CN115128954A - Global projection synchronization method of quaternion memristive neural network based on open-loop control and application of global projection synchronization method - Google Patents
Global projection synchronization method of quaternion memristive neural network based on open-loop control and application of global projection synchronization method Download PDFInfo
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Abstract
The invention belongs to the field of memristive neural networks and secret communication, and particularly relates to a global projection synchronization method of a quaternion memristive neural network based on open-loop control and application thereof. The method is different from the traditional method that the system is separated into a real number system and three complex number systems, but the system is considered as a whole to be researched. Meanwhile, a corresponding driving system and a corresponding response system are established by utilizing a discrete multi-time-lag memristive neural network, and an open-loop controller is designed, so that an encrypted plaintext signal can be transmitted in a channel to achieve a better security effect. Compared with the traditional chaotic neural network, the chaotic neural network has better confidentiality effect and lower network energy consumption, and provides a better solution for encrypted communication.
Description
Technical Field
The invention relates to the field of memristive neural networks and secret communication, in particular to a global projection synchronization method of a quaternion memristive neural network based on open-loop control and application thereof.
Background
Nowadays, with the arrival of the world of everything interconnection, communication technology is rapidly developed, and further, requirements on security and confidentiality of communication are higher and higher, while existing communication or encryption means have certain defects, and therefore, a new communication encryption method needs to be developed continuously to achieve high reliability. The chaotic signal has the characteristics of wide spectrum, strong nonlinearity, non-periodicity, noise-like property and the like, and is used for secret communication in the 90 s of the 20 th century. In 1983, professor of Chua begonia proposed a famous Chua's circuit and opened up the precedent of the theory of chaotic communication. In 1990, Pecora and Carroll of the U.S. naval laboratory firstly proposed chaotic synchronization based on a drive-response synchronization method, then people's research on chaotic secure communication enters a new stage, and a plurality of new synchronization methods, security technologies and the like are proposed, and in recent years, ultrahigh-dimensional memristive chaotic circuits and systems become research hotspots and new fields of scholars.
Memristors are considered a fourth type of passive circuit element, whose novel circuit elements have many features. In the aspect of practical value, the application of the memristor mainly comprises: novel non-volatile, secure communication and neural networks. Researchers find memristors to resemble neurons in the human brain, and due to this characteristic, more and more researchers build neural networks based on memristors, study the dynamic behavior of the neural networks by simulating the human brain with memristors instead of resistors. Therefore, the memristor and the neural network are combined to be applied to secret communication, and the secret performance can be greatly improved.
In the past decades, real-valued neural networks (RVNN) and complex-valued neural networks (CVNN) have been widely used in the fields of signal processing, associative memory, automatic intelligent control, etc. due to their respective characteristics. However, CVNN and RVNN have certain limitations when dealing with multidimensional data. In view of this, some researchers have proposed a quaternion neural network (QVNN) that can be used to process multidimensional data. Therefore, it is necessary to study the dynamic behavior of the QVNN. Meanwhile, the memristor does not consume energy and has a memory characteristic, so that the memristor has important practical significance for the research of the quaternary memristor neural network.
Since, in secure communication, the transmitted signal needs to be transformed without distortion after being transmitted to the receiving end, this leads to the concept of synchronization. The essence of synchronous control is to force one system to track the other by applying the appropriate controller.
So far, the synchronization of the neural network has been successfully applied to many fields such as secret communication, public channel cryptography, neurocryptography, etc., and the synchronization of the chaotic system and the neural network has become an important research field. Meanwhile, the research results in synchronization are also many, including projection synchronization, desynchronization, phase synchronization, full synchronization, exponential synchronization, Mittag-Leffler synchronization and the like. The projection synchronization means that the neural network can be synchronized to a scale factor, which indicates that different types of synchronization can be realized by selecting different projection coefficients. When the projection coefficients take 1, 0 and-1, full synchronization, stabilization and desynchronization can be achieved, respectively.
Disclosure of Invention
In order to achieve the above object, the present invention provides a global projection synchronization method of a quaternion memristive neural network based on open-loop control, the synchronization method includes the following steps:
s1: describing a discrete multi-time-lag quaternary memristive neural network;
s2: designing an open-loop controller;
s3: implementation of a communication encryption scheme.
To be further explained, the S1 specifically includes:
establishing a discrete multi-time-lag quaternary memristor neural network driving system:
wherein D α Notation indicating fractional order derivative, alpha indicating order, 0<α<1；x i (t)＝(x 1 (t),...,x n (t)) T Representing the state variable of the ith neuron, c i Is a normal number, τ j For discrete time delays, I i Representing an external input vector as a constant vector, f i (. and g) i (. is a non-linear activation function, a ij (x j (t)) and b ij (x j (t)) is the connecting memristor weight, and takes the following values:
establishing a discrete multi-time-lag quaternary memristor neural network response system:
wherein D α Notation indicating fractional order derivative, alpha indicating order, 0<α<1; representing the state variable of the ith neuron, c i Is a normal number, τ j For discrete time delays, I i Representing an external input vector as a constant vector, f i (. and g) i (. is) a non-linear activation function, a ij (x j (t)) and b ij (x j (t)) is the weight of the connected memristors, and the value is the same as the drive x i (t)＝(x 1 (t),...,x n (t)) T System, U i (t) is the controller to be designed.
To be further explained, the S2 specifically includes:
constructing an error function
Fourthly, designing a controller.
To be further explained, the constructive error function is specifically:
the error function is defined as: e.g. of the type i (t)＝y i (t)-βx i (t), wherein i ═ 1, 2.., n, β ∈ R denote projection factors reflecting the synchronous proportionality between the drive and response networks;
the controller is specifically designed as follows:
selecting the following controllers: u shape i (t)＝U i1 (t)+U i2 (t)+U i3 (t)
Wherein k is 1 ＝k 2 2 is an arbitrary normal number, and β 2 is a projection coefficient.
To be further explained, the step S3 specifically includes:
because the signals processed in the computer are all binary signals, the communication content needs to be discretized into binary bit stream signals M s (k) Driving the discretization state of the system, and modulating the signals to obtain a modulation signal C s (k)。
Will X i (k) And C s (k) Transmitting from the transmitting end to the receiving end, i.e. the response system is designed with X received by the synchronous controller i (k) Y with response system i (k) Acquisition is carried out, and then the state of the response system is adjusted to be consistent and synchronous with the state of the drive system, i.e. the state of the response system is adjusted
The communication signal is then demodulated from C s (k) Is separated out to obtain a decrypted signal R s (k) Due to X i (k) And Y i (k) Are synchronized, therefore M s (k)＝R s (k) This completes the complete process of secure communication.
The application of the global projection synchronization method based on the open-loop control quaternion memristive neural network in secret communication is further explained.
In the technical scheme, the invention provides the following technical effects and advantages:
different from the traditional separation technology, the invention takes the fractional order quaternion memristor neural network (FOQVMNN) as a whole, thereby greatly reducing the energy consumption of the system. Meanwhile, a quaternion neural network (QVNN) is provided on the basis of a Real Value Neural Network (RVNN) and a Complex Value Neural Network (CVNN) for processing high-dimensional data, and the confidentiality is improved.
To avoid decomposing the QVNN into two CVNNs or four RVNNs, a new quaternion-sign function is introduced on the basis of the real and complex-sign functions. Meanwhile, a novel open-loop controller is designed to ensure the global projection synchronization criterion of the FOQVMNN with multiple delays, and the FOQVMNN is applied to the field of secret communication, so that the complexity of a secret communication system is greatly improved, and the cracking difficulty of the system is improved.
A new 1-norm Lyapunov function is established on the basis of a quaternion symbolic function. In addition, based on the designed open-loop controller and the proposed theorem, some sufficient conditions for guaranteeing the global projection synchronization of the system are given.
The invention has wider application range and can be used for transmitting sound, characters, pictures, videos and the like in a secret way.
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In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
FIG. 1 is a block diagram of the general architecture of encrypted communications;
FIG. 2 is a flowchart of a global projection synchronization method design of a fractional quaternion memristive neural network based on open-loop control in implementation 2 of the present invention;
FIG. 3a shows x without open-loop controller in the embodiment 2 of the present invention 1 (t) and y 1 (t) a real part diagram of the trace plot;
FIG. 3b shows x without open-loop controller in the embodiment 2 of the present invention 1 (t) and y 1 (t) an imaginary diagram of the trajectory diagram;
FIG. 3c shows x without open-loop controller in embodiment 2 of the present invention 1 (t) and y 1 (t) an imaginary diagram of the trajectory diagram;
FIG. 3d shows x without open-loop controller in the embodiment 2 of the present invention 1 (t) and y 1 (t) an imaginary diagram of the trajectory diagram;
FIG. 4a shows x without open-loop controller in the embodiment 2 of the present invention 2 (t) and y 2 (t) a real part diagram of the trace plot;
FIG. 4b shows x without open-loop controller in the embodiment 2 of the present invention 2 (t) and y 2 (t) an imaginary diagram of the trajectory diagram;
FIG. 4c shows x without open-loop controller in the embodiment 2 of the present invention 2 (t) and y 2 (t) an imaginary diagram of the trajectory diagram;
FIG. 4d shows x without open-loop controller in the embodiment 2 of the present invention 2 (t) and y 2 (t) an imaginary diagram of the trajectory diagram;
FIG. 5 is a state diagram of an error system without an open-loop controller in accordance with embodiment 2 of the present invention;
FIG. 6a shows x under the open-loop controller in the embodiment 2 of the present invention 1 (t) and y 1 (t) a real part diagram of the trace plot;
FIG. 6b shows x under the open-loop controller in the embodiment 2 of the present invention 1 (t) and y 1 (t) an imaginary diagram of the trajectory diagram;
FIG. 6c is a schematic representation of the present inventionImplementation 2 x under the open-loop controller 1 (t) and y 1 (t) an imaginary diagram of the trajectory diagram;
FIG. 6d shows x under the open-loop controller in the embodiment 2 of the present invention 1 (t) and y 1 (t) an imaginary diagram of the trajectory diagram;
FIG. 7a shows x under the open-loop controller in the embodiment 2 of the present invention 2 (t) and y 2 (t) a real part diagram of the trace plot;
FIG. 7b shows x under the open-loop controller in embodiment 2 of the present invention 2 (t) and y 2 (t) an imaginary diagram of the trajectory diagram;
FIG. 7c shows x under the open-loop controller in the embodiment 2 of the present invention 2 (t) and y 2 (t) an imaginary diagram of the trajectory diagram;
FIG. 7d shows x under the open-loop controller in the embodiment 2 of the present invention 2 (t) and y 2 (t) an imaginary diagram of the trajectory diagram;
fig. 8 is a state trajectory diagram of an error system with an open-loop controller added in embodiment 2 of the present invention.
Detailed Description
In order to make the technical solution and implementation of the present invention more clearly explained and illustrated, several preferred embodiments for implementing the technical solution of the present invention are described below.
The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses. It should be understood that throughout the drawings, identical or similar reference numerals indicate identical or similar parts and features. The drawings are only schematic representations of the concepts and principles of the embodiments of the disclosure, and do not necessarily show specific dimensions or proportions of the various embodiments of the disclosure. While certain features of the present disclosure and certain embodiments thereof may be shown in exaggerated form in particular drawing to illustrate relevant details or structures of embodiments of the present disclosure, the various publications, patents, and published patent specifications cited herein, the disclosures of which are incorporated herein by reference in their entirety, are hereby expressly and completely described in connection with the embodiments of the present disclosure, it being understood that the embodiments described are only some examples of the invention.
Example 1
The embodiment provides a global projection synchronization method of a quaternion memristive neural network based on open-loop control, which is used for realizing that a driving network and a response network of a fractional order quaternion memristive neural network system achieve global projection synchronization, and the projection e i The (t) synchronization method comprises the following specific steps:
firstly, defining an error function of a system, and enabling:
e i (t)＝y i (t)-βx i (t)
wherein x is i (t) represents a state variable of the drive system; y is i (t) state variables of the response system; beta represents a projection factor reflecting the synchronous proportional relationship between the drive system and the response system.
Secondly, designing an open-loop controller U i (t) is:
U i (t)＝U i1 (t)+U i2 (t)+U i3 (t)
wherein k is i Representing the gain of the controller.
In this embodiment, a driving system model of the fractional order quaternion memristive neural network is as follows:
wherein D α Notation indicating fractional order derivative, alpha indicating order, 0<α<1；x i (t)＝(x 1 (t),...,x n (t)) T Representing the state variable of the ith neuron, c i Is a normal number, τ j For discrete time delays, I i Representing an external input vector as a constant vector, f i (. and g) i (. is a non-linear activation function, a ij (x j (t)) and b ij (x j (t)) is the connection memristance weight.
In this embodiment, a response system model of the fractional order quaternion memristive neural network is:
wherein D α Notation indicating fractional order derivative, alpha indicating order, 0<α<1；x i (t)＝(x 1 (t),...,x n (t)) T Representing the state variable of the ith neuron, c i Is a normal number, τ j For discrete time delays, I i Representing an external input vector as a constant vector, f i (. and g) i (. is a non-linear activation function, a ij (x j (t)) and b ij (x j (t)) is the connecting memristive weight, U i (t) is the controller to be designed.
Example 2
The present embodiment mainly includes two parts:
the first part is to theoretically prove the effectiveness of the designed synchronous controller in the projection synchronization method for providing the fractional quaternion memristive neural network in the embodiment 1.
And the second part is that the theoretical analysis of the first part is simulated and verified by a numerical simulation method.
(theoretical proof and simulation experiment are not used to limit the invention, simulation experiment may not be performed in other embodiments, or other experimental schemes may be used to perform experiments to verify the performance of the neural network system.)
First, theoretical demonstration
1. The condition is assumed as follows:
first, the general study on projection synchronization of a quaternary memristive neural network generally divides the system into four subsystems, including one real part system and three imaginary part systems. Since the quaternion sign function and the associated fractional order inequality are introduced herein, the system need not be divided into four subsystems, but rather the system is considered as a whole for study.
Secondly, considering the discontinuity of memristive weights, in the sense of the filiopov solution, according to the differential inclusion and extremum mapping theory, we can obtain a drive-response system and an error system as follows:
a driving system:
the response system:
error system:
Wherein
Wherein, T j Indicating a handover jump time, T j >0。
For a drive network and a response network of any system, if global projection synchronization needs to be achieved through a designed open-loop controller, the following conditions need to be met:
H 1 -vH 2 >0
wherein v >1
2. Proof of derivation
Constructing a Lyapunov function as:
according to
Is provided with
And (3) according to the nature of quaternion, obtaining the following inequalities:
by Lipschitz conditions:
|f i (x)-f i (x’)| 1 ≤F i |x-x’| 1
|g(x)-g i (x’)| 1 ≤G i |x-x’| 1
comprises the following steps:
wherein
The four parts are arranged to obtain:
according to the fractional order Razumikhin theorem, the method comprises the following steps:
D α V(t)≤-H 1 V(t)+H 2 V(t-τ j )≤-(H 1 -vH 2 )V(t)
wherein
In summary, the synchronization method provided by this embodiment can implement global projection synchronization of the fractional order quaternion memristive neural network.
Two, numerical simulation
In this embodiment, taking a two-dimensional fractional quaternion memristive neural network system with multiple time lags as an example, a model for determining a driving system of the neural network system is:
wherein
The memristive connection weight of the quaternion value satisfies:
meanwhile, the model of the response system of the corresponding two-dimensional fractional order quaternion memristor neural network system with multiple time lags is as follows:
wherein, the values of part of parameters are as follows: the projection coefficient beta is 2, and the gain k is controlled 1 ＝k 2 2, v 1.2 was chosen, and the Lipschitz constant was taken to be N i ＝M i 1, (i) 1,2) to ensure H 1 -vH 2 >And 0, the values of other parameters are consistent with those in the driving system.
Fig. 2 is a flowchart of a global projection synchronization method of a fractional order quaternion memristive neural network based on open-loop control in embodiment 1 of the present disclosure; FIG. 3 shows x without open-loop controller in embodiment 2 of the present invention 1 (t) and y 1 (t) (the graph comprises a real part graph and three imaginary parts graphs, wherein the real part graph is shown in figure 3a, and the three imaginary parts graphs are shown in figures 3b, 3c and 3 d); FIG. 4 shows x without open-loop controller in embodiment 2 of the present invention 2 (t) and y 2 (t) (the graph comprises a real part graph and three imaginary parts graphs, wherein the real part graph is shown in figure 4a, and the three imaginary parts graphs are shown in figures 4b, 4c and 4 d); FIG. 5 is a state diagram of an error system without an open-loop controller in accordance with embodiment 2 of the present invention; FIG. 6 shows x in embodiment 2 of the present invention with an open-loop controller added 1 (t) and y 1 (t) (the graph comprises a real part graph and three imaginary parts graphs, the real part graph is shown in figure 6a, and the three imaginary parts graphs are shown in figures 6b, 6c and 6 d); FIG. 7 shows the addition of ring opening in the practice 2 of the present inventionX under controller 2 (t) and y 2 (t) (the graph comprises a real part graph and three imaginary parts graphs, wherein the real part graph is shown in figure 7a, and the three imaginary parts graphs are shown in figures 7b, 7c and 7 d); fig. 8 is a state trajectory diagram of an error system with an open-loop controller added in embodiment 2 of the present invention.
By combining the above, the change trend of the curve in the simulation result obtained from the simulation experiment can be found out as follows: the fractional order quaternion memristor neural network provided by the embodiment can realize global projection synchronization of a system under an open-loop controller.
Example 3
The embodiment is based on the embodiment 2, namely, the driving-response system is realized to achieve global projection synchronization, and the driving-response system is applied to secret communication.
As shown in fig. 1, in a communication system having a signal sending end, a signal receiving end, and a channel, a method for implementing secure communication by using a fractional order quaternion memristive neural network system is as follows:
because the signals processed in the computer are all binary signals, the communication content needs to be discretized into binary bit stream signals M s (k) Driving the discretization state of the system, and modulating the signals to obtain a modulation signal C s (k)。
Will X i (k) And C s (k) Transmitting from the transmitting end to the receiving end, i.e. the response system is designed with X received by the synchronous controller i (k) Y with responsive system i (k) The acquisition is carried out, and then the state of the response system is adjusted to be consistent and synchronous with the state of the driving system.
The communication signal is then demodulated from C s (k) Is separated out to obtain a decrypted signal R s (k) Due to X i (k) And Y i (k) In synchronism, therefore C s (k)＝R s (k)。
While certain exemplary embodiments of the present invention have been described above by way of illustration only, it will be apparent to those of ordinary skill in the art that the described embodiments may be modified in various different ways without departing from the spirit and scope of the present invention. Accordingly, the drawings and description are illustrative in nature and should not be construed as limiting the scope of the invention.
Claims (6)
1. A global projection synchronization method of a quaternion memristive neural network based on open-loop control is characterized by comprising the following steps: the synchronization method comprises the following steps:
s1: describing a discrete multi-time-lag quaternary memristive neural network;
s2: designing an open-loop controller;
s3: implementation of a communication encryption scheme.
2. The global projection synchronization method of the open-loop control-based quaternion memristive neural network is characterized by comprising the following steps of: the S1 specifically includes:
establishing a discrete multi-time-lag quaternary memristor neural network driving system:
wherein D α Notation indicating fractional derivative, alpha indicating order, 0<α<1；x i (t)＝(x 1 (t),...,x n (t)) T Representing the state variable of the ith neuron, c i Is a normal number, tau j For discrete time delays, I i Representing an external input vector as a constant vector, f i (. and g) i (. is a non-linear activation function, a ij (x j (t)) and b ij (x j (t)) is the connecting memristor weight, and takes the following values:
establishing a discrete multi-time-lag quaternary memristor neural network response system:
wherein D α Notation indicating fractional order derivative, alpha indicating order, 0<α<1; representing the state variable of the ith neuron, c i Is a normal number, τ j For discrete time delays, I i Representing an external input vector as a constant vector, f i (. and g) i (. is a non-linear activation function, a ij (x j (t)) and b ij (x j (t)) is the weight of the connecting memristor, which takes the same value as the drive x i (t)＝(x 1 (t),...,x n (t)) T System, U i (t) is the controller to be designed.
3. The global projection synchronization method of the open-loop control-based quaternion memristive neural network is characterized by comprising the following steps of: the S2 specifically includes:
constructing an error function
And fourthly, designing a controller.
4. The global projection synchronization method of the open-loop control-based quaternion memristive neural network, according to claim 3, is characterized in that:
constructing an error function specifically as follows:
the error function is defined as: e.g. of the type i (t)＝y i (t)-βx i (t), wherein i ═ 1, 2.., n, β ∈ R denote projection factors reflecting the synchronous proportionality between the drive and response networks;
the controller is specifically designed as follows:
selecting the following controllers:
wherein k is 1 ＝k 2 2 is an arbitrary normal number, and β 2 is a projection coefficient.
5. The global projection synchronization method of the open-loop-control-based quaternion memristive neural network is characterized by comprising the following steps of: the step S3 specifically includes:
because the signals processed in the computer are all binary signals, the communication content needs to be discretized into binary bit stream signals M s (k) Driving the discretization state of the system, and modulating the signals to obtain a modulation signal C s (k)；
Will X i (k) And C s (k) Transmitting from the transmitting end to the receiving end, i.e. the response system is designed with X received by the synchronous controller i (k) Y with response system i (k) Acquisition is performed and then the state of the response system is adjusted to be in consistent synchronization with the state of the drive system, i.e.
The communication signal is then demodulated from C s (k) Is separated out to obtain a decrypted signal R s (k) Due to X i (k) And Y i (k) Synchronous, hence M s (k)＝R s (k) This completes the complete process of secure communication.
6. The application of the global projection synchronization method based on the open-loop control quaternion memristive neural network according to any one of claims 1 to 5 in secret communication.
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| CN117335957A (en) * | 2023-10-10 | 2024-01-02 | 盐城工学院 | Secret communication method for BAM memristor neural network correction function projection synchronization |
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| CN115860075A (en) * | 2022-12-08 | 2023-03-28 | 盐城工学院 | Synchronous control method of fractional order memristor neural network |
| CN115903511A (en) * | 2022-12-08 | 2023-04-04 | 盐城工学院 | Self-adaptive index synchronous control method of random memristor neural network |
| CN115903511B (en) * | 2022-12-08 | 2023-05-19 | 盐城工学院 | Self-adaptive index synchronous control method for random memristor neural network |
| CN116203838A (en) * | 2022-12-08 | 2023-06-02 | 盐城工学院 | Finite time synchronization control method for fractional order memristor neural network |
| CN117335957A (en) * | 2023-10-10 | 2024-01-02 | 盐城工学院 | Secret communication method for BAM memristor neural network correction function projection synchronization |
| CN117335957B (en) * | 2023-10-10 | 2024-03-26 | 盐城工学院 | Secret communication method for BAM memristor neural network correction function projection synchronization |
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