CN115145156A - Self-adaptive anti-synchronization method of inertia memristor neural network - Google Patents
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Abstract
The invention provides a self-adaptive anti-synchronization method of an inertia memristor neural network, which comprises the following steps: step S1: establishing a driving system and a response system of the inertial memristor neural network with unbounded distributed time lag based on the inertial memristor neural network; step S2: establishing an anti-synchronization error system according to the driving system and the response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1; and step S3: the adaptive controller is designed so that the drive system and the response system are desynchronized. The invention can realize the self-adaptive desynchronization of the inertial memristor neural network without boundary distribution time lag.
Description
Technical Field
The invention relates to the field of information and communication science, in particular to a self-adaptive anti-synchronization method of an inertial memristor neural network.
Background
The resistance of the memristor is determined by the charge flowing through the memristor, so that the charge flowing through the memristor can be obtained by measuring the resistance of the memristor, and the memory function of the memristor is realized. Based on the characteristics of the memristor, the memristor neural network very suitable for simulating the human brain is constructed by replacing the resistor in the traditional neural network circuit. In recent years, the advantages of memristive neural networks have been gradually shown, and have been of high interest to scientists.
The anti-synchronization is an important dynamic behavior in the memristor neural network, and has important application prospects in the aspects of artificial intelligence cooperative control, safety communication and the like. The desynchronization of the memristive neural network can also be applied to the field of information security, such as: image encryption and associative memory. Therefore, the research on the self-adaptive desynchronization method of the inertial memristor neural network with unbounded distributed time lag is a piece of positive work.
Disclosure of Invention
In view of this, the present invention provides an adaptive desynchronization method for an inertial memristive neural network, which can implement adaptive desynchronization of the inertial memristive neural network with unbounded distributed time lag.
The invention is realized by adopting the following scheme: an adaptive anti-synchronization method of an inertial memristive neural network comprises the following steps:
step S1: establishing a driving system and a response system of the inertial memristor neural network with unbounded distributed time lag based on the inertial memristor neural network;
step S2: establishing an anti-synchronization error system according to the driving system and the response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1;
and step S3: the adaptive controller is designed to make the driving system and the response system achieve adaptive desynchronization.
Further, step S1 specifically includes:
step S11: establishing a state equation of a driving system of an inertial memristive neural network with unbounded distributed time lag:
step S12: establishing a state equation of a response system of an inertial memristive neural network with unbounded distributed time lag:
wherein x is i (t) and y i (t) represents the state variable, α, for the ith neuron at time t i ，β i Is constant and satisfies a i >0，β i >0，f j (x j (t)) and f j (y j (t)) represents the activation function of the jth neuron, τ j (t) is time lag, K pq (t)：
Is a non-negative delay core real value function of unbounded distribution time lag, and the initial value of the driving system (1) satisfies x i (s)＝φ i (s)，
Initial value of response system (2) is satisfied
Wherein a is ij (x i (t))，b ij (x i (t))，c ij (x i (t))，a ij (y i (t))，b ij (y i (t))，c ij (y i (t)) represents memristor weights, satisfying:
wherein, the first and the second end of the pipe are connected with each other,
is to switch threshold values and
further, step S2 specifically includes:
step S21: setting the desynchronization error of the driving system and the response system as follows:
e i (t)＝y i (t)+x i (t) (4)
obtaining an anti-synchronization error system (5):
further, step S3 specifically includes:
step S31: the expression of the constructed adaptive controller is as follows:
wherein, γ i (t) and xi i (t) is the control gain(s),
ρ i >0，m i the (t) is specifically:
the adaptive controller (6) is brought into the desynchronization error system (5), and two conditions of the desynchronization error system (5) are obtained:
(1) When in use
Or
Obtaining an anti-synchronization error system (7):
(2) When in use
Or
Obtaining an anti-synchronization error system (8):
according to the above cases (1) and (2), an anti-synchronization error system (9) is obtained:
in the formula (f) j (e j (t))＝f j (x j (t))+f j (y j (t))，f j (e j (t-τ j (t)))＝f j (x j (t-τ j (t))+f j (y j (t-τ j ())))。
The invention is based on Lyapunov stability theory, combines with self-adaptive controller, and proves the desynchronization of the driving system and the response system, which specifically comprises the following steps:
the specific steps for constructing the Lyapunov general function are as follows:
the Lyapunov harmonic function is derived and an error system (9) is substituted into the derivative of the Lyapunov harmonic function to obtain:
wherein the constant alpha, if present i >0，β i >0，
And makes the following inequality hold
Then
The system (11) further takes the form:
consistent with the assumptions of the present invention, it has proven effective to derive the adaptive desynchronization stability theory of the present invention.
Compared with the prior art, the invention has the following beneficial effects:
1. under the same system parameters and controller gains, compared with the existing method, the anti-synchronization process of the driving-response system is simpler and easier to understand;
2. the adaptive controller designed by the invention can effectively realize the anti-synchronization of the driving system and the response system, so that the adaptive controller has wider application scenes and improves the stability of the system.
Drawings
FIG. 1 is a flow chart of an adaptive desynchronization method of an inertial memristive neural network of the present invention;
FIG. 2 shows an exemplary embodiment 1 of the present invention in which the desynchronization error e is absent in the controller 1 (t)、e 2 (t) curve;
FIG. 3 shows an embodiment 1 of the present invention in which there is an adaptive controller for a lower desynchronization error e 1 (t)、e 2 (t) curve;
FIG. 4 shows an adaptive controller controlling gain γ according to embodiment 1 of the present invention 1 (t)、γ 2 (t)、ξ 1 (t)、ξ 2 (t) curve;
FIG. 5 shows an embodiment 1 of the present invention in which the driving system and the response system state x are controlled by the adaptive controller 1 (t) and y 1 (t) an anti-synchronization curve;
FIG. 6 shows an embodiment 1 of the present invention in which the actuation system and the response system states x are controlled by adaptive controllers 2 (t) and y 2 (t) anti-synchronization curve.
Detailed Description
To facilitate an understanding of this patent, it will now be described more fully with reference to the accompanying drawings. It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application.
As shown in fig. 1, the present embodiment provides an adaptive desynchronization method for an inertial memristive neural network, including the following steps:
step S1: establishing a driving system and a response system of the inertial memristor neural network with unbounded distributed time lag based on the inertial memristor neural network;
step S2: establishing an anti-synchronization error system according to the driving system and the response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1;
and step S3: the adaptive controller is designed to make the driving system and the response system achieve adaptive desynchronization.
In this embodiment, step S1 specifically includes:
step S11: establishing a state equation of a driving system of an inertia memristive neural network with unbounded distributed time lag:
step S12: establishing a state equation of a response system of an inertial memristive neural network with unbounded distributed time lag:
wherein x is i (t) and y i (t) for the ithState variable, alpha, of a neuron at time t i ，β i Is constant and satisfies a i >0，β i >0，f j (x j (t)) and f j (y j (t)) represents the activation function of the jth neuron, τ j (y) is time lag, K pq (t)：
Is a non-negative delay core real-valued function with unbounded distributed time lag, the initial value of the driving system (14) satisfies x i (s)＝φ i (s)，
Initial value of response system (15) is satisfied
And a is ij (x i (t))，b ij (x i (t))，c ij (x i (y))，a ij (y i (y))，b ij (y i (t))，c ij (y i (t)) represents memristor weights, satisfying:
wherein the content of the first and second substances,
is to switch threshold values and
further, step S2 specifically includes:
step S21: setting the desynchronization error of the driving system and the response system as follows:
e i (t)＝y i (t)+x i (t) (17)
obtaining an anti-synchronization error system (18):
further, step S3 specifically includes:
step S31: the expression of the constructed adaptive controller is as follows:
wherein, γ i (t) and xi i (t) is the control gain(s),
ρ i >0，m i the (t) is specifically:
and (2) bringing an adaptive controller (19) into the desynchronization error system (18) to obtain two conditions of the desynchronization error system (18):
(1) When in use
Or
Obtaining an anti-synchronization error system (20):
(2) When in use
Or
Obtaining an anti-synchronization error system (21):
according to the above cases (1) and (2), the obtained desynchronization error system is (22):
in the formula (f) j (e j (t))＝f j (x j (t))+f j (y j (t))，f j (e j (t-τ j (t)))＝f j (x j (t-τ j (t)))+f j (y j (t-τ j (t)))。
For the drive system and the response system, if the anti-synchronization needs to be achieved through the designed adaptive controller, three assumptions need to be satisfied first:
assume that 1: activation function f j (. Cndot.) is Ripphiz continuous, i.e. with a constant F j >0, such that
|F j (y j (s))-f j (x j (s))|≤F j |y j (s)-x j (s)| (23)
Wherein all of y j (s)，
Assume 2: time lag tau j (t) (j =1,2, …, n) satisfies
Wherein, tau 1 And τ 2 Is a normal number.
Assume that 3: the normal number κ exists ij (I, j =1,2, …, n) such that the following holds
The invention is based on Lyapunov stability theory, combines with a self-adaptive controller, and proves the anti-synchronization of a driving system and a response system, and the specific contents are as follows:
the specific steps for constructing the Lyapunov general function are as follows:
the Lyapunov harmonic function is derived and an error system (22) is substituted into the derivative of the Lyapunov harmonic function to obtain:
further obtaining:
according to the inequality of hypothesis 1 and Young
The inequality obtained is specifically:
the above inequality is substituted into the derivative equation of Lypunov, and according to assumption 2, the inequality is obtained as follows:
further obtaining:
let η be i >0，
And the following conditions are satisfied:
when the condition (28) is satisfied,
further obtaining:
according to the above proof procedure, the drive system (14) and the response system (15) can be desynchronized under the influence of the adaptive controller (19).
Specific example 1:
the inertial memristor neural network model driving system (30) with no boundary distribution time lag is as follows
An inertial memristive neural network model response system (31) with no boundary distribution time lag is as follows
Wherein the activation function is f j (x j (·))＝tanh(x j (·))，K ij ＝e -θ And τ j (t)＝0.1e t /(1+e t ) I, j =1,2. The parameter is selected as alpha 1 ＝α 2 ＝1，β 1 ＝β 2 ＝0.8，κ ij ＝1，τ 1 ＝1.25，τ 2 ＝0.5，á 11 ＝-2，à 11 ＝-2.2，á 12 ＝0.5，à 12 ＝1，á 21 ＝6，à 21 ＝4，á 22 ＝-2.4，à 22 ＝3，
0.1. Adaptive controller parameter settings
γ 1 (t)＝γ 2 (t)＝ξ 1 (t)＝ξ 2 (t) =0. Initial conditions are set to x 1 (t)＝x 2 (t)＝1，
y 1 (t)＝y 2 (t)＝-0.8，
The following is a simulation experiment performed based on the specific parameters selected above. Shown in FIG. 2 of the simulation results is the desynchronization error e without controller 1 (t)，e 2 (t) Curve, shown in FIG. 3 of the simulation results, is the desynchronization error e with adaptive controller 1 (t)，e 2 (t) Curve, simulation results FIG. 4 shows the control gain γ of the adaptive controller 1 (t)，γ 2 (t)，ξ 1 (t)，ξ 2 (t) curves, results of simulation experiments shown in FIGS. 5 and 6, respectively, are driving a system under adaptive controller and responding to a system state x 1 (t) and y 1 (t)、x 2 (t) and y 2 (t) desynchronization curve.
The present invention is not limited to the above preferred embodiments, and any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. An adaptive desynchronization method of an inertial memristive neural network is characterized by comprising the following steps:
step S1: establishing a driving system and a response system of the inertial memristor neural network with unbounded distributed time lag based on the inertial memristor neural network;
step S2: establishing an anti-synchronization error system according to the driving system and the response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1;
and step S3: the adaptive controller is designed so that the drive system and the response system are desynchronized.
2. The adaptive desynchronization method of the inertial memristive neural network according to claim 1, wherein the step S1 is specifically:
step S11: establishing a state equation of a driving system of an inertial memristive neural network with unbounded distributed time lag:
step S12: establishing a state equation of a response system of an inertial memristive neural network with unbounded distributed time lag:
wherein x is i (t) and y i (t) represents the state variable, α, for the ith neuron at time t i ，β i Is constant and satisfies a i ＞0，β i ＞0，f j (x j (t)) and y j (y j (t)) represents the activation function of the jth neuron, τ j (t) is time lag, K pq (t)：
Is a non-negative delay core real value function of unbounded distributed time lag, and the initial value of the driving system satisfies x i (s)＝φ i (s)，
s∈[-∞，0]，φ i (s)，
Initial value of response system satisfies
s∈[-∞，0]，
Wherein a is ij (x i (t))，b ij (x i (t))，c ij (x i (t))，a ij (y i (t))，b ij (y i (t))，c ij (y i (t)) represents memristor weights, satisfying:
wherein, gamma is i Is a switching threshold and gamma i ＞0。
3. The adaptive desynchronization method of the inertial memristive neural network according to claim 1, wherein the step S2 is specifically:
step S21: setting the desynchronization error of the driving system and the response system as follows:
e i (t)＝y i (t)+x i (t)
the obtained anti-synchronization error system is as follows:
4. the adaptive desynchronization method of the inertial memristive neural network according to claim 1, wherein the step S3 is specifically:
step S31: the expression of the constructed adaptive controller is as follows:
wherein, gamma is i (t) and xi i (t) is the control gain(s),
ρ i ＞0，m i the (t) is specifically:
the adaptive controller is brought into the anti-synchronization error system to obtain two conditions of the anti-synchronization error system:
(1) When | x i (t)|≤γ i ，|y i (t)|≤γ i Or | x i (t)|＞γ i ，|y i (t)|≤γ i The obtained anti-synchronization error system is as follows:
(2) When | x i (t)|＞γ i ，|y i (t)|＞γ i Or | x i (t)|≤γ i ，|y i (t)|＞γ i The obtained anti-synchronization error system is as follows:
according to the above cases (1) and (2), the obtained desynchronization error system is:
in the formula (f) j (e j (t))＝f j (x j (t))+f j (y j (t))，f j (e j (t-τ j (t)))＝f j (x j (t-τ j (t)))+f j (y j (t-τ j (b))。
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