A method and system for controlling fixed-time synchronization of a multimodal memristor neural network

Abstract

The present invention discloses a multimodal memristor neural network fixed time synchronization control method and system, including establishing a multimodal memristor neural network drive system and a multimodal memristor neural network response system with random interference; according to the established multimodal memristor neural network drive system and response system, setting a synchronization error and building a synchronization error system; according to the synchronization error system, building a fixed time synchronization controller, and applying the fixed time synchronization controller to the response system so that the response system is synchronized with the drive system at a fixed time; building a multimodal memristor neural network model and using the multimodal memristor neural network model for numerical simulation to verify the fixed time synchronization effect between the drive system and the response system. The present invention has high control accuracy and has higher practical value in complex and changeable practical application scenarios.

Description

Technical Field

[0001] The present invention relates to the field of new generation information technology, and in particular to a multi-modal memristor neural network fixed time synchronization control method and system. Background Art

[0002] Memristor, an electronic component with nonlinear resistance characteristics, can change its resistance value according to the current flowing through it and maintain the resistance value after power failure, similar to the adjustment of synaptic weights of biological neuron synapses under the stimulation of electrical signals, thus showing memory function. Therefore, memristor is considered to be one of the ideal components for simulating biological neuron synapses. Therefore, in the field of complex network and nonlinear system research, the synchronous control of memristor neural network has always been a hot topic of research, especially in application fields such as automatic control, biomedical engineering, and information processing.

[0003] The Markov jump system is a multi-modal hybrid system, and the jumps between different modes follow the principle of Markov chain. In recent years, the Markov chain theory has been applied to the study of neural networks to describe and process the randomness of network state transitions. By integrating the unique characteristics of memristors with the randomness of Markov chains, a new type of Markov memristor neural network can be constructed, which can more effectively adapt to dynamic changes and uncertain environments. Traditional neural network synchronization methods mainly focus on synchronization in a certain average sense, but these methods often cannot ensure efficiency and accuracy in practical applications, especially in the face of dynamic changes and external interference. Therefore, the present invention proposes a control method and system for achieving synchronization within a fixed time. The method can not only achieve network synchronization within a preset fixed time, but also effectively deal with the uncertainty of network parameters and the interference of the external environment. The implementation of the synchronization control method depends on the precise regulation of the nonlinear dynamic characteristics of the memristor and the accurate grasp of the Markov chain state transition law. Summary of the invention

[0004] The purpose of the present invention is to provide a method and system for fixed-time synchronization control of a multimodal memristor neural network, which can realize fixed-time synchronization control of multiple multimodal memristor neural networks to solve the fixed-time synchronization problem of multimodal memristor neural networks.

[0005] To achieve the above object, the present invention adopts the following technical solution: a fixed time synchronization control method of a multimodal memristor neural network, comprising the following steps:

[0006] Step S1: Establishing a multimodal memristor neural network driving system and a multimodal memristor neural network response system with random interference, specifically including the following steps:

[0007] Step S1-1: Establish a multimodal memristor neural network as follows:

[0008]

[0009] Wherein, i={1,2,…,N}, N represents the number of nodes of the multimodal memristor neural network; represents the state variable of the i-th node at time t; f(x i (t)) = [f1(x i1 (t)),…,f n (x in (t))] T and f(x i (t-τ(t)))=[f1(x i1 (t-τ(t))),…,f n (x in (t-τ(t)))] T represents the activation function of the neuron and satisfies where |f i (x)|≤M, M and is a positive constant, and y≠x is a known parameter; represents the inertia term; τ(t) represents the time-varying lag, Represents the external input of the system; and represents a positive definite diagonal matrix; represents n-dimensional Euclidean space, represents an n×n real matrix; and Represents the memristor connection weight, as follows:

[0010]

[0011] Where, q,l={1,2,…,n}, is the switching threshold, and are all constants; φ i (s) and ψ i (s) is a continuous bounded function; r t Represents the current mode of the memristor neural network, which is a right-continuous Markov process whose value belongs to the set And there are the following modal transition probabilities:

[0012]

[0013] Among them, Δt>0 and satisfies π rp ≥0(p≠r) represents the transition probability from the rth mode to the pth mode, c represents the coupling strength, Γ(r t) represents the internal coupling positive definite matrix, G(r t )=(g ij (r i )) N×N represents the coupling weight configuration matrix; if the i-th node is connected to the j-th node (i≠j), then g ij (r t )>0, otherwise g ij (r t )=0, and the diagonal elements of G are defined as

[0014] Since the right side of the equal sign of the multimodal memristor neural network is discontinuous, by using set-valued mapping, differential inclusion theory and measurable selection theorem, there exists We can further get:

[0015]

[0016] in, is a real number and a ql (r t ) generated convex closure; is a real number and b ql (r t ) generated convex closure;

[0017] Step S1-2: Establish a multi-modal memristor neural network driving system:

[0018] The multimodal memristor neural network established in step S1-1 is subjected to variable substitution and order reduction processing to establish a multimodal memristor neural network driving system as follows:

[0019]

[0020] in, I n represents the n-order identity matrix; φ p (s),φ p (s) and Δ p (s) is a continuous bounded function;

[0021] Step S1-3: According to the driving system of step S1-2, a corresponding multimodal memristor neural network response system with random interference is established as follows:

[0022]

[0023] in, represents the state variable of the i-th node at time t; σ(t, e(t), r t ): and σ(t,z(t),r t ): represents the random interference intensity of the system and satisfies |σ(t,e i (t),r t )| 2 ≤Ξ i1 (r)|e i (t)| 2 ,|σ(t,z i (t),r t )| 2 ≤Ξ i2 (r)|z i (t)| 2 ; Among them i1 (r) and i2 (r) is a positive constant, e i (t) and z i (t) is the synchronization error between the multimodal memristor neural network driving system and the response system; w(t) represents the error defined in the complete probability space Brownian motion on is a white noise sequence, where Ω is the sample space, is a subset of the sample space, is the probability; u i1 (t) and u i2 (t) is a fixed time synchronization controller; and is a continuous bounded function; and represents the memristor connection weight, and The other performance indicators in the response system are the same as the performance indicators in the multimodal memristor neural network in step S1-1;

[0024] Step S2: According to the multimodal memristor neural network driving system and response system established in step S1, a synchronization error is set and a synchronization error system is constructed, which specifically includes the following steps:

[0025] Step S2-1: Setting the synchronization error between the multimodal memristor neural network driving system and the response system to:

[0026] Step S2-2: According to the synchronization error, a synchronization error system is constructed as follows:

[0027]

[0028] in,

[0029] Step S3: Based on the synchronization error system constructed in step S2, a fixed time synchronization controller u is constructed i1 (t) and u i2 (t), applying the fixed time synchronization controller to the response system so that the response system is synchronized with the drive system at a fixed time;

[0030] Step S4: construct a multimodal memristor neural network model and use the multimodal memristor neural network model to perform numerical simulation to verify the fixed time synchronization effect between the drive system and the response system.

[0031] Furthermore, step S3 specifically includes the following steps:

[0032] Step S3-1: Construct a fixed time synchronization controller as:

[0033]

[0034] Among them, α i1 (r), α i2 (r), α i2 (r), β i1 (r), β i2 (r), β i3 (r), β i4 (r) and θ i (r) are all positive numbers, sign(·) is the sign function; μ>1, 0<ν<1; k is a positive integer; fixed time synchronization controller u i1 (t) and u i2 (t) has two control modes, [t k ,s k ) represents u i1 (t) and u i2 (t) is the kth working time interval of the first control mode, [s k ,t k+1 ) represents u i1 (t) and u i2 (t) is the kth working time interval of the second control mode; the relevant parameters in the fixed time synchronization controller satisfy the following inequality:

[0035]

[0036] Where, i,j=1,2,…,N,q,l=1,2,…,n, γ r is a positive constant;

[0037] Step S3-2: Applying the fixed time synchronization controller to the response system, so that the response system is synchronized with the drive system at a fixed time;

[0038] Furthermore, the response system is synchronized with the drive system at a fixed time, and the upper bound T of the fixed time is:

[0039]

[0040] in,

[0041]

[0042] Furthermore, the present invention also provides a fixed-time synchronization control system of a multimodal memristor neural network applied to the above method, comprising:

[0043] A construction module for constructing a multimodal memristor neural network drive system and a response system, then setting a synchronization error according to the multimodal memristor neural network drive system and the response system, constructing a synchronization error system, and constructing a fixed time synchronization controller;

[0044] A fixed time synchronization condition calculation module, used to determine and calculate the fixed time synchronization sufficient condition of the multimodal memristor neural network according to the synchronization error system constructed in the construction module and in combination with the fixed time synchronization controller;

[0045] A setting module is used to set parameters of the system and the fixed time synchronization controller according to the result of the fixed time synchronization condition calculation module, so as to achieve the fixed time synchronization of the multimodal memristor neural network response system with the drive system under the action of the fixed time synchronization controller, and give the value of the fixed time upper limit;

[0046] The verification module builds a multimodal memristor neural network model and uses the multimodal memristor neural network model to perform numerical simulation, and verifies the fixed-time synchronization effect between the drive system and the response system according to the value of the fixed time upper limit given in the setting module.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. In the present invention, considering the challenges faced by the system such as dynamic changes and uncertainties, random interference and communication delay, time-varying time delay and random interference are specially introduced, so that the network has higher practical value in complex and changeable actual application scenarios.

[0049] 2. In the present invention, the stability and anti-interference ability of the network under external interference are enhanced by precisely controlling the nonlinear dynamic characteristics of the memristor and accurately grasping the state transfer law of the Markov chain.

[0050] 3. In the present invention, a fixed time synchronization controller is proposed, which can achieve accurate synchronization of the network within a predetermined fixed time, thereby significantly improving the synchronization efficiency. Even in the face of dynamic changes in network parameters or external interference, the controller can ensure the accuracy and stability of synchronization. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0052] In the attached picture:

[0053] Figure 1 It is a flow chart of a first specific embodiment of a method and system for controlling fixed-time synchronization of a multi-modal memristor neural network according to the present invention;

[0054] Figure 2 is the e of the synchronous error system without controller in the numerical simulation of the present invention. i (t) state trajectory, where (a) is the e of the synchronous error system without the action of the controller. i1 (t) state trajectory; (b) is the e of the synchronous error system without the action of the controller i2 (t) state trajectory;

[0055] Figure 3 is the z of the synchronous error system without controller in the numerical simulation of the present invention. i (t) state trajectory, where (a) is the z of the synchronous error system without the action of the controller i1 (t) state trajectory; (b) is the z of the synchronous error system without the action of the controller i2 (t) state trajectory;

[0056] Figure 4 is the e of the synchronization error system under the action of the fixed time synchronization controller in the numerical simulation of the present invention. i (t) state trajectory, where (a) is the e of the synchronization error system under the action of the fixed-time synchronization controller. i1 (t) state trajectory; (b) is the e of the synchronization error system under the action of the fixed-time synchronization controller. i2 (t) state trajectory;

[0057] Figure 5 is the z of the synchronization error system under the action of the fixed time synchronization controller in the numerical simulation of the present invention. i(t) state trajectory, where (a) is the z of the synchronization error system under the action of the fixed-time synchronization controller. i1 (t) state trajectory; (b) is the z of the synchronization error system under the action of the fixed-time synchronization controller i2 (t) state trajectory;

[0058] Figure 6 is the Markov process r in the numerical simulation of the present invention t Graph of

[0059] Figure 7 A structural block diagram of a multimodal memristor neural network fixed-time synchronization control system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0060] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0061] Embodiment 1

[0062] like Figure 1 As shown, this embodiment provides a fixed time synchronization control method for a multi-modal memristor neural network. The fixed time synchronization control method includes the following steps:

[0063] Step S1: Establishing a multimodal memristor neural network driving system and a multimodal memristor neural network response system with random interference, specifically including the following steps:

[0064] Step S1-1: Establish a multimodal memristor neural network as follows:

[0065]

[0066] Wherein, i={1,2,…,N}, N represents the number of nodes of the multimodal memristor neural network; represents the state variable of the i-th node at time t; f(x i (t)) = [f1(x i1 (t)),…,f n (x in (t))] T and f(x i (t-τ(t)))=[f1(x i1 (t-τ(t))),…,f n (x in (t-τ(t)))] T represents the activation function of the neuron and satisfies where |f i (x)|≤M, M and is a positive constant, and y≠x is a known parameter; represents the inertia term; τ(t) represents the time-varying lag, Represents the external input of the system; and represents a positive definite diagonal matrix; represents n-dimensional Euclidean space, represents an n×n real matrix; and Represents the memristor connection weight, as follows:

[0067]

[0068] Where, q,l={1,2,…,n}, is the switching threshold, and are all constants; φ i (s) and ψ i (s) is a continuous bounded function; r t Represents the current mode of the memristor neural network, which is a right-continuous Markov process whose value belongs to the set And there are the following modal transition probabilities:

[0069]

[0070] Among them, Δt>0 and satisfies π rp ≥0(p≠r) represents the transition probability from the rth mode to the pth mode, c represents the coupling strength, Γ(r t ) represents the internal coupling positive definite matrix, G(r t )=(g ij (r t )) N×N represents the coupling weight configuration matrix; if the i-th node is connected to the j-th node (i≠j), then g ij (r t )>0, otherwise g ij (r t )=0, and the diagonal elements of G are defined as

[0071] Since the right side of the equal sign of the multimodal memristor neural network is discontinuous, by using set-valued mapping, differential inclusion theory and measurable selection theorem, there exists We can further get:

[0072]

[0073] in, is a real number and a ql (r t ) generated convex closure; is a real number and b ql (r t ) generated convex closure;

[0074] Step S1-2: Establish a multi-modal memristor neural network driving system:

[0075] The multimodal memristor neural network established in step S1-1 is subjected to variable substitution and order reduction processing to establish a multimodal memristor neural network driving system as follows:

[0076]

[0077] in, I n represents the n-order identity matrix; φ p (s), ψ p (s) and Δ p (s) is a continuous bounded function;

[0078] Step S1-3: According to the driving system of step S1-2, a corresponding multimodal memristor neural network response system with random interference is established as follows:

[0079]

[0080] in, represents the state variable of the i-th node at time t; σ(t, e(t), r t ): and σ(t,z(t),r t ): represents the random interference intensity of the system and satisfies |σ(t,e i (t),r t )| 2 ≤Ξ i1 (r)|e i (t)| 2 ,|σ(t,z i (t),r t )| 2 ≤Ξ i2 (r)|z i (t)| 2 ; Among them i1 (r) and i2(r) is a positive constant, e i (t) and z i (t) is the synchronization error between the multimodal memristor neural network driving system and the response system; w(t) represents the error defined in the complete probability space Brownian motion on is a white noise sequence, where Ω is the sample space, is a subset of the sample space, is the probability; u i1 (t) and u i2 (t) is a fixed time synchronization controller; and is a continuous bounded function; and represents the memristor connection weight, and The other performance indicators in the response system are the same as the performance indicators in the multimodal memristor neural network in step S1-1;

[0081] Step S2: According to the multimodal memristor neural network driving system and response system established in step S1, a synchronization error is set and a synchronization error system is constructed, which specifically includes the following steps:

[0082] Step S2-1: Setting the synchronization error between the multimodal memristor neural network driving system and the response system to:

[0083] Step S2-2: According to the synchronization error, a synchronization error system is constructed as follows:

[0084]

[0085] in,

[0086] Step S3: Based on the synchronization error system constructed in step S2, a fixed time synchronization controller u is constructed i1 (t) and u i2 (t), applying the fixed time synchronization controller to the response system so that the response system is synchronized with the drive system at a fixed time;

[0087] Step S4: construct a multimodal memristor neural network model and use the multimodal memristor neural network model to perform numerical simulation to verify the fixed time synchronization effect between the drive system and the response system.

[0088] In this embodiment, step S3 specifically includes the following steps:

[0089] Step S3-1: Construct a fixed time synchronization controller as:

[0090]

[0091]

[0092] Among them, α i1 (r), α i2 (r), α i2 (r), β i1 (r), β i2 (r), β i3 (r), β i4 (r) and θ i (r) are all positive numbers, sign(·) is the sign function; μ>1, 0<ν<1; k is a positive integer; fixed time synchronization controller u i1 (t) and u i2 (t) has two control modes, [t k ,s k ) represents u i1 (t) and u i2 (t) is the kth working time interval of the first control mode, [s k ,t k+1 ) represents u i1 (t) and u i2 (t) is the kth working time interval of the second control mode; the relevant parameters in the fixed time synchronization controller satisfy the following inequality:

[0093]

[0094] Where, i,j=1,2,…,N,q,l=1,2,…,n, γ r is a positive constant;

[0095] Step S3-2: Applying the fixed time synchronization controller to the response system, so that the response system is synchronized with the drive system at a fixed time;

[0096] In this embodiment, the response system is synchronized with the drive system at a fixed time, and the upper limit T of the fixed time is:

[0097]

[0098] in,

[0099]

[0100] It is worth noting that the present invention takes into account the challenges faced by the system, such as dynamic changes and uncertainties, random interference and communication delays, and especially introduces time-varying time delays and random interference, so that the network has higher practical value in complex and changeable practical application scenarios; by accurately regulating the nonlinear dynamic characteristics of the memristor and accurately grasping the state transition law of the Markov chain, the stability and anti-interference ability of the network under external interference are enhanced; a fixed-time synchronization controller is proposed, which can achieve accurate synchronization of the network within a predetermined fixed time, thereby significantly improving the synchronization efficiency. Even in the face of dynamic changes in network parameters or external interference, the controller can ensure the accuracy and stability of synchronization.

[0101] Embodiment 2

[0102] This embodiment mainly includes two parts:

[0103] The first is to theoretically prove the effectiveness of the fixed-time synchronization controller constructed in the fixed-time synchronization control method of the multimodal memristor neural network proposed in Example 1.

[0104] The second is to verify through numerical simulation whether the multimodal memristor neural network response system with random interference in Example 1 is synchronized with the drive system at a fixed time under the action of the fixed time synchronization controller.

[0105] (Neither the theoretical proof nor the simulation experiment is used to limit the present invention. In other embodiments, the simulation experiment may not be performed, and other experimental schemes may be used to perform experiments to verify the performance of the neural network system.)

[0106] 1. Theoretical Proof

[0107] The following are the lemmas that will be used in the proof.

[0108] Lemma 1: Define a random function The infinitesimal operator of is:

[0109]

[0110] in,

[0111] Lemma 2: For any matrix Q, and vector Then the following inequality holds:

[0112] 2x T y≤x T Qx+y T Q -1 y

[0113] Lemma 3: Let a i≥0 (i = 1, 2, 3, …, n), 0 < p < 1 and q > 1, then the following inequality holds:

[0114]

[0115] Lemma 4: Assume that V(t) is a non - negative continuous function and satisfies the following conditions:

[0116]

[0117] where t ∈ [0, +∞), t0 = 0, k = 0, 1, 2, …, α > 0, b > 0, μ > 1, 0 < v < 1, then V(t) ≡ 0; for any where T0 is the value of the fixed time upper - bound, and the specific expression is:

[0118]

[0119] where,

[0120] Next, construct the following stochastic Lyapunov functional as:

[0121]

[0122] When t k ≤ t ≤ s k According to Lemma 1, calculate to get:

[0123]

[0124] where trace(·) is the trace of the matrix.

[0125] According to the following inequality can be obtained:

[0126]

[0127] where,

[0128] where,

[0129] Therefore, it can be further obtained that:

[0130]

[0131] where,

[0132] According to Lemma 2, there exists a matrix Q > 0; define Then it can be obtained that:

[0133]

[0134] According to Lemma 3, we can get:

[0135]

[0136] in,

[0137] Substituting into the inequality, we get:

[0138]

[0139] Therefore, we can get:

[0140]

[0141] in,

[0142] Taking the mathematical expectation on both sides of the above equation, we get:

[0143]

[0144] Similarly, when s k <t<t k+1 When , we can get:

[0145]

[0146] Therefore, we can get:

[0147]

[0148] Therefore, according to Lemma 4, the multimodal memristor neural network response system with random interference is synchronized with the drive system at a fixed time under the action of the fixed time synchronization controller, and the upper bound of the fixed time is: Proof completed.

[0149] 2. Numerical Simulation

[0150] In this embodiment, the following multimodal memristor neural network system with 4 nodes is considered:

[0151]

[0152] Among them, o = 1, 2, 3, 4, r t is a Markov chain with value x i (t) = (x i1 (t),x i2 (t))T ,f(x i (t)) = (tanh(x i1 (t)),tanh(x i2 (t))) T , we can calculate J(1)=(1.4,0.8) T , J(2)=(1.2,1.6) T ;τ(t)=0.3|cost|; A(x i (t),r t )=(a ql (x i (t),r t )) 2×2 ,B(x i (t),r t )=(b ql (x i (t),r t )) 2×2 , the memristor connection weights are as follows:

[0153]

[0154]

[0155] Coupling strength c = 1,

[0156] Substituting variables for the above system, the drive system is obtained as follows:

[0157]

[0158] The corresponding response system description is:

[0159]

[0160] Among them, σ(t, e i (t), 1) = (0.15sin(e i1 (t)), 0.15sin(e i2 (t))) T ,σ(t,e i (t),2)=(0.21e i1 (t), 0.21e i2 (t)) T ,σ(t,z i (t),1)=(0.02z i1 (t), 0.02z i2 (t))T ,σ(t,z i (t),2)=(0.05sin(z i1 (t)), 0.05sin(z i2 (t))) T ;

[0161] According to the above parameter settings, the sufficient condition for fixed time synchronization should satisfy the inequality: α i1 (r)≥1.9821, β i2 (r)≥3.13,θ i (r)≥7.911, β i1 (r)≥1.3315; Select the fixed time synchronization controller related parameters α i1 (1) = 2.1, α i1 (2) = 3.3, α i2 (1) = α i2 (2) = 1, α i3 (1) = α i3 (2)=2.8, μ=1.2, v=0.6, β i1 (1) = 1.5, β i1 (2) = 1.8, β i2 (1) = 4, β i2 (2) = 4.2, β i3 (1) = β i3 (2) = 1, β i4 (1) = β i4 (2) = 1.9, θ i (1) = θ i (2) = 8; [t k ,s k ]=([2k,2k+0.4]∪(2k+1.3,2k+1.9)), φ=0.25; therefore, the upper bound of the fixed time can be calculated as: T≈4.2; the specific simulation experimental results are as follows: Figure 2 is the e of the synchronous error system without controller i (t) state trajectory, where (a) is the e of the synchronous error system without the action of the controller. i1 (t) state trajectory; (b) is the e of the synchronous error system without the action of the controller i2 (t) state trajectory; Figure 3 is the z of the synchronous error system without controller i (t) state trajectory, where (a) is the z of the synchronous error system without the action of the controller i1 (t) state trajectory; (b) is the z of the synchronous error system without the action of the controller i2 (t) state trajectory; Figure 4is the e of the synchronization error system under the action of the fixed-time synchronization controller i (t) state trajectory, where (a) is the e of the synchronization error system under the action of the fixed-time synchronization controller. i1 (t) state trajectory; (b) is the e of the synchronization error system under the action of the fixed-time synchronization controller. i2 (t) state trajectory; Figure 5 is the z of the synchronization error system under the fixed time synchronization controller i (t) state trajectory, where (a) is the z of the synchronization error system under the action of the fixed-time synchronization controller. i1 (t) state trajectory; (b) is the z of the synchronization error system under the action of the fixed-time synchronization controller i2 (t) state trajectory; Figure 6 is a Markov process r t The curve graph of Figure 2 and Figure 3 It can be seen that without a controller, the state trajectory of the synchronization error system continues to oscillate. This proves that the drive system and the response system cannot be synchronized without the action of a controller. Figure 4 and Figure 5 It can be seen that after adding the fixed-time synchronization controller, the state trajectory of the synchronization error system gradually converges to 0. This proves that the multimodal memristor neural network response system with random interference is synchronized with the drive system at a fixed time under the action of the fixed-time synchronization controller, verifying the synchronization performance.

[0162] Embodiment 3

[0163] This embodiment mainly includes the following contents:

[0164] Based on the same inventive concept, this embodiment provides a fixed-time synchronization control system for a multimodal memristor neural network, and the principle of solving the problem is similar to the fixed-time synchronization control method based on a multimodal memristor neural network, which will not be described in detail. Figure 7 , Figure 7 A structural block diagram of a fixed-time synchronization control system of a multimodal memristor neural network provided by an embodiment of the present invention. The fixed-time synchronization control system may specifically include:

[0165] A construction module 100 is used to construct a multimodal memristor neural network drive system 101 and a multimodal memristor neural network response system 102 with random interference, and then set a synchronization error 103 according to the multimodal memristor neural network drive system and the response system, construct a synchronization error system 104, and construct a fixed time synchronization controller 105;

[0166] A fixed time synchronization condition calculation module 200, for determining and calculating a sufficient condition for fixed time synchronization of the multimodal memristor neural network according to the synchronization error system constructed in the construction module and in combination with the fixed time synchronization controller;

[0167] A setting module 300 is used to set parameters of the system and the controller according to the result of the fixed time synchronization condition calculation module 200, so as to achieve the fixed time synchronization of the multimodal memristor neural network response system with random interference with the drive system under the action of the fixed time synchronization controller, and give the value of the fixed time upper limit;

[0168] Verification module 400 builds a multimodal memristor neural network model and uses the multimodal memristor neural network model to perform numerical simulation, and verifies the fixed time synchronization effect between the drive system and the response system according to the value of the fixed time upper limit given in the setting module 300.

[0169] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A fixed-time synchronization control method for a multimodal memristor neural network, characterized in that: The following steps are involved: Step S1: Establishing a multimodal memristor neural network driving system and a response system, specifically including the following steps: Step S1-1: Establish a multimodal memristor neural network as follows: Wherein, i={1,2,…,N}, N represents the number of nodes of the multimodal memristor neural network; represents the state variable of the i-th node at time t; f(x i (t)) = [f1(x i1 (t)),…,f n (x in (t))] T and f(x i (t-τ(t)))=[f1(x i1 (t-τ(t))),…,f n (x in (t-τ(t)))] T represents the activation function of the neuron and satisfies where |f(x)|≤M, M and is a positive constant, and y≠x is a known parameter; represents the inertia term; τ(t) represents the time-varying lag, Represents the external input of the system; and represents a positive definite diagonal matrix; represents n-dimensional Euclidean space, represents an n×n real matrix; and Represents the memristor connection weight, as follows: Among them, q, l = {1, 2,..., n}, θ i is the switching threshold, and are all constants; φ i (s) and ψ i (s) is a continuous bounded function; r t Represents the current mode of the memristor neural network, which is a right-continuous Markov process whose value belongs to the set And there are the following modal transition probabilities: Among them, Δt>0 and satisfies π rp ≥0(p≠r) represents the transition probability from the rth mode to the pth mode, c represents the coupling strength, Γ(r t ) represents the internal coupling positive definite matrix, G(r t )=(g ij (r t )) N×N represents the coupling weight configuration matrix; if the i-th node is connected to the j-th node (i≠j), then g ij (r t )>0, otherwise g ij (r t )=0, and the diagonal elements of G are defined as Since the right side of the equal sign of the multimodal memristor neural network is discontinuous, by using set-valued mapping, differential inclusion theory and measurable selection theorem, there exists Then we further get: in, is a real number and a ql (r t ) generated convex closure; is a real number and b ql (r t ) generated convex closure; Step S1-2: Perform variable substitution and order reduction processing on the multimodal memristor neural network established in step S1-1 to establish a multimodal memristor neural network driving system as follows: in, I n represents the n-order identity matrix; φ p (s), ψ p (s) and Δ p (s) is a continuous bounded function; Step S1-3: According to the driving system of step S1-2, a corresponding multimodal memristor neural network response system with random interference is established as follows: in, Represents the state variable of the i-th node at time t; and represents the random interference intensity of the system and satisfies |σ(t,e i (t),r t )| 2 ≤Ξ i1 (r)|e i (t)| 2 ,|σ(t,z i (t),r t )| 2 ≤Ξ i2 (r)|z i (t)| 2 ; Among them i1 (r) and i2 (r) is a positive constant, e i (t) and z i (t) is the synchronization error between the multimodal memristor neural network driving system and the response system; w(t) represents the error defined in the complete probability space Brownian motion on is a white noise sequence, where Ω is the sample space, is a subset of the sample space, is the probability; u i1 (t) and u i2 (t) is a fixed time synchronization controller; and is a continuous bounded function; and represents the memristor connection weight, and The other performance indicators in the response system are the same as the performance indicators in the multimodal memristor neural network in step S1-1; Step S2: According to the multi-modal memristor neural network driving system and response system established in S1, the synchronization error is set and the synchronization error system is constructed, which specifically includes the following steps: Step S2-1: Setting the synchronization error between the multimodal memristor neural network driving system and the response system to: Step S2-2: According to the synchronization error, a synchronization error system is constructed as follows: in, Step S3: Based on the synchronization error system constructed in step S2, design a fixed time synchronization controller u i1 (t) and u i2 (t), applying the fixed time synchronization controller to the response system so that the response system is synchronized with the drive system at a fixed time, specifically comprising the following steps: Step S3-1: Design a fixed time synchronization controller as follows: Among them, α i1 (r), α i2 (r), α i2 (r), β i1 (r), β i2 (r), β i3 (r), β i4 (r) and θ i (r) are all positive constants, sign(·) is the sign function; μ > 1, 0 < v < 1; k belongs to positive integers; the fixed-time synchronization controller u i1 (t) and u i2 (t) both have two control modes, [t k , s k represents the k-th working time interval of the first control mode of u i1 (t) and u i2 (t), (s k , t k+1 ) represents the k-th working time interval of the second control mode of u i1 (t) and u i2 (t); the relevant parameters in the fixed-time synchronization controller satisfy the following inequalities: where \(i,j = 1,2,\cdots,N\) and \(q,l = 1,2,\cdots,n\) \(0 < Q\) and Step S3-2: Applying the fixed time synchronization controller to the response system, so that the response system is synchronized with the drive system at a fixed time; Step S4: construct a multimodal memristor neural network model and use the multimodal memristor neural network model to perform numerical simulation to verify the fixed time synchronization effect between the drive system and the response system.

2. The method for fixed-time synchronization control of a multimodal memristor neural network according to claim 1, characterized in that: The response system is synchronized with the drive system at a fixed time, and the upper bound T of the fixed time of synchronization is: in, 3. A fixed-time synchronization control system of a multimodal memristor neural network applied to the method of any one of claims 1-2, characterized in that: include: A construction module for constructing a multimodal memristor neural network drive system and a response system, then setting a synchronization error according to the multimodal memristor neural network drive system and the response system, constructing a synchronization error system, and constructing a fixed time synchronization controller; A fixed time synchronization condition calculation module, used to determine and calculate the fixed time synchronization sufficient condition of the multimodal memristor neural network according to the synchronization error system constructed in the construction module and in combination with the fixed time synchronization controller; A setting module is used to set parameters of the system and the fixed time synchronization controller according to the result of the fixed time synchronization condition calculation module, so as to achieve the fixed time synchronization of the multimodal memristor neural network response system with the drive system under the action of the fixed time synchronization controller, and give the value of the fixed time upper limit; The verification module builds a multimodal memristor neural network model and uses the multimodal memristor neural network model to perform numerical simulation, and verifies the fixed-time synchronization effect between the drive system and the response system according to the value of the fixed time upper limit given in the setting module.

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