A finite-time synchronization and quantized control method of memristor neural networks

Abstract

The application discloses a finite time synchronization and quantization control method of a memristor neural network, and comprises the following steps: step 1, constructing a memristor neural network system model; step 2, constructing a controller for the memristor neural network system model in step 1; step 3, constructing definitions and lemmas required for time synchronization and quantization control of the memristor neural network; and step 4, combining steps 1 to 3 to perform time synchronization and quantization control on the memristor neural network. The application proposes a new control theory and analysis method for finite time synchronization and quantization control of the memristor neural network based on theories such as comprehensive differential equations, neural networks, quantization control and finite time stability, and provides a new idea and approach for synchronization and control research of the memristor neural network.

Description

Technical Field

[0001] This invention belongs to the field of electronic information technology, specifically relating to a finite-time synchronization and quantization control method for memristor neural networks. Background Technology

[0002] Artificial Neural Networks (NNs), proposed and established by McCulloch and Pitts in 1943, have undergone more than half a century of development. As a newly emerging interdisciplinary field, NNs take the physiological structure of the human brain as their starting point to explore the mechanisms of human intelligent activities and simulate human intelligence, playing a significant role in promoting the development of human society and the advancement of high technology. Therefore, NNs have become a hot topic and focus of research in the field of artificial intelligence since the 1980s. Currently, NNs are widely used in combinatorial optimization, image processing, pattern recognition, signal processing, automatic control, and other fields.

[0003] Memristive Neural Networks (MNNs) are variable-weight networks that incorporate memristors as electronic synapses into neural network systems, creating networks that more closely resemble the structure of the human brain and more effectively simulate its functions. The concept of memristors was proposed in 1971, and their physical model and structure were realized by HP Labs in 2008. Due to the advantages of memristors, such as nanoscale size, low power consumption, easy storage, and variable resistance, MNNs not only overcome the shortcomings of traditional neural networks, such as inflexible synapses and large circuit areas, but also enable neural networks to have greater computational power and information capacity, greatly promoting the application of neural networks in associative storage and information processing.

[0004] Synchronization in neural networks, as a crucial characteristic of dynamical networks, has become a significant topic in neural network dynamics. Synchronization refers to the process by which two or more coupled systems, starting from different initial values, eventually reach the same state of motion over time. Extensive observation and research have revealed that this phenomenon is widespread in nature and human society. Examples include the synchronized flashing of fireflies, the synchronized chirping of crickets, the synchronized firing of neural networks in brain regions, and the synchronized pacing of heart cells. As one of the most common cooperative behaviors in neural networks, synchronization is now widely applied in fields such as image encryption, intelligent aerospace, MRI, and information processing.

[0005] Synchronization control of networks has become a highly researched topic in recent years. Numerous studies have shown that synchronization behavior has two sides. Synchronization in some systems is beneficial to humans, such as the synchronized behavior of cardiac cells, which enables the heart to beat rhythmically. However, synchronization in other systems is detrimental, such as routers synchronously transmitting signals, leading to network congestion. Therefore, synchronization control is essential to ensure that these systems better serve humanity. The core idea of ​​synchronization control is to generate or enhance beneficial synchronization behaviors and eliminate or weaken harmful ones, thereby achieving the goal of maximizing benefits and minimizing harms. Synchronization control of neural networks integrates control theory, complexity science, systems science, and other disciplines, and is mainly applied in social, engineering, biological, and information fields, showing broad application and development prospects.

[0006] As research into neural network synchronization deepens, different types of synchronization have been proposed, such as complete synchronization, projective synchronization, cluster synchronization, generalized synchronization, lag synchronization, and phase synchronization. In recent years, the synchronization control of MNNs has attracted considerable attention due to its advantages in pattern recognition, associative memory, parallel computing, and optimization computation. MNNs can achieve exponential synchronization, lag synchronization, complete synchronization, and anti-synchronization under different control methods (such as adaptive control, feedback control, and intermittent control). However, most existing results on MNNs, including those mentioned above, are actually asymptotic, meaning that synchronization is only achieved when time approaches infinity. In practical applications, systems typically need to achieve synchronization within a finite time, i.e., finite-time synchronization.

[0007] Finite-time synchronization has wide applications in many practical physical and engineering systems, such as robot control, motor control systems, braking systems, and aircraft systems. Therefore, finite-time synchronization, as a time-optimal control method, has attracted increasing attention from scholars. For example, Jiang et al. explored finite-time synchronization of memristor recurrent neural networks based on the Lyapunov method and the differential inclusion principle. Velmurugan et al. studied how coupled neural networks can achieve finite-time synchronization under discontinuous feedback control strategies. Shen et al. derived sufficient conditions for achieving finite-time synchronization of coupled neural networks through discontinuous controllers.

[0008] It is worth noting that although finite-time synchronization has a finite convergence time, a key problem is that the estimation of the synchronization resting time depends on the initial conditions of the system. Therefore, the estimated synchronization resting time will differ depending on the initial conditions of the system. However, this has certain limitations in practical applications, because the finite-time synchronization of the system under a set of initial conditions does not mean that the system is finite-time synchronized under all initial conditions. Furthermore, when the system is affected by external disturbances or other factors that make the initial conditions unknowable or even impossible, we cannot estimate the system's synchronization resting time, nor can we determine the system's finite-time synchronization. To address the difficulties and limitations of finite-time synchronization caused by initial condition factors, Polyakov proposed a new concept of finite-time stability—fixed-time stability—which requires that the system be globally finite-time stable and that the resting time is a constant independent of the system's initial conditions. Polyakov's fixed-time stability criterion theorem provides the theoretical basis for subsequent research on fixed-time synchronization. Summary of the Invention

[0009] To address the aforementioned technical problems, this invention provides a finite-time synchronization and quantization control method for memristor neural networks. This method, based on theories of integrated differential equations, neural networks, quantization control, and finite-time stability, proposes a new control theory and analysis approach for the finite-time synchronization and quantization control of memristor neural networks, providing new ideas and approaches for the research on the synchronization and control of memristor neural networks.

[0010] The objective of this invention is achieved through the following technical solution: a finite-time synchronization and quantization control method for memristor neural networks, comprising the following steps:

[0011] Step 1: Construct a memristor neural network system model;

[0012] Step 2: Construct a controller for the memristor neural network system model from Step 1;

[0013] Step 3: Construct the definitions and lemmas required for time synchronization and quantization control of memristor neural networks;

[0014] Step 4: Combining steps 1 to 3, perform time synchronization and quantization control on the memristor neural network.

[0015] Preferably, the memristor neural network system model established in step 1 is as follows:

[0016]

[0017] Where i = 1, 2, ..., n; x i (t) corresponds to capacitor c i voltage; d i>0 indicates the rate at which the i-th neuron resets its potential to a resting state; g j (x j (t) is the activation function; J i J i It is an external bias; a ij (x i (t) represents the memristor synaptic connection weight, which is defined as follows:

[0018]

[0019] in Indicates memristor P ij The memristor coefficient; P ij Represents the feedback function g j (x j (t) and x i The memristor between (t); based on the characteristics of the memristor and its current-voltage properties, the memristor synaptic weight can be expressed in the following form:

[0020]

[0021] Where T i >0 indicates a toggle transition; is a constant and

[0022] Preferably, in step 2, the controller control strategy of the memristor neural network system model is as follows:

[0023] U i (t)=-α i q(e i (t))-β i sign(q(e i (t)))-λ i sign(q(e i (t)))|q(e i (t))| ω

[0024] Where, α i ,β i , λ i Both ω and q(·) are positive constants; q(·) is a logarithmic quantizer.

[0025] Preferably, in step 2, a non-uniform quantizer is used as the logarithmizer, as described below:

[0026] First, given the quantization set:

[0027] Λ={±b j :b j =ρ lb0, f=0, ±1, ±2,…}∪{0}

[0028] Where b0 > 0 is the scaling parameter; 0 < ρ < 1 is the quantization density. The quantizer q(·) maps each interval to a quantization level, and its functional expression is:

[0029]

[0030] Here, v is the input to the quantizer, and q(v) is the output of the quantizer. It is the quantization parameter; the quantizer q(·) can be further expressed as:

[0031] q(v)=(1+Δ)v

[0032] Where: Δ∈[-δ, δ];

[0033] The controller, derived from the quantizer, can be written in the following form:

[0034] U i (t)=-α i (1+Δ)e i (t)-β i sign((1+Δ)e i (t))-λ i sign((1+Δ)e i (t))(1+Δ) ω |e i (t)| ω

[0035] From the definition of Δ, we know that 1 + Δ ∈ (0, 2), therefore:

[0036] sign((1+Δ)e i (t))=sign(e i (t))

[0037] Therefore, the finite-time quantization control strategy can ultimately be written as:

[0038] U i (t)=-α i (1+Δ)e i (t)-β i sign((1+Δ)e i (t))-λ i sign(e i (t))(1+Δ) ω |e i (t)| ω (2-11) From the differential inclusion theory and the measurable choice theory, we know that there exists a measurable function:

[0039]

[0040] Equation (2-11) is equivalent to the following form:

[0041] U i (t)=-α i (1+Δ)e i (t)-β i S(e i (t))-λ i S(e i (t))(1+Δ) ω |e i (t)| ω .

[0042] Preferably, the definitions required for constructing the memristor neural network time synchronization and quantization control in step 3 include:

[0043] Definition 1: Consider the following system:

[0044]

[0045] in Let be a nonlinear, discontinuous, but locally measurable function; for any x(t) represents the system (2-3) in the interval [0, 1]. The solution in the Filippov sense on; for any compact interval x(t) is absolutely continuous and satisfies the following differential:

[0046]

[0047] Set-valued mapping Defined as:

[0048]

[0049] here Indicates the convex closure. Represents a set The Lebesgue measure; B(x, ρ) is an open sphere with center x and radius ρ > 0, denoted as:

[0050]

[0051] Then system (2-1) can be reduced to the following form:

[0052]

[0053] in:

[0054]

[0055] Based on the definition of Filippov's solution and the differential inclusion theory, equation (2-4) can be further simplified to:

[0056]

[0057] According to the measurable choice theory, there exists a measurable function. Make:

[0058]

[0059] If system (2-1) is defined as the driving system, then its response system is:

[0060]

[0061] Among them U i (t) represents the controller to be designed;

[0062] The response system (2-6) can be written as:

[0063]

[0064] in:

[0065]

[0066] Based on the differential inclusion theory, system (2-7) can be written as:

[0067]

[0068] According to the theory of measurable choice, there exists a measurable function. Make:

[0069]

[0070] Define error e i (t)-y i (t)-x i (t) Then, from systems (2-5) and (2-9), we can obtain the following error system:

[0071]

[0072] in:

[0073] g j (e j (t))=g j (y j (t)-g j (x j (t)).

[0074] Preferably, the definitions required for constructing the memristor neural network time synchronization and quantization control in step 3 also include:

[0075] Definition 2: If there exists a constant T(e(0)) ≥ 0 such that:

[0076] And e(t)≡0,

[0077] Where e(0)=y(0)-x(0)∈R n R n Let represent the set of n-dimensional real vectors, then systems (2-1) and (2-6) are said to achieve finite-time synchronization; furthermore, if for any initial value e(0)∈R n Both have a constant T. max Make T(e(0))≤T max If so, then systems (2-1) and (2-6) are said to achieve fixed-time synchronization.

[0078] Preferably, the lemmas required for constructing the time synchronization and quantization control of the memristor neural network in step 3 include:

[0079] Lemma 1: If there exists a regular, positive definite, and radially unbounded function Such that for any solution x(t) of the system, the following conditions are met:

[0080]

[0081] Where a, b>0, 0≤μ1≤1, μ2≥0, then the following conclusion holds:

[0082] (1) If 0 ≤ μ2 ≤ 1, then the zero solution of the system is finite-time stable and the resting time is estimated as follows:

[0083]

[0084] Where V(0) = V(x(0)) and μ * =max{μ1, μ2}, μ ** =min{μ1, μ2};

[0085] (2) If μ2 > 1, then the zero solution of the system is time-stable and the resting time is estimated as follows:

[0086]

[0087] Preferably, the lemma required for constructing the time synchronization and quantization control of the memristor neural network in step 3 also includes:

[0088] Lemma 2: Let x i For any ≥0, i=1,2,…,n, 0<p<q, ω>1, then the following inequalities hold:

[0089]

[0090] Preferably, in step 3, when constructing the definitions and lemmas required for time synchronization and quantization control of the memristor neural network, the following assumptions are introduced:

[0091] Assumption 1: Activation function g j (·) is Lipschitz continuous, meaning there exists a positive constant L such that:

[0092] |g j (s1)-g j (s2)|≤L|s1-s2|, s1, s2∈R

[0093] Assumption 2: There exists a real number M > 0 such that:

[0094]

[0095] Preferably, in step 4, the method for time synchronization and quantization control of the memristor neural network is as follows:

[0096] According to Theorem 1: Under Assumption 1, Assumption 2, and the controller (2-11), if:

[0097] d i -Lφ+α i (1-δ)≥0

[0098] in Then the following conclusion holds true:

[0099] (1) If 0 < ω < 1, then systems (2-1) and (2-6) achieve finite-time synchronization and the resting time is estimated as follows:

[0100]

[0101] (2) If ω>1, then systems (2-1) and (2-6) achieve fixed-time synchronization and the rest time is estimated as follows:

[0102]

[0103] in:

[0104]

[0105] Compared with the prior art, the present invention has the following advantages:

[0106] This invention provides a finite-time synchronization and quantization control method for memristor neural networks, comprising the following steps: Step 1, constructing a memristor neural network system model; Step 2, constructing a controller for the memristor neural network system model in Step 1; Step 3, constructing the definitions and lemmas required for time synchronization and quantization control of the memristor neural network; Step 4, combining Steps 1 to 3, performing time synchronization and quantization control on the memristor neural network. This invention addresses the finite-time synchronization and quantization control of memristor neural networks, proposing a new control theory and analysis method based on theories of integrated differential equations, neural networks, quantization control, and finite-time stability, providing new ideas and approaches for the research on synchronization and control of memristor neural networks. Attached Figure Description

[0107] Figure 1 This is a flowchart of the finite-time synchronization and quantization control method for memristor neural networks in an embodiment of the present invention;

[0108] Figure 2 This is a schematic diagram of the time evolution of system (4-1) in an embodiment of the present invention;

[0109] Figure 3 This is a schematic diagram of the time evolution of x1(t) and y1(t) when ω=0.5 in an embodiment of the present invention;

[0110] Figure 4 This is a schematic diagram of the time evolution of x2(t) and y2(t) when ω=0.5 in an embodiment of the present invention;

[0111] Figure 5 This is a schematic diagram of the time evolution of x3(t) and y3(t) when ω=0.5 in an embodiment of the present invention;

[0112] Figure 6 This is a schematic diagram illustrating the asymptotic behavior of the synchronization error when x = 0.5 in an embodiment of the present invention;

[0113] Figure 7 This is a schematic diagram of the time evolution of x1(t) and y1(t) when ω=0.5 in an embodiment of the present invention;

[0114] Figure 8 This is a schematic diagram of the time evolution of x2(t) and y2(t) when ω=0.5 in an embodiment of the present invention;

[0115] Figure 9 This is a schematic diagram of the time evolution of x3(t) and y3(t) when ω=0.5 in an embodiment of the present invention;

[0116] Figure 10 This is a schematic diagram of the asymptotic behavior of the synchronization error when x = 0.5 in an embodiment of the present invention. Detailed Implementation

[0117] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0118] like Figure 1 As shown, the technical solution of the present invention provides a finite-time synchronization and quantization control method for memristor neural networks, comprising the following steps:

[0119] Step 1: Construct a memristor neural network system model;

[0120] Step 2: Construct a controller for the memristor neural network system model from Step 1;

[0121] Step 3: Construct the definitions and lemmas required for time synchronization and quantization control of memristor neural networks;

[0122] Step 4: Combining steps 1 to 3, perform time synchronization and quantization control on the memristor neural network.

[0123] In one embodiment of the present invention, the memristor neural network system model established in step 1 is as follows:

[0124]

[0125] Where i = 1, 2, ..., n; x i (t) corresponds to capacitor C i voltage; d i >0 indicates the rate at which the i-th neuron resets its potential to a resting state; g j (x j (t) is the activation function; J i J i It is an external bias; s ij (x i (t) represents the memristor synaptic connection weight, which is defined as follows:

[0126]

[0127] in Indicates memristor P ij The memristor coefficient; P ij Represents the feedback function g j (x j (t) and x i The memristor between (t); based on the characteristics of the memristor and its current-voltage properties, the memristor synaptic weight can be expressed in the following form:

[0128]

[0129] Where T i >0 indicates a toggle transition; is a constant and

[0130] In one embodiment of the present invention, in step 2, for the purpose of studying the synchronization of the system, the controller control strategy of the memristor neural network system model is as follows:

[0131] U i (t)=-α i q(e i (t))-β i sign(q(e i (t)))-λ i sign(q(e i (t)))|q(e i (t))| ω

[0132] Where, α i ,β i , λ i Both ω and q(·) are positive constants; q(·) is a logarithmic quantizer that divides the defined interval into different intervals, each of which corresponds to a quantized value, so it can be regarded as a mapping of piecewise constants.

[0133] In one embodiment of the present invention, in step 2, a non-uniform quantizer is used as the logarithmizer, which has advantages over a uniform quantizer in reducing the amount of transmitted data, as described below:

[0134] First, given the quantization set:

[0135] Λ={+b j :b j =ρ j b o j = 0, +1, +2, ... ∪ {0}

[0136] Where b0 > 0 is the scaling parameter; 0 < ρ < 1 is the quantization density. The quantizer q(·) maps each interval to a quantization level, and its functional expression is:

[0137]

[0138] Here, v is the input to the quantizer, and q(v) is the output of the quantizer. It is the quantization parameter; the quantizer q(·) can be further expressed as:

[0139] q(v)=(1+Δ)v

[0140] Where: Δ∈[-δ, δ];

[0141] The controller, derived from the quantizer, can be written in the following form:

[0142] U i (t)=-α i (1+Δ)e i (t)-β i sign((1+Δ)e i (t))-λ i sign((1+Δ)e i (t))(1+Δ) ω |e i (t)| ω

[0143] From the definition of Δ, we know that 1 + Δ ∈ (0, 2), therefore:

[0144] sign((1+Δ)e i (t))=sign(e i (t))

[0145] Therefore, the finite-time quantization control strategy can ultimately be written as:

[0146] U i (t)=-α i (1+Δ)e i (t)-β i sign((1+Δ)e i (t))-λ i sign(e i (t))(1+Δ) ω |e i (t)| ω (2-11)

[0147] By differential inclusion theory and measurable choice theory, there exists a measurable function:

[0148]

[0149] Equation (2-11) is equivalent to the following form:

[0150] U i (t)=-α i (1+Δ)e i (t)-β i s(e i (t))-λ i s(e i (t))(1+Δ) ω |e i (t)| ω .

[0151] In one embodiment of the present invention, the definitions required for constructing the memristor neural network time synchronization and quantization control in step 3 (preliminary knowledge) include:

[0152] Definition 1: Consider the following system:

[0153]

[0154] in Let be a nonlinear, discontinuous, but locally measurable function; for any x(t) represents the system (2-3) in the interval [0, 1]. The solution in the Filippov sense on; for any compact interval x(t) is absolutely continuous and satisfies the following differential:

[0155]

[0156] Set-valued mapping Defined as:

[0157]

[0158] here Indicates the convex closure. Represents a set The Lebesgue measure; B(x,ρ) is an open sphere with center x and radius ρ>0, denoted as:

[0159]

[0160] Then system (2-1) can be reduced to the following form:

[0161]

[0162] in:

[0163]

[0164] Based on the definition of Filippov's solution and the differential inclusion theory, equation (2-4) can be further simplified to:

[0165]

[0166] According to the measurable choice theory, there exists a measurable function. Make:

[0167]

[0168] If system (2-1) is defined as the driving system, then its response system is:

[0169]

[0170] Among them U i (t) represents the controller to be designed;

[0171] The response system (2-6) can be written as:

[0172]

[0173] in:

[0174]

[0175] Based on the differential inclusion theory, system (2-7) can be written as:

[0176]

[0177] According to the theory of measurable choice, there exists a measurable function. Make:

[0178]

[0179] Define error e i (t)=y i (t)-x i (t) Then, from systems (2-5) and (2-9), we can obtain the following error system:

[0180]

[0181] in:

[0182] g j (e j (t))=g j (y j (t))-g i (x j (t)).

[0183] Definition 2: If there exists a constant T(e(0)) ≥ 0 such that:

[0184] And e(t)≡0,

[0185] Where e(0)=y(0)-x(0)∈R n R n Let represent the set of n-dimensional real vectors, then systems (2-1) and (2-6) are said to achieve finite-time synchronization; furthermore, if for any initial value e(0)∈R n Both have a constant T. max Make T(e(0))≤T maxIf so, then systems (2-1) and (2-6) are said to achieve fixed-time synchronization.

[0186] In one embodiment of the present invention, the lemma required for constructing the time synchronization and quantization control of the memristor neural network in step 3 includes:

[0187] Lemma 1: If there exists a regular, positive definite, and radially unbounded function Such that for any solution x(t) of the system, the following conditions are met:

[0188]

[0189] Where a, b>0, 0≤μ1≤1, μ2≥0, then the following conclusion holds:

[0190] (1) If 0 ≤ μ2 ≤ 1, then the zero solution of the system is finite-time stable and the resting time is estimated as follows:

[0191]

[0192] Where V(0) = V(x(0)) and μ * =max{μ1,μ2},μ ** =min{μ1,μ2};

[0193] (2) If μ2 > 1, then the zero solution of the system is time-stable and the resting time is estimated as follows:

[0194]

[0195] Lemma 2: Let x i If ≥0, i=1,2,…,n,0<p<q,ω>1, then the following inequalities hold:

[0196]

[0197] As a further optimization of the above embodiments, the following assumptions are introduced when constructing the definitions and lemmas required for time synchronization and quantization control of memristor neural networks:

[0198] Assumption 1: Activation function g j (·) is Lipschitz continuous, meaning there exists a positive constant L such that:

[0199] |g j (s1)-g j (s2)|≤L|s1-s2|, s1, s2∈R

[0200] Assumption 2: There exists a real number M > 0 such that:

[0201]

[0202] In one embodiment of the present invention, step 4, the method for time synchronization and quantization control of the memristor neural network is as follows:

[0203] According to Theorem 1: Under Assumption 1, Assumption 2, and the controller (2-11), if:

[0204] d i -Lφ+α i (1-δ)≥0

[0205] in Then the following conclusion holds true:

[0206] (1) If 0 < ω < 1, then systems (2-1) and (2-6) achieve finite-time synchronization and the resting time is estimated as follows:

[0207]

[0208] (2) If ω>1, then systems (2-1) and (2-6) achieve fixed-time synchronization and the rest time is estimated as follows:

[0209]

[0210] in:

[0211]

[0212] The above conclusion will now be proven, and the process is as follows:

[0213] Construct the following Lyapunov function:

[0214]

[0215] Differentiating V(t) along the error system (2-10) with respect to t, we get:

[0216] From assumption 1, we can obtain:

[0217]

[0218] From hypothesis 2 and From the definition, we can obtain:

[0219] From (3-1), (3-2), and the conditions of the theorem, we can obtain:

[0220]

[0221]

[0222] By Lemma 2, we can obtain:

[0223]

[0224] Furthermore, we can obtain:

[0225]

[0226] By Lemma 1, Theorem 1 is proved.

[0227] When the memristor parameter a in model (2-1) ij (x i (t))≡a ij At that time, model (2-1) degenerates into a general cellular neural network.

[0228]

[0229] The response system corresponding to the drive system (3-3) is as follows:

[0230]

[0231] Based on Theorem 1, the following corollary holds:

[0232] Corollary 1: Under assumption 1, setup 2, and controller (2-11), if:

[0233]

[0234] Then the following conclusion holds true:

[0235] (1) If 0 < ω < 1, then systems (3-3) and (3-4) achieve finite-time synchronization and the resting time is estimated as follows:

[0236] (2) If ω>1, then systems (3-3) and (3-4) achieve fixed-time synchronization and the estimated rest time is:

[0237]

[0238] in:

[0239]

[0240] The following example illustrates the beneficial effects of the above embodiments:

[0241] Suppose the MNNs model is as follows:

[0242]

[0243] Where: i = 1, 2, 3, d1 = 1.8, d2 = 0.5, d3 = 1.1, g1(x1(t)) = -0.05tanh(x1(t)), g2(x2(t)) -0.15sin(x2(t)), g3(x3(t)) -0.35tanh(x3(t)), J1 -0.5, J2 = 0.7, J3 = 2.4 and:

[0244]

[0245] like Figure 2 As shown, the time evolution of system (4-1) under the initial conditions x1(0)=3.2, x2(0)=1.2, x3(0)=-1.4 was simulated. With MNNs(4-1) as the driving system, its corresponding response system is:

[0246]

[0247] Where: i = 1, 2, 3, y1(0) = 0.5, y2(0) = 2.5, y3(0) = -0.9V(0) = 4.895, other parameters are the same as system (4-1):

[0248] Choosing L = 1, ρ = 0.55, δ ≈ 0.29, β1 = β2 = β3 = 1, according to Theorem 1, when 0 < ω < 1, systems (4-1) and (4-2) can achieve finite-time synchronization; Figures 3 to 5 as well as Figure 6 The time evolution and asymptotic behavior of the synchronization error of the system when the parameter ω = 0.5 were simulated respectively, and the resting time was estimated to be t1 = 1.3s; when ω > 1, according to Theorem 1, the system (4-1) and (4-2) achieve fixed-time synchronization. Figures 7 to 9 and Figure 10 The time evolution of the system and the synchronous behavior of the error were simulated when the parameter ω = 1.5, and the resting time was estimated to be t2 = 4.35s.

[0249] A typical application scenario of the finite-time synchronization and quantization control method for memristor neural networks provided in this invention is described below:

[0250] Memristor Neural Network - Smart Grid Distributed Energy Storage Cluster Collaborative Control Application Process

[0251] 1. System Modeling

[0252] In the scenario of distributed energy storage clusters in smart grids, the core energy storage station managed by the grid dispatch center is regarded as the driving system, and its dynamic characteristics such as charging and discharging power and state of charge (SOC) are described by a memristor neural network (MNN) model. Each distributed energy storage unit (such as energy storage battery packs in communities and industrial parks) is regarded as the response system, and the operating state of each unit (such as real-time charging and discharging current and SOC) corresponds to the potential state of neurons in the MNN. A quantization controller to be designed is introduced into the response system to achieve state synchronization with the driving system.

[0253] 2. Controller Deployment and Quantization Process

[0254] A quantized feedback controller is deployed in each distributed energy storage unit. The controller input is the state error (such as SOC deviation and power output difference) between the core energy storage station and the unit. Unlike traditional continuous signal control, this scheme first converts the continuous error signal into a finite discrete quantization level through a logarithmizer, and then transmits it via power line carrier or narrowband Internet of Things (NB-IoT). After receiving the quantized error signal, the controller applies a preset control law (combined with α) to... i β i , λ i (and the nonlinear protocol of ω parameter) generates control commands to dynamically adjust the charging and discharging power of the energy storage unit or switch the operating mode, so that its state quickly approaches that of the core energy storage station.

[0255] 3. Synchronization type and scene adaptation

[0256] The system synchronization characteristics are determined by the key parameter ω:

[0257] Peak load preparation phase: Set 0<ω<1 to achieve finite-time synchronization (Theorem 1, Conclusion 1) to ensure that all energy storage units reach the preset charging and discharging state within a precisely estimated time and respond quickly to load demand;

[0258] Stable operation phase: ω = 1 corresponds to exponential synchronization, maintaining the stability of the cluster state;

[0259] Sudden interference scenario: Set ω>1 to achieve fixed-time synchronization (Theorem 1, Conclusion 2). The upper limit of the synchronization time is independent of the initial state. It can cope with the coordination needs of some energy storage units with unknown initial states and after communication interruption recovery, and ensure that the cluster recovers stability within a certain time.

[0260] 4. Technological advantages

[0261] The core advantages of this solution include:

[0262] ① Quantization Communication Optimization: By quantizing the error signal, the amount of data transmitted between energy storage units is greatly reduced, adapting to the bandwidth-constrained communication environment in the power grid and reducing transmission delay and energy consumption;

[0263] ②Deterministic fast convergence: The finite / fixed-time synchronization characteristic ensures that the cluster state reaches the target within a defined time range, meeting the stringent requirements of the power grid for response speed;

[0264] ③ Enhanced robustness: Fixed-time synchronization is not sensitive to the initial state and can cope with uncertainties such as the dispersion of the initial SOC of energy storage units and sudden failures;

[0265] ④ Memristor characteristics enable: Utilize the high storage and low power consumption characteristics of MNNs to enhance the intelligent decision-making capabilities and energy efficiency of energy storage clusters;

[0266] ⑤ Scalability: By adjusting parameters, it can degenerate into continuous signal control, or be adapted to diverse grid energy storage architectures based on different types of energy storage unit models.

[0267] The finite-time synchronization and quantization control method of memristor neural networks provided in this embodiment of the invention offers a feasible solution for the efficient collaboration of smart grid energy storage clusters.

[0268] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A finite-time synchronization and quantization control method for memristor neural networks, characterized in that: The method includes the following steps: Step 1: Construct a memristor neural network system model; Step 2: Construct a controller for the memristor neural network system model from Step 1; Step 3: Construct the definitions and lemmas required for time synchronization and quantization control of memristor neural networks; Step 4: Combining Steps 1 to 3, perform time synchronization and quantization control on the memristor neural network.

2. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 1, characterized in that: The memristor neural network system model established in step 1 is as follows: Where i = 1, 2, ..., n; x i (i) corresponds to capacitor C i voltage; d i >0 indicates the rate at which the i-th neuron resets its potential to a resting state; g i (x i (t) is the activation function; J i J i It is an external bias; a ij (x i (t) represents the memristor synaptic connection weight, which is defined as follows: in Indicates memristor P ij The memristor coefficient; P ij Represents the feedback function g j (x j (t) and x i The memristor between (t); based on the characteristics of the memristor and its current-voltage properties, the memristor synaptic weight can be expressed in the following form: Where T i >0 indicates a toggle transition; is a constant and 3. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 2, characterized in that: In step 2, the controller control strategy of the memristor neural network system model is as follows: U i (t)=-α i q(e i (t))-β i sign(q(e i (t)))-λ i sign(q(e i (t)))|q(e i (t))| ω Where, α i ,β i , λ i Both ω and q(·) are positive constants; q(·) is a logarithmic quantizer.

4. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 3, characterized in that: In step 2, a non-uniform quantizer is used as the quantizer, as described below: First, given the quantization set: Λ-{±b j ;b j -ρ j b0, j=0, ±1, ±2,…}∪{0} Where b0 > 0 is the scaling parameter; 0 < ρ < 1 represents the quantization density. The quantizer q(·) maps each interval to a quantization series, and its functional expression is: Here, v is the input to the quantizer, and q(v) is the output of the quantizer. It is the quantization parameter; the quantizer q(·) can be further expressed as: q(v)=(1+Δ)v Where: Δ∈[-δ, δ]; The controller, derived from the quantizer, can be written in the following form: U i (t)=-a i (1+Δ)e i (t)-β i sign((1+Δ)e i (t)) -l i sign((1+Δ)e i (t))(1+Δ) ω |e i (t)| ω By the definition of Δ, we know that 1 + Δ ∈ (0.2), therefore: sign((1+Δ)e i (t))=sign(e i (t)) Therefore, the finite-time quantization control strategy can ultimately be written as: U i (t)--a i (1+Δ)e i (t)-β i sign((1+Δ)e i (t))-l i sign(e i (t))(1+Δ) ω |e i (t)| ω (2-11)(2-11) By differential inclusion theory and measurable choice theory, there exists a measurable function: Equation (2-11) is equivalent to the following form: U i (t)=-α i (1+Δ)ei(t)-β i s(e i (t))-λ i s(e i (t))(1+Δ) ω |e i (t)| ω 。 5. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 4, characterized in that: The definitions required for constructing the memristor neural network time synchronization and quantization control in step 3 include: Definition 1: Consider the following system: in Let be a nonlinear, discontinuous, but locally measurable function; for any x(t) represents the system (2-3) in the interval [0, 1]. The solution in the Filippov sense on; for any compact interval x(t) is absolutely continuous and satisfies the following differential: Set-valued mapping Defined as: here Indicates the convex closure. Represents a set The Lebesgue measure; B(x, ρ) is an open sphere with center x and radius ρ > 0, denoted as: Then system (2-1) can be reduced to the following form: in: Based on the definition of Filippov's solution and the differential inclusion theory, equation (2-4) can be further simplified to: According to the measurable choice theory, there exists a measurable function. Make: If system (2-1) is defined as the driving system, then its response system is: Among them U i (t) represents the controller to be designed; The response system (2-6) can be written as: in: Based on the differential inclusion theory, system (2-7) can be written as: According to the theory of measurable choice, there exists a measurable function. Make: Define error e i (t)=y i (t)-x i (t) Then, from systems (2-5) and (2-9), we can obtain the following error system: in: g j (e j (t))=g j (y j (t))-g j (x j (t))。 6. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 5, characterized in that: The definitions required for constructing the memristor neural network time synchronization and quantization control in step 3 also include: Definition 2: If there exists a constant T(e(0)) ≥ 0 such that: and Where e(0)=y(0)-x(0)∈R n R n Let represent the set of n-dimensional real vectors, then systems (2-1) and (2-6) are said to achieve finite-time synchronization; furthermore, if for any initial value e(0)∈R n Both have a constant T. max Make T(e(0))≤T max If so, then systems (2-1) and (2-6) are said to achieve fixed-time synchronization.

7. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 6, characterized in that: The lemmas required for constructing the time synchronization and quantization control of the memristor neural network in step 3 include: Lemma 1: If there exists a regular, positive definite, and radially unbounded function Such that for any solution x(t) of the system, the following conditions are met: Where a, b>0, 0≤μ1≤1, μ2≥0, then the following conclusion holds: (1) If 0 ≤ μ2 ≤ 1, then the zero solution of the system is finite-time stable and the resting time is estimated as follows: V(0)=V(x(0)) * =max{μ1,μ2},μ ** =min{μ1,μ2}; (2) If μ2 > 1, then the zero solution of the system is time-stable and the resting time is estimated as follows:

8. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 7, characterized in that: The lemma required for constructing the time synchronization and quantization control of the memristor neural network in step 3 also includes: Lemma 2: Let x i If ≥0, i=1,2,…,n,0<p<q,ω>1, then the following inequalities hold:

9. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 8, characterized in that: In step 3, when constructing the definitions and lemmas required for memristor neural network time synchronization and quantization control, the following assumptions are introduced: Assumption 1: Activation function g j (·) is Lipschitz continuous, meaning there exists a positive constant L such that: |g i (s1)-g i (s2)|≤L|s1-s2|,s1,s2∈R Assumption 2: There exists a real number M > 0 such that:

10. The finite-time synchronization and quantization control method for a memristor neural network as described in claim 9, characterized in that: In step 4, the method for time synchronization and quantization control of the memristor neural network is as follows: According to Theorem 1: Under Assumption 1, Assumption 2, and the controller (2-11), if: d i -Lφ+α i (1-d)≥0 in Then the following conclusion holds true: (1) If 0 < ω < 1, then systems (2-1) and (2-6) achieve finite-time synchronization and the resting time is estimated as follows: (2) If ω>1, then systems (2-1) and (2-6) achieve fixed-time synchronization and the rest time is estimated as follows: in:

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