA0003030895850000046
ei(t)＝xi(t)-asμi(t) is the error vector and the normal a is used to represent the projection factor.
In one embodiment of the invention, at the μiWithin a cluster, if and only if for any initial state
Figure BDA0003030895850000047
Figure BDA0003030895850000048
Presence of positive parameters
Figure BDA0003030895850000049
So that the following inequality holds
Figure BDA00030308958500000410
In one embodiment of the present invention, is defined as
Figure BDA00030308958500000411
Figure BDA00030308958500000412
Figure BDA00030308958500000413
Obtaining the following neural network model with mixed time-varying time lag, nonlinearity and non-constant error coupling:
Figure BDA00030308958500000414
wherein: hypothesis error state vector ei(t) is right-continuous, present
Figure BDA00030308958500000415
Figure BDA00030308958500000416
Figure BDA00030308958500000417
In one embodiment of the present invention, the holdback pulse feedback controller expression is:
Figure BDA00030308958500000418
wherein: the pulse intensity rho ∈ (-2, -1) U (-1, 0), δ (·) denotes a dirac function; for pulse signals, time series
Figure BDA00030308958500000420
Is strictly monotonically increasing.
In one embodiment of the present invention, the function is a lyapunov function, and the expression is:
Figure BDA00030308958500000419
where P is a normally positive definite matrix.
The invention also provides a coupling neural network bounded clustering projection synchronous regulation control system applied to the method, which comprises the following steps: the building module is used for building a coupling neural network with a plurality of clusters of nonlinearity, non-constant and mixed time-varying time lag, and setting a target neural network for each cluster; the setting module is used for establishing an error coupling neural network according to the coupling neural network and a target neural network; the cluster synchronization module is used for designing a containment pulse feedback controller according to the error coupling neural network model and selecting a corresponding function based on the containment pulse feedback controller so as to realize bounded cluster projection synchronization between the neural network and a target neural network in each cluster; and the simulation module is used for verifying the bounded clustering projection synchronization effect between the target neural network and the coupling neural network by building a network model and performing numerical simulation by using the network model.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the bounded clustering projection synchronous regulation control method and system of the coupling neural network have the following advantages:
1. the signal transmission delay of different neural networks in the coupled neural network and the internal difference between different neural networks are fully considered, and a coupled neural network model which has the characteristics of system time-varying time lag, general coupling time-varying time lag and distributed coupling time-varying time lag and has nonlinearity and non-constant characteristics under the condition of parameter mismatching is constructed;
2. aiming at the difference of nonlinear activation functions of different neural networks, a class of containment pulse controllers for realizing cluster synchronization of the coupled neural networks are designed, and a small part of neural networks with larger state errors in different clusters are selected as controlled objects to feed back error state information of the controlled objects, so that effective control can be realized under the condition of less consumption;
3. based on the Lyapunov stability theorem, the concept of average pulse interval and some linearization methods, a more accurate judgment condition of bounded clustering projection synchronization of a coupled neural network is given by using a matrix measurement method without negativity, the exponential convergence speed of the bounded clustering projection synchronization and a corresponding synchronization error bound are given by using a parameter variation method, and compared with the traditional upper and lower definite boundaries of given pulses, the conservative type of the synchronization judgment condition is also reduced;
4. the existence condition of bounded clustering projection synchronization is considered, and the value of the synchronization error bound is optimized. The existence of a synchronous error boundary can be ensured by controlling the pulse intensity of the control pulse controller and the scale of the selected controlled object, and the synchronous error can be correspondingly reduced by adjusting the pulse frequency.
Drawings
In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the embodiments of the present disclosure taken in conjunction with the accompanying drawings, in which
Fig. 1 is a diagram showing a structure of a coupled neural network in embodiment 2.
Fig. 2 is a pulse time series diagram in example 2.
Fig. 3 is a graph showing the effect of the cluster containment control strategy of the neural network in example 2.
Fig. 4 is a diagram of the evolution of the error state of the neural network in embodiment 2.
Fig. 5 is a state 1 evolution graph of the neural network in cluster 1 in example 2.
Fig. 6 is a state 2 evolution graph of the neural network in cluster 1 in example 2.
Fig. 7 is a state 1 evolution graph of the neural network in cluster 2 in example 2.
Fig. 8 is a state 2 evolution graph of the neural network in cluster 2 in example 2.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
Example 1
The embodiment provides a bounded clustering projection synchronous regulation control method of a coupled neural network, which comprises the following steps:
the method comprises the following steps: non-identical neural networks are considered and divided into a plurality of clusters, and a target neural network is set for each subclass, wherein the target neural network can be regarded as a leader and other neural networks can be regarded as followers. Firstly, establishing a coupled neural network model with nonlinear, non-constant and mixed time-varying time lag as follows:
Figure BDA0003030895850000061
wherein:
Figure BDA0003030895850000062
is the state vector of the node; assuming that N neural networks can be divided into l clusters and that N ≧ l > 0 exists, if the ith neural networkThe network and the jth neural network are in the z-th cluster, then μ is definedi＝μjZ, otherwise, is mui≠μj；
Figure BDA0003030895850000063
Figure BDA0003030895850000064
Figure BDA0003030895850000065
Is the μiA connection weight matrix of the neural network in each cluster;
Figure BDA0003030895850000066
is the external input vector of the neuron; f. ofk(·)：Rn→RnAnd k is 1, 2, 3 denotes the activation function of the neuron, among them
Figure BDA0003030895850000071
Figure BDA0003030895850000072
Figure BDA0003030895850000073
Figure BDA0003030895850000074
Figure BDA0003030895850000075
Normal number sigma1，σ2Is the coupling strength of the coupled neural network; Γ, γ denotes the internal coupling matrix of the coupled neural network, for simplicity we assume Γ, γ to be the identity matrix; tau is1(t)，τ2(t) and τ3(t) respectively represents system time-varying time lag, state coupling time-varying time lag and distributed coupling time-varying time lag, and tau is more than or equal to 01(t)≤τ1，0≤τ2(t)≤τ2，0≤τ3(t)≤τ3And defines the maximum time lag as τ ═ max { τ ═ max1(t)，τ2(t)，τ3(t)}；G＝(gij)m×mAnd D ═ D (D)ij)m×mIs an external coupling matrix based on a coupling neural network topological structure, and the matrixes G and D meet the dissipation condition, namely meet the dissipation condition
Figure BDA0003030895850000076
And
Figure BDA0003030895850000077
furthermore, if there is a connection between the ith and jth neural networks, then there is gij＝gji＞0(dij＝dji> 0), otherwise gij＝0(dij＝0)；ui(t) is a controller, which is designed in detail later.
Confirming the leader node: since the invention determines the form of leader following in each cluster, a target neural network needs to be set in each cluster as a leader. The following μiThe leader of each cluster is:
Figure BDA0003030895850000078
wherein:
Figure BDA0003030895850000079
is the state vector of the neural network,
Figure BDA00030308958500000710
is the connection weight matrix of the neural network, and exists
Figure BDA00030308958500000711
Figure BDA00030308958500000712
Figure BDA00030308958500000713
This embodies the parameter mismatch feature; at the μiAll neural networks in the individual clustering equations (equation (1)) can be considered followers of the target neural network (equation (2)).
In order to obtain more accurate results, the invention introduces a matrix measurement method, and defines a matrix measurement muq(M) is as follows
Figure BDA00030308958500000714
Wherein: i is an n-dimensional unit vector, | | · | | non-woven phosphorqQ is 1, 2, and infinity represents the induction norm. For the induced norm of the state vector of the target neural network (equation (2)), there is a constraint:
Figure BDA00030308958500000715
wherein
Figure BDA00030308958500000716
Is a normal number.
Step two: the state information of each node is obtained through a sensor, and an error vector e can be obtained based on projection synchronizationi(t)＝xi(t)-asμi(t) the state information, the normal a, is used to represent the projection factor, resulting in an error-coupled neural network with non-linearity, non-constant homocoupling, and multiple time lags as follows:
Figure BDA00030308958500000717
Figure BDA0003030895850000081
wherein:
Figure BDA0003030895850000082
Figure BDA0003030895850000083
Figure BDA0003030895850000084
Figure BDA0003030895850000085
Figure BDA0003030895850000086
Figure BDA0003030895850000087
f 3ejt ═ f3(xj (t)) -f3(as μ j (t)). By processing the error coupling neural network model, the neural network synchronization problem in each cluster can be converted into an error coupling neural network global stability problem, and the error coupling neural network model is easier to process.
Step three: defining a symbol assuming that the z-th neural network in the coupled neural network is also the j-th neural network in the i-th cluster sorted by the largest error
Figure BDA0003030895850000088
In order to realize network synchronization between the neural network (formula (1)) and the target neural network (formula (2)) in each cluster, the neural networks in each cluster are sorted into two groups according to the magnitude of state errors based on the induced norm, and the neural networks are grouped as follows:
Figure BDA0003030895850000089
Figure BDA00030308958500000810
then (a) is contained in the μiLarger induction norm in individual cluster
Figure BDA00030308958500000811
A neural network, using
Figure BDA00030308958500000812
To represent; (b) contains the muiInduced norm in individual clusterIs smaller
Figure BDA00030308958500000813
A neural network, using
Figure BDA00030308958500000814
To indicate. Is selected by
Figure BDA00030308958500000815
The inner neural network is controlled, the state information of the error coupling neural network is transmitted to the inner neural network, and a holddown pulse feedback controller is designed, and the expression of the holddown pulse feedback controller is as follows:
Figure BDA00030308958500000816
wherein: the pulse intensity rho ∈ (-2, -1) U (-1, 0), δ (·) denotes a dirac function; for the pulse signal, assume that this time series ζ ═ { t ═ t1，t2… is strictly monotonically increasing.
Consider the μiThe initial state of the neural network in each cluster (equation (1)) and the target neural network (equation (2)) can be defined as
Figure BDA00030308958500000817
Figure BDA00030308958500000818
The following neural network model with mixed time-varying time lag, nonlinearity and non-constant homocoupling can be further obtained:
Figure BDA0003030895850000091
wherein: hypothesis error state vector ei(t) is right-continuous, i.e. exists
Figure BDA0003030895850000092
Figure BDA0003030895850000093
Figure BDA0003030895850000094
At the μiWithin a cluster, if and only if for any initial state
Figure BDA0003030895850000095
And the presence of a positive parameter
Figure BDA0003030895850000096
So that the following inequality holds
Figure BDA0003030895850000097
It means that the neural network (equation (1)) is bounded cluster projection synchronized with the target neural network (equation (2)).
Bounded cluster synchronization conditions with mixed skew and nonlinear, non-constant coupled neural networks (equation (1)) under parameter mismatch conditions are discussed. All mathematical expressions are based on the lyapunov theorem of stability, the mean pulse interval, the matrix measure method and the parametric variational method. The invention utilizes the designed holdback pulse controller (formula (4)) to obtain the sufficient condition of bounded clustering projection synchronization between the neural network (formula (1)) and the target neural network (formula (2)).
Step four: based on the action of the pulse containment controller, a matrix measurement method is utilized to select the following Lyapunov functions:
Figure BDA0003030895850000098
where P is a normally positive definite matrix.
For t ═ tk，
Figure BDA00030308958500000912
According to collections
Figure BDA0003030895850000099
And collections
Figure BDA00030308958500000910
Can derive the definition of
Figure BDA00030308958500000911
Figure BDA0003030895850000101
Wherein:
Figure BDA0003030895850000102
and ρ ∈ (-2, -1) U (-1, 0), then there is
Figure BDA0003030895850000103
On the other hand, for
Figure BDA0003030895850000104
The derivation of V (t) along the trajectory of the controlled error coupling neural network (6) can be obtained
Figure BDA0003030895850000105
Based on the properties of the linearization method and the matrix measurement method, there is a normal number ω1，ω2，ω3The following inequality can be made true:
Figure BDA0003030895850000106
Figure BDA0003030895850000107
thus, the inequality (9) can be written as follows:
Figure BDA0003030895850000108
wherein:
Figure BDA0003030895850000111
Figure BDA0003030895850000112
Figure BDA0003030895850000113
Figure BDA0003030895850000114
Figure BDA0003030895850000115
Figure BDA0003030895850000116
Figure BDA0003030895850000117
there is always a synchronization error bound for the bounded synchronization phenomenon, as in inequality (9)
Figure BDA0003030895850000118
Figure BDA0003030895850000119
Based on the state constraint of the target neural network, a linearization method can be used to obtain the synchronization error:
Figure BDA00030308958500001110
by substituting the obtained synchronization error bound (equation (11)) into the inequality (10), the following equation can be obtained:
Figure BDA00030308958500001111
from the known conditions and comparative reasoning, it can be found that the function v (t) is a solution satisfying the following impulse system:
Figure BDA00030308958500001112
wherein: ε is an arbitrary value greater than zero and the function v (t) ≧ V (t).
Then, according to the parameter variation method, v (t) can be calculated as:
Figure BDA00030308958500001113
wherein: w (t, s) is according to a linear pulse system
Figure BDA00030308958500001114
The obtained Cauchy matrix is calculated by utilizing the idea of average pulse interval, and the following parameters are obtained:
Figure BDA00030308958500001115
wherein T isaIs the average pulse interval of the pulse train ζ.
Substituting cauchy matrix W (t, s) into equation (14) can be calculated as:
Figure BDA0003030895850000121
wherein:
Figure BDA0003030895850000122
Figure BDA0003030895850000123
using the above parameters, define the equation as
Figure BDA0003030895850000124
Calculate g (0) separately+) G (+ ∞) and derivativesg' (λ), the calculation is as follows:
Figure BDA0003030895850000125
g(+∞)＞0，#
Figure BDA0003030895850000126
the above results show that g (λ) monotonically increases over the interval (0, + ∞) and that there is only one unique solution within this interval. For the
Figure BDA0003030895850000127
There is the following formula:
Figure BDA0003030895850000128
next, it is confirmed that the inequality (16) is satisfied under the condition of t > 0, and it is noted that t is present even if the inequality (16) is not satisfied under the condition of t > 0*> 0 such that the inequality (16) is greater than 0 < t*The conditions are true.
Substituting the inequality (16) into the inequality (15) yields the following equation:
Figure BDA0003030895850000129
Figure BDA0003030895850000131
let ε → 0 in the above formula, so that for t > 0, there are further results:
Figure BDA0003030895850000132
this indicates that the controlled error coupling neural network (equation (6)) can achieve exponential synchronization within the synchronization error bound, which can be written as:
Figure BDA0003030895850000133
therefore, under the action of the holddown pulse controller (equation (5)), the bounded clustering projection synchronization can be finally realized between the coupling neural network (equation (1)) and the target neural network (equation (2)) at the convergence speed of lambda. In particular, a function is constructed
Figure BDA0003030895850000134
The derivative of which gives a maximum value of f (γ) in the range of (0, 1) is:
Figure BDA0003030895850000135
in other words, when
Figure BDA0003030895850000136
The synchronization error bound reaches its minimum value. The synchronous error margin can be adjusted only by selecting proper pulse frequency
Figure BDA0003030895850000137
Thereby obtaining a smaller synchronization error bound.
The following conclusions can therefore be drawn:
for impulse effect ζ ═ t1，t2… }, and assuming that the average pulse interval is less than Ta. Exist of
Figure BDA0003030895850000138
Figure BDA0003030895850000139
Figure BDA0003030895850000141
Figure BDA0003030895850000142
Figure BDA0003030895850000143
Figure BDA0003030895850000144
Make inequality
Figure BDA0003030895850000145
That is, the bounded clustering projection synchronization between the coupled neural network (equation (1)) and the target neural network (equation (2)) can be finally realized with the convergence speed of λ under the action of the holdback pulse controller (equation (5)), wherein the synchronization error bound can be expressed as:
Figure BDA0003030895850000146
the synchronization effect between the target neural network and other neural networks is verified by building a network model and performing numerical simulation by using the network model.
Example 2
In order to verify the correctness of the method in embodiment 1, a network model is built for simulation verification. The neural network is a network mathematical model for constructing a structure similar to the brain neuron connection for information processing, and data can be processed by utilizing the nonlinear mapping capability of the neural network. Meanwhile, the method can be realized by applying power electronic devices, for example, in a memristive neural network, a closed loop simulated neuron circuit is formed by using a transistor, a resistor and a capacitor, and synaptic connections of the neural network are simulated by using nonlinear devices such as a memristor and a memristor, a memristor and the like, and the method comprises the following specific steps:
step 1: the coupled neural network model is determined as follows:
Figure BDA0003030895850000147
wherein:
Figure BDA0003030895850000148
Figure BDA0003030895850000149
Figure BDA00030308958500001410
Figure BDA00030308958500001411
Figure BDA00030308958500001412
Figure BDA00030308958500001413
ω1＝ω2＝ω3＝1，σ1＝σ2＝0.4，
Figure BDA00030308958500001414
selecting the activation function as f1(u)＝f2(u)＝f3(u)＝tanh(u)。
Selecting a neural network with ideal parameters as a synchronous target, and determining a target neural network model as follows:
Figure BDA00030308958500001415
wherein:
Figure BDA0003030895850000151
Figure BDA0003030895850000152
Figure BDA0003030895850000153
Figure BDA0003030895850000154
Figure BDA0003030895850000155
Figure BDA0003030895850000156
in order to verify the correctness of the present invention, a coupled neural network composed of 6 neural networks is selected, as shown in fig. 1, wherein the numbers 1, 2, 3, 4, 5, 6 represent 6 neural networks and are divided into two clusters, and the selection scheme of a specific controlled object is that when the coupled neural network is operated, one neural network with a larger error norm is selected from the two clusters at each pulse time according to the pulse sequence, and the error feedback information in the controller is applied to the two neural networks.
Step 2: according to the known method, selecting a coupling matrix
G=
[-2，1，1，0，0，0；1，-2，1，0，0，0；1，1，-3，1，0，0；0，1，-3，1，1；0，0，0，1，-2，1；0，0，0，1，1，-2]. In addition, the pulse sequence
Figure BDA0003030895850000158
As shown in fig. 2, and assuming an average pulse interval PaNot more than 0.02, and the pulse control intensity is rho 1.2.
And step 3: constructing a Simulink model of the coupling neural network (1), obtaining a simulation result, and defining the synchronous error of the neural network
Figure BDA0003030895850000157
Fig. 3-fig. 4 are obtained, which show that the error between any two nodes in two clusters is within the synchronization error bound, i.e. the bounded cluster projection synchronization is realized. Meanwhile, each state change curve of each neural network in two clusters is given in fig. 4, and it can be seen from fig. 5 to 8 that due to the existence of non-constant and parameter mismatching characteristics, not only the state of the neural networks in different clusters has a deviation, but also the states of different neural networks in the same cluster have a deviation, but under the action of the holdback pulse controller, the state errors can be controlled within a certain range.
Example 3
Based on the same inventive concept, the embodiment provides a coupling neural network bounded clustering projection synchronous regulation control system, and the principle of solving the problem is similar to the coupling neural network bounded clustering projection synchronous regulation control method, and is not repeated.
The control system includes: the building module is used for building a coupling neural network with a plurality of clusters of nonlinearity, non-constant and mixed time-varying time lag, and setting a target neural network for each cluster; the setting module is used for establishing an error coupling neural network according to the coupling neural network and a target neural network; the cluster synchronization module is used for designing a containment pulse feedback controller according to the error coupling neural network model and selecting a corresponding function based on the containment pulse feedback controller so as to realize bounded cluster projection synchronization between the neural network and a target neural network in each cluster; and the simulation module is used for verifying the bounded clustering projection synchronization effect between the target neural network and the coupling neural network by building a network model and performing numerical simulation by using the network model.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.

Claims (10)

1. The bounded clustering projection synchronous regulation control method of the coupling neural network is characterized by comprising the following steps:
the method comprises the following steps: establishing a coupling neural network with a plurality of clusters of non-linearity, non-constant and mixed time-varying time lag, and setting a target neural network for each cluster;
step two: establishing an error coupling neural network according to the coupling neural network and a target neural network;
step three: designing a containment pulse feedback controller according to the error coupling neural network model, and selecting a corresponding function based on the containment pulse feedback controller so as to realize bounded clustering projection synchronization between a neural network and a target neural network in each cluster;
step four: and verifying the bounded clustering projection synchronization effect between the target neural network and the coupling neural network by building a network model and performing numerical simulation by using the network model.
2. The coupled neural network bounded clustered projection synchronous tuning control method as claimed in claim 1, wherein the model of the coupled neural network is:
Figure FDA0003030895840000011
wherein:
Figure FDA0003030895840000012
is the state vector of the node; n neural networks are divided into l clusters, N is more than or equal to l and is more than 0, and the ith neural network and the jth neural network define mu in the zth clusteri＝μjZ, otherwise, is mui≠μj；
Figure FDA0003030895840000013
Is the μiA connection weight matrix of the neural network in each cluster;
Figure FDA0003030895840000014
is the external input vector of the neuron; f. ofk(·)：Rn→RnAnd k is 1, 2, 3 denotes the activation function of the neuron, among them
Figure FDA0003030895840000015
Figure FDA0003030895840000016
Normal number sigma1，σ2Is the coupling strength of the coupled neural network; gamma, gamma represents an internal coupling matrix of the coupling neural network, and gamma is an identity matrix; tau is1(t)，τ2(t) and τ3(t) respectively represents system time-varying time lag, state coupling time-varying time lag and distributed coupling time-varying time lag, and tau is more than or equal to 01(t)≤τ1，0≤τ2(t)≤τ2，0≤τ3(t)≤τ3And defines the maximum time lag as τ ═ max { τ ═ max1(t)，τ2(t)，τ3(t)}；G＝(gij)m×mAnd D ═ D (D)ij)m×mIs an external coupling matrix based on a coupling neural network topological structure, and the matrixes G and D meet the dissipation condition, namely meet the dissipation condition
Figure FDA0003030895840000021
And
Figure FDA0003030895840000022
if there is a connection between the ith neural network and the jth neural network, then there is gij＝gji＞0(dij＝dji> 0), otherwise gij＝0(dij＝0)；uiAnd (t) is a controller.
3. The coupled neural network bounded clustered projection synchronous tuning control method as claimed in claim 1, wherein the model of the target neural network is:
Figure FDA0003030895840000023
wherein:
Figure FDA0003030895840000024
is the state vector of the neural network,
Figure FDA0003030895840000025
is a connection weight matrix of the neural network, and exists
Figure FDA0003030895840000026
4. The coupled neural network bounded cluster projection synchronization regulation control method of claim 3, wherein a matrix measure μ is definedq(M)：
Figure FDA0003030895840000027
Wherein: i is an n-dimensional unit vector, | | · | | non-woven phosphorqQ is 1, 2, infinity, representing an induced norm for which there is a constraint:
Figure FDA0003030895840000028
wherein
Figure FDA0003030895840000029
Is a normal number.
5. The coupled neural network bounded clustered projection synchronous tuning control method as claimed in claim 1, wherein the model of the error coupled neural network is:
Figure FDA00030308958400000210
wherein:
Figure FDA00030308958400000211
Figure FDA0003030895840000031
Figure FDA0003030895840000032
ei(t)＝xi(t)-asμi(t) is the error vector and the normal a is used to represent the projection factor.
6. The coupled neural network bounded cluster projection synchronization regulation control method of claim 1, wherein at μ ™ theiWithin a cluster, if and only if for any initial state
Figure FDA0003030895840000033
Presence of positive parameters
Figure FDA0003030895840000034
So that the following inequality holds
Figure FDA0003030895840000035
7. The coupled neural network bounded clustered projection synchronous tuning control method as claimed in claim 5, wherein the definition is
Figure FDA0003030895840000036
Obtain the following mixed time-varying time-lag, nonlinear and non-constant error couplingCombining neural network models:
Figure FDA0003030895840000037
wherein: hypothesis error state vector ei(t) is right-continuous, present
Figure FDA0003030895840000038
Figure FDA0003030895840000039
8. The coupled neural network bounded cluster projection synchronous regulation control method of claim 1, wherein the holdback pulse feedback controller expression is:
Figure FDA00030308958400000310
wherein: the pulse intensity rho ∈ (-2, -1) U (-1, 0), δ (·) denotes a dirac function; for a pulse signal, the time series ζ ═ { t ═ t1，t2… is strictly monotonically increasing.
9. The coupled neural network bounded clustering projection synchronous regulation control method as claimed in claim 1, wherein the function is a lyapunov function, and the expression is:
Figure FDA0003030895840000041
where P is a normally positive definite matrix.
10. A coupled neural network bounded clustered projection synchronous regulation control system applied to the method of any one of claims 1 to 9, comprising:
the building module is used for building a coupling neural network with a plurality of clusters of nonlinearity, non-constant and mixed time-varying time lag, and setting a target neural network for each cluster;
the setting module is used for establishing an error coupling neural network according to the coupling neural network and a target neural network;
the cluster synchronization module is used for designing a containment pulse feedback controller according to the error coupling neural network model and selecting a corresponding function based on the containment pulse feedback controller so as to realize bounded cluster projection synchronization between the neural network and a target neural network in each cluster;
and the simulation module is used for verifying the bounded clustering projection synchronization effect between the target neural network and the coupling neural network by building a network model and performing numerical simulation by using the network model.
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