CN115145156B - Self-adaptive anti-synchronization method of inertial memristor neural network - Google Patents
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Abstract
The invention provides a self-adaptive anti-synchronization method of an inertial memristor neural network, which comprises the following steps: step S1: based on the inertial memristor neural network, a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag are established; step S2: establishing an anti-synchronization error system according to a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1; step S3: the adaptive controller is designed such that the drive system and the response system are desynchronized. The invention can realize 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 a memristor is determined by the charge flowing through it, so that the amount of charge flowing through it, which is the memory function of the memristor, can be obtained by measuring the resistance of the memristor. Based on the characteristics of the memristor, a memristor neural network which is very suitable for simulating human brain is constructed by replacing the resistor in the traditional neural network circuit. In recent years, memristive neural networks have been highly focused by scientists as their advantages are increasingly apparent.
The desynchronization is an important dynamic behavior in the memristive neural network, and has important application prospects in the aspects of cooperative control, safety communication and the like of artificial intelligence. The desynchronization of memristive neural networks may also be applied in the field of information security, for example: image encryption and associative memory. Therefore, the research on the self-adaptive anti-synchronization method of the inertial memristor neural network with unbounded distribution time lag is a work with positive significance.
Disclosure of Invention
Therefore, the invention aims to provide an adaptive anti-synchronization method of an inertial memristor neural network, which can realize the adaptive anti-synchronization of the inertial memristor neural network with unbounded distribution time lag.
The invention is realized by adopting the following scheme: an adaptive anti-synchronization method of an inertial memristor neural network comprises the following steps:
step S1: based on the inertial memristor neural network, a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag are established;
step S2: establishing an anti-synchronization error system according to a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1;
step S3: the adaptive controller is designed such that the drive system and the response system achieve an adaptive anti-synchronization.
Further, the step S1 specifically includes:
step S11: establishing a state equation of a driving system of an inertial memristive neural network with unbounded distributed time lags:
step S12: establishing a state equation of a response system of an inertial memristive neural network with unbounded distributed time lags:
wherein x is i (t) and y i (t) represents the state variable at time t for the ith neuron, α i ，β i Is constant and satisfies alpha 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 And (t) is time lag, kij (t):
is a non-negative delay core real value function related to unbounded distributed time lags, the initial value of the driving system (1) satisfies x i (s)＝φ i (s)，/>
s∈[-∞，0]，φ i (s)，/>
The initial value of the response system (2) satisfies +.>
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, respectively satisfying:
wherein, gamma i Is a switching threshold and gamma i ＞0。
Further, the step S2 specifically includes:
step S21: the anti-synchronization error of the driving system and the response system is set as follows:
e i (t)＝y i (t)+x i (t) (4)
obtaining an anti-synchronization error system (5):
further, the step S3 specifically includes:
step S31: the constructed adaptive controller expression is:
wherein, gamma i (t) and ζ i (t) is the control gain,
ρ i ＞0，m i the (t) is specifically as follows: />
Bringing the adaptive controller (6) into the anti-synchronization error system (5), two cases of the anti-synchronization error system (5) are obtained:
(1) When |x i (t)|≤γ i ，|y i (t)|≤γ i Or |x i (t)|＞γ i ，|y i (t)|≤γ i Obtaining an anti-synchronization error system (7):
(2) When |x i (t)|＞γ i ，|y i (t)|＞γ i Or |x i (t)|≤γ i ，|y i (t)|＞γ i Obtaining an anti-synchronization error system (8):
according to the above cases (1) and (2), an anti-synchronization error system (9) is obtained:
wherein 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)))。
The invention is based on Lyapunov stability theory, combines the self-adaptive controller, and proves that the driving system and the response system are in anti-synchronization, and specifically comprises the following steps:
the construction of Lyapunov general functions is specifically as follows:
deriving the Lyapunov generalization function, and bringing an error system (9) into the derivative of the Lyapunov generalization function to obtain:
wherein, if a constant alpha is present i ＞0，β i ＞0，
And makes the following inequality hold
Then
The system (11) further takes the form:
consistent with the hypothesis of the present invention, it has proven to be effective to derive the adaptive anti-synchronization stability theory of the present invention.
Compared with the prior art, the invention has the following beneficial effects:
1. compared with the prior art, under the condition of the same system parameters and controller gains, the method has the advantages that the anti-synchronization process of the driving-responding system is simpler and easier to understand;
2. the self-adaptive controller designed by the invention can effectively enable the driving system and the response system to achieve anti-synchronization, so that the self-adaptive controller has wider application scenes and improves the stability of the system.
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FIG. 1 is a flow chart of an adaptive anti-synchronization method of an inertial memristive neural network of the present disclosure;
FIG. 2 shows the anti-synchronization error e without controller in embodiment 1 of the present invention 1 (t)、e 2 A curve of (t);
FIG. 3In embodiment 1 of the present invention, there is an adaptive controller-based anti-synchronization error e 1 (t)、e 2 A curve of (t);
FIG. 4 shows the control gain gamma of the adaptive controller according to embodiment 1 of the present invention 1 (t)、γ 2 (t)、ξ 1 (t)、ξ 2 A curve of (t);
FIG. 5 shows the driving system and the response system state x under the control of the adaptive controller in embodiment 1 of the present invention 1 (t) and y 1 An anti-synchronization curve of (t);
FIG. 6 shows the driving system and response system state x under the control of the adaptive controller in embodiment 1 of the present invention 2 (t) and y 2 An anti-synchronization curve of (t).
Detailed Description
To facilitate an understanding of this patent, the patent will be described more fully below 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 present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application.
As shown in fig. 1, the embodiment provides an adaptive anti-synchronization method of an inertial memristor neural network, including the following steps:
step S1: based on the inertial memristor neural network, a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag are established;
step S2: establishing an anti-synchronization error system according to a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1;
step S3: the adaptive controller is designed such that the drive system and the response system achieve an adaptive anti-synchronization.
In this embodiment, step S1 specifically includes:
step S11: establishing a state equation of a driving system of an inertial memristive neural network with unbounded distributed time lags:
step S12: establishing a state equation of a response system of an inertial memristive neural network with unbounded distributed time lags:
wherein x is i (t) and y i (t) represents the state variable at time t for the ith neuron, α i ，β i Is constant and satisfies alpha 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 ij (t)：
Is a non-negative delay core real value function with respect to unbounded distributed time lags, the initial value of the drive system (14) satisfies x i (s)＝φ i (s)，/>
The initial value of the response system (15) satisfies +.>
And a 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, respectively satisfying: />
Wherein the method comprises the steps of，γ i Is a switching threshold and gamma i ＞0。
Further, the step S2 specifically includes:
step S21: the anti-synchronization error of the driving system and the response system is set as follows:
e i (t)＝y i (t)+x i (t) (17)
obtaining an anti-synchronization error system (18):
further, the step S3 specifically includes:
step S31: the constructed adaptive controller expression is:
wherein, gamma i (t) and ζ i (t) is the control gain,
ρ i ＞0，m i the (t) is specifically as follows:
bringing the adaptive controller (19) into the anti-synchronization error system (18), two cases of the anti-synchronization error system (18) are obtained:
(1) When |x i (t)|≤γ i ，|y i (t)|≤γ i Or |x i (t)|＞γ i ，|y i (t)|≤γ i Obtaining an anti-synchronization error system (20):
(2) When |x i (t)|＞γ i ，|y i (t)|＞γ i Or |x i (t)|≤γ i ，|y i (t)|＞γ i Obtaining an anti-synchronization error system (21):
according to the above cases (1) and (2), the anti-synchronization error system is obtained as (22):
wherein 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 desynchronization needs to be achieved by the designed adaptive controller, three assumptions first need to be satisfied:
suppose 1: activation function f j (. Cndot.) is Lipohsz continuous, i.e. there is 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 y j (s)，
Suppose 2: time lag τ j (t) (j=1, 2, …, n) satisfies
Wherein τ 1 And τ 2 Is a positive constant.
Suppose 3: storing the articlesAt normal several kappa ij (I, j=1, 2, …, n) such that the following formula holds
The invention is based on Lyapunov stability theory, and combines the self-adaptive controller to prove the anti-synchronization of the driving system and the response system, and the specific contents are as follows:
the construction of Lyapunov general functions is specifically as follows:
deriving the Lyapunov generalization function and bringing an error system (22) into the derivative of the Lyapunov generalization function to obtain:
the method further comprises the following steps:
according to hypothesis 1 and Young inequality
The inequality obtained is specifically:
the above inequality is taken into the derivative equation of Lypunov and, according to assumption 2, the inequality is found to be specifically:
the method further comprises the following steps:
let eta i ＞0，
And satisfying the following conditions:
when the condition (28) is satisfied,
the method further comprises the following steps:
according to the above proving process, the driving system (14) and the response system (15) can reach an anti-synchronization under the influence of the adaptive controller (19).
Example 1
Inertial memristor neural network model driving system (30) with borderless distribution time lag is as follows
Inertial memristor neural network model response system (31) with borderless 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 chosen to be 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，
The adaptive controller parameter is set to +.>
γ 1 (t)＝γ 2 (t)＝ξ 1 (t)＝ξ 2 (t) =0. The initial condition is set to x 1 (t)＝x 2 (t)＝1，/>
y 1 (t)＝y 2 (t)＝-0.8，/>
The following was a simulation experiment based on the specific parameters selected above. Shown in FIG. 2, which shows the simulation results, is the anti-synchronization error e without the addition of a controller 1 (t)，e 2 (t) curve, FIG. 3 shows the anti-synchronization error e of the adaptive controller 1 (t)，e 2 (t) curve, FIG. 4 of simulation experiment results shows the control gain γ of the adaptive controller 1 (t)，γ 2 (t)，ξ 1 (t)，ξ 2 (t) curves, FIGS. 5 and 6 of simulation experiment results show the driving system and response system states x under the adaptive controller, respectively 1 (t) and y 1 (t)、x 2 (t) and y 2 An anti-synchronization curve of (t).
The foregoing description of the preferred embodiment of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (3)
1. The self-adaptive anti-synchronization method of the inertial memristor neural network is characterized by comprising the following steps of:
step S1: based on the inertial memristor neural network, a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag are established; the step S1 specifically comprises the following steps:
step S11: establishing a state equation of a driving system of an inertial memristive neural network with unbounded distributed time lags:
step S12: establishing a state equation of a response system of an inertial memristive neural network with unbounded distributed time lags:
wherein x is i (t) and y i (t) represents the state variable at time t for the ith neuron, α i ，β i Is constant and satisfies alpha 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 ij (t)：
Is a non-negative delay core real value function related to unbounded distribution time lag, and the initial value of a driving system meets 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, respectively satisfying:
wherein, gamma i Is a switching threshold and gamma i ＞0；
Step S2: establishing an anti-synchronization error system according to a driving system and a response system of the inertial memristor neural network with unbounded distribution time lag established in the step S1;
step S3: the adaptive controller is designed such that the drive system and the response system are desynchronized.
2. The adaptive anti-synchronization method of an inertial memristor neural network according to claim 1, wherein step S2 specifically comprises:
step S21: the anti-synchronization error of the driving system and the response system is set as follows:
e i (t)＝y i (t)+x i (t)
the obtained anti-synchronization error system is as follows:
3. the adaptive anti-synchronization method of an inertial memristor neural network according to claim 2, wherein step S3 specifically comprises:
step S31: the constructed adaptive controller expression is:
wherein, gamma i (t) and ζ i (t) is the control gain,
ρ i ＞0，m i the (t) is specifically as follows:
the self-adaptive controller is brought into the anti-synchronous error system, and two conditions of the anti-synchronous error system are obtained:
(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 Obtain the inverseThe synchronous error system is as follows:
according to the above cases (1) and (2), an anti-synchronization error system is obtained as follows:
wherein 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)))。
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