Time-delay neural network non-fragile state estimation method and device, medium and product

Abstract

The invention provides a time-delay neural network non-fragile state estimation method and device, a medium and a product, and relates to the field of networked system control. In order to obtain state information of a time-delay memristor neural network circuit system, a non-fragile state estimator is established by introducing a dynamic saturation function. Determining an estimation error system based on the established system model and the estimation system model, and performing augmentation processing to obtain an augmented system model; through constructing an energy function and setting a constraint condition of an estimation error, a matrix analysis technology and a linear matrix inequality method are used to obtain a sufficient condition satisfying augmented system performance constraint, and a gain parameter of a non-fragile state estimator model is determined to obtain a final non-fragile state estimator model. And determining the state of the neurons of the time-delay neural network. According to the method, the conditions of negative effects and estimation performance reduction caused by time lag and abnormal disturbance interference in actual production can be inhibited or attenuated.

Description

Technical Field

[0001] The present application relates to the field of networked system control, and particularly to a non-fragile state estimation method, device, medium and product for a time-delay neural network. Background Art

[0002] A neural network system is a non-linear dynamic system composed of a large number of neurons. By simulating the structure of the human brain's nervous system, an artificial neural network can perform parallel processing, storage, and associative memory of information. Based on this characteristic, neural networks are widely used in many fields closely related to human life, such as image processing, signal recognition, healthcare, and control systems.

[0003] As a basic component of the nervous system, the synapses of neurons play a role in information transmission and processing, and are closely related to functions such as learning and memory. In reality, traditional CMOS (Complementary Metal Oxide Semiconductor) circuits are often used to simulate neural networks. Due to physical defects such as a large number of required components, large transistor volume, and high circuit power consumption, and when simulating relatively complex neural networks or facing the current demand for processing massive data, the effect is not ideal, which also indirectly affects the theoretical analysis and application of neural networks. Therefore, in traditional neural network circuits, synapses composed of resistors cannot effectively simulate the dynamic behavior of synapses between biological neurons.

[0004] As is well known, the state information of neurons plays an important role in the wide application of neural networks in fields such as signal processing and fault diagnosis. However, since neural networks are constructed by large-scale integrated circuits, it is difficult to directly obtain the state information of all neurons under the premise of limited measurement resources. Therefore, exploring the state estimation problem of neural networks has an important role in solving many applications in real life. In a neural network circuit system, the limited amplifier switching speed and signal transmission speed make time delay inevitable in the nervous system. Therefore, in a real environment, the nervous system is easily interfered by time delay. For the design, learning, and research of existing nervous system estimation methods, the existing estimation methods usually cannot suppress or attenuate the negative impact brought by this time delay. Summary of the Invention

[0005] The purpose of the present application is to provide a non-fragile state estimation method, device, medium and product for a time-delay neural network, which can suppress or attenuate the negative impact brought by time delay while avoiding the situation that the estimation performance decreases due to singular value interference during measurement.

[0006] To achieve the above object, the present application provides the following solutions:

[0007] In the first aspect, the present application provides a non-fragile state estimation method for a time-delay neural network, including:

[0008] A time-delay memristive neural network system is established by replacing the resistive weights in the artificial neural network circuit system with memristors; the time-delay memristive neural network system includes: a neural network dynamic model and a measurement output model;

[0009] Regarding the switching characteristics of the memristor, a time-delay neural network system with parameter uncertainties is obtained by analyzing and processing the weights of the time-delay memristive neural network system;

[0010] Based on the time-delay neural network system with parameter uncertainties, a non-fragile state estimator model with saturation constraints is established;

[0011] The estimation error is determined by using the time-delay neural network system with parameter uncertainties and the non-fragile state estimator model, and an error system is constructed;

[0012] Based on the error system and the time-delay neural network system with parameter uncertainties, augmentation processing is performed to obtain an augmented system model of the estimation error;

[0013] Set the constraint conditions of the estimation error;

[0014] Based on the constraint conditions of the estimation error, an energy function containing time-delay boundary information is constructed, and sufficient conditions to meet the set performance requirements are derived by using matrix analysis techniques and linear matrix inequality methods;

[0015] According to the sufficient conditions, the gain parameters of the non-fragile state estimator model are determined to obtain the final non-fragile state estimator model;

[0016] The neuron states of the time-delay memristive neural network system are obtained by using the final non-fragile state estimator model.

[0017] Optionally, the neural network dynamic model is expressed as:

[0018]

[0019] In the formula, v i (t) is the state of the i-th neuron at time t, is the first derivative of the neuron state, a ij (v j (t)) and b ij (v j (t)) are both the memristive weights of the j-th neuron state v j (t) at time t, d i is the self-feedback coefficient of the i-th neuron state, is the activation function of the j-th neuron, h(t) is the time-varying time delay at time t, ω(t) is the external perturbation at time t, and ζ(t) is the impulse perturbation or singular value perturbation at time t. and are both dimensional coefficients, y j (t) is the measured output of the j-th neuron at time t, v j (*) is the state of the j-th neuron at time *, is the perturbation coefficient.

[0020] Optionally, according to the physical characteristics of the memristor, the weights of the memristive neural network are analyzed and processed;

[0021] According to the state-dependent characteristics of the memristive weight coefficient, the memristive weight coefficients a ij (·), b ij (·) are expressed as:

[0022]

[0023] where, is the switching threshold, á ij , à ij , are both constants;

[0024] Define:

[0025]

[0026] a ij = min{à ij , á ij},

[0027] It is deduced that Define Based on this, the matrix is expressed as:

[0028] Satisfying the norm-bounded uncertainty, there is:

[0029]

[0030] where, is an unknown matrix and satisfies are both known constant matrices, and are both memristive synaptic connection weights, and are the uncertain terms after the transformation of the memristive weights, and I is the unit vector. and is the vector form to which the maximum memristance switches.

[0031] Optionally, the neural network with switching characteristics is represented as:

[0032]

[0033] wherein, is the first-order derivative of the neuron state in vector form, is the neuron inhibition rate, ν(t) is the neuron state at time t, is the activation function, γ(t) is the estimation error of the neuron state at time t, h 1 (t) is the first time-varying time delay at time t, h 2 (t) is the second time-varying time delay at time t, H is the coefficient matrix of known dimension, and ω(t) is the external disturbance at time t.

[0034] Optionally, the non-fragile state estimator model is represented as:

[0035]

[0036] wherein, is the derivative of the neuron state estimate of, is the estimate of the non-fragile state estimator model at time t, and are both memristive synaptic connection weights, is the neuron inhibition rate, is the activation function, γ is the expectation of the random variable γ(t), is the estimation gain matrix, is the estimate of the measured output y(t) at time t, is the estimator gain change matrix, is the saturation function, E 1 is the matrix coefficient of known dimension.

[0037] Optionally, the error is defined as: Then the error system is represented as:

[0038]

[0039] wherein, is the derivative form of the error r(t), r(t) is the estimation error of the neuron state at time t, and are both memristive synaptic connection weights, is the neuron inhibition rate, is a known scalar, h 1 (t) is the first time-varying time delay at time t, h 2 (t) is the second time-varying time delay at time t, v(*) is the neuron state at time *, γ(t) is a random variable, E 1 , H, and M are all real matrices of known dimensions, is a non-linear function, is the estimation error of the neuron state at time t, ω(t) is the external disturbance at time t.

[0040] Optionally, define The augmented system model is expressed as:

[0041]

[0042] where,

[0043]

[0044] In the formula, are all coefficient matrices of the augmented system, is the non-linear term containing the random variable, v(t) is the augmented form of the neuron state error, is a non-linear function, g(v(t)) and are the activation function and the corresponding error form respectively, T is the transpose of the matrix.

[0045] In a second aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the computer program to implement the steps of the time-delay neural network non-fragile state estimation method provided above.

[0046] In a third aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the time-delay neural network non-fragile state estimation method provided above are implemented.

[0047] In a fourth aspect, the present application provides a computer program product, including a computer program, and when the computer program is executed by a processor, the steps of the time-delay neural network non-fragile state estimation method provided above are implemented.

[0048] According to the specific embodiments provided by the present application, the present application has the following technical effects:

[0049] The present application provides a non-fragile state estimation method, device, medium and product for a time-delay neural network. In order to better restore the characteristics of the neural network, a network weight is constructed by a memristor, and a time-delay memristive neural network circuit system is established. Considering the existence of abnormal disturbances in actual production, a class of dynamic saturation functions is introduced to ensure the stability of the augmented system model. While considering the influence of time delay, the situation of the estimation performance degradation caused by the singular value interference during measurement is avoided. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0051] Figure 1 It is a schematic flowchart of a non-fragile state estimation method for a time-delay neural network provided by an embodiment of the present application;

[0052] Figure 2 It is the response curve diagram of the neuron state v 1 (t) of the memristive neural network provided by an embodiment of the present application and its estimated value ;

[0053] Figure 3 It is the response curve diagram of the neuron state v 2 (t) of the memristive neural network provided by an embodiment of the present application and its estimated value ;

[0054] Figure 4 It is the response curve diagram of the neuron state v 3 (t) of the memristive neural network provided by an embodiment of the present application and its estimated value ;

[0055] Figure 5 It is the response curve diagram of the neuron state v 1 (t) of the memristive neural network provided by an embodiment of the present application under the action of a traditional estimator and its estimated value after being affected by an abnormal disturbance;

[0056] Figure 6 It is the response curve diagram of the neuron state v 2 (t) of the memristive neural network provided by an embodiment of the present application under the action of a traditional estimator and its estimated value after being affected by an abnormal disturbance;

[0057] Figure 7 It is the response curve diagram of the neuron state v3 (t) and its estimated value Response curve diagram;

[0058] Figure 8 It is the singular value perturbation diagram that appears when measuring the output of the time-delay neural network system provided by an embodiment of the present application;

[0059] Figure 9 It is the response curve diagram of the neuron state v(t) and its estimated value that are not affected by abnormal perturbations under the action of the estimator provided by an embodiment of the present application Response curve diagram;

[0060] Figure 10 It is a schematic structural diagram of a computer device provided by an embodiment of the present application. Detailed implementation manners

[0061] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0062] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0063] In an exemplary embodiment, the present application provides a non-fragile state estimation method for a time-delay neural network. This method is executed by a computer device, and specifically, it can be executed alone by a computer device such as a terminal or a server, or jointly executed by a terminal and a server. In the embodiments of the present application, this method is described by taking it as an example applied to a server. As Figure 1 shown, this method includes:

[0064] Step 100: Replace the resistance weights in the artificial neural network circuit system with memristors to establish a time-delay memristive neural network system. Among them, the time-delay memristive neural network system includes: a neural network dynamic model and a measurement output model.

[0065] The memristive neural network dynamic model with noise and singular perturbation interference is expressed as:

[0066]

[0067] In the formula, v i (t) is the state of the i-th neuron at time t, is the first-order derivative form of the neuron, a ij (v j(t)) and b ij (v j (t)) are both the j-th neuron states v j (t) of the memristive weight. d i is the self-feedback coefficient of the i-th neuron state, d i > 0. h(t) is the time-varying time delay at time t. ω(t) is the external disturbance at time t, is the set of real numbers. ζ(t) is the impulse disturbance or singular value disturbance at time t. and are both dimension coefficients, and are both known appropriate dimension coefficients. y j (t) is the measured output of the j-th neuron at time t, v j (*) is the j-th neuron state at time *, is the disturbance coefficient. is the activation function of the j-th neuron and satisfies the following assumptions:

[0068] Assumption 1, for l ∈ N, the activation function of the neural network system satisfies:

[0069]

[0070] where, v 1 ≠ v 2 , l - , l + is a real number, and

[0071] Step 101: Regarding the switching characteristics of the memristor, a time-delay neural network system with parameter uncertainties is obtained by analyzing and processing the weights of the time-delay memristive neural network system. Among them, considering the time-delay neural network system constructed by the memristor as a class of switching systems, the conventional analysis methods are not applicable. Therefore, in this step, by analyzing and discussing the physical characteristics of the memristor, the weights of the time-delay neural network system constructed by the memristor are analyzed and processed, and then a system model that can be processed by the conventional right-end continuous system analysis method is obtained, that is, a neural network with switching characteristics.

[0072] In the actual application process, according to the physical characteristics of the memristor, the weights of the memristive neural network are analyzed and processed.

[0073] According to the state-dependent characteristics of the memristive weight coefficient, the memristive weight coefficients a ij (·), b ij (·) can be expressed as:

[0074]

[0075] wherein, is the switching threshold, á ij , à ij , are all constants.

[0076] Define:

[0077] a ij = min{à ij , á ij}.

[0078]

[0079] Furthermore, it can be deduced that Define Based on this, the matrix can be expressed as: and satisfies norm-bounded uncertainty:

[0080]

[0081] wherein, is an unknown matrix and satisfies is a known constant matrix.

[0082] Assume that the time-delay h(t) is bounded and satisfies h 1 ≤ h(t) ≤ h 3 , where the scalars h 1 and h 3 represent the upper and lower bounds of the time-delay. There exists h 2 satisfying 0 ≤ h 1 ≤ h 2 ≤ h 3 , such that h(t) ∈ [h 1 , h 2 or h(t) ∈ (h 2 , h 3 . The probability that the time-varying time-delay h(t) ∈ [h 1 , h 2 is The probability that it is distributed in the interval (h 2 , h 3 is are known scalars and satisfy

[0083] To characterize the stochastic distribution characteristics of the time-varying time-delay, two sets are defined here and introduce the following time-varying delay h 1 (t) and h 2 (t):

[0084]

[0085] It can be deduced from the above that define the random variable γ(t) as:

[0086]

[0087] Considering that the time-varying delay has the characteristics of random distribution, the neural network with parameter uncertainty is expressed as:

[0088]

[0089] In the formula, is the derivative form of the state. is the neuron inhibition rate, ν(t) is the neuron state at time t. and are both memristive synaptic connection weights, and are the uncertain terms after the transformation of the memristive weight. is the activation function, L 1 ,L 2 are both real matrices with appropriate dimensions. γ(t) is the estimation error of the neuron state at time t, h 1 (t) is the first time-varying delay at time t, h 2 (t) is the second time-varying delay at time t, and H is the perturbation coefficient with a known dimension.

[0090] Step 102: Based on the time-delay neural network system with parameter uncertainty, establish a non-fragile state estimator model with saturation constraints. In this step, considering the influence of the complex environment on the estimation gain and the influence of the complex and changeable environment and measurement output by outliers, introduce a class of dynamic saturation functions. Since the measurement outliers do not appear continuously for a long time, when establishing the non-fragile state estimator model, consider ζ(t)≡0. Based on this, the non-fragile state estimator model is expressed as:

[0091]

[0092] In the formula, is the estimated value of the neuron state of the derivative, is the estimated value of the non-fragile state estimator model at time t, Rn 为 The n-dimensional Euclidean space. γ is the expected value of the random variable. To estimate the gain matrix and satisfy the additive boundary condition, and and F k (t) is an unknown function, and I is the unit vector. is the estimated value of the measured output y(t) at time t, is the estimator gain change matrix. E 1 is the coefficient matrix of a known dimension. is a class of adaptive saturation functions, where the vector s(t) = [s 1 (t), s 2 (t), … s n (t)] T . The non - negative saturation threshold ∈(t) = [∈ 1 (t), ∈ 2 (t), …, ∈ m (t)] T ∈R m . Assume that the saturation function satisfies:

[0093]

[0094] In the formula, σ k is a given real parameter, σ k > 0, k = 1, 2, …, m. is a non - negative dynamic variable and satisfies:

[0095]

[0096] In the formula, is a given real number, the positive definite matrix Ψ = Ψ T > 0.

[0097] Step 103: Determine the estimation error using the time - delay neural network system with parameter uncertainties and the non - fragile state estimator model, and construct the error system. Here, the estimation error is defined as: and Based on this, the obtained error system is expressed as:

[0098]

[0099] In the formula, is the first - order derivative of the error, r(t) is the estimation error of the neuron state at time t, γ(t) is the random variable, is a known scalar, is the estimation error of the neuron state at time t, ω(t) is the external disturbance at time t. φ(·) is a nonlinear function, V, E 1 are real matrices of known appropriate dimensions.

[0100] Step 104: Based on the error system and the time-delay neural network system with parameter uncertainties, perform augmentation processing to obtain an augmented system model of the estimation error.

[0101] For convenient analysis, introduce Based on this, the augmented system model is expressed as:

[0102]

[0103] In the formula, is the derivative form of v(t), and

[0104]

[0105] Step 105: Set the constraint conditions of the estimation error, and based on the constraint conditions of the estimation error, construct an energy function containing time-delay boundary information, and use matrix analysis techniques and linear matrix inequality methods to derive sufficient conditions to meet the set performance requirements. The goal of the estimator design in this application is to make the following constraint conditions hold:

[0106] (1) When ω(t) = 0, the estimation error satisfies the asymptotic stability condition.

[0107] (2) Given a disturbance attenuation level μ > 0, under zero initial conditions, the estimation error satisfies:

[0108]

[0109] Theorem 1 Assume that the system activation function satisfies the restriction condition (8), and the scalars h 1 , h 2 and h 3 are known. For the error system, given H ∞ performance index μ > 0, combined with the neural network with switching characteristics, if there exist positive definite symmetric matrices scalar σ > 0, symmetric matrix W = diag{W 1 , W 2}, and matrices of any appropriate dimensions that satisfy the following matrix inequalities:

[0110]

[0111] If it holds, the augmented error system of the memristive neural network is asymptotically stable. Among them.

[0112]

[0113]

[0114] The gain matrix of the desired estimator can be obtained by solving. Construct a Lyapunov function containing time-delay boundary information according to the matrix form of the estimated error augmented system, and the specific form is as follows:

[0115]

[0116] Where:

[0117]

[0118] V(v(t)) is the Lyapunov function at time t, is the weak infinitesimal operator. Differentiate each term of V(v(t)) along the trajectory of the memristive neural network [i.e., formula (9)]:

[0119]

[0120] It can be deduced from Assumption 1 that:

[0121]

[0122] By the Schur complement lemma and the S-produce lemma, combined with equations (11), (12), (14)-(19), it can be deduced that

[0123] Step 106: Determine the gain parameters of the non-fragile state estimator model according to the sufficient conditions to obtain the final non-fragile state estimator model. Among them, through matrix calculation, determine the gain parameters of the non-fragile state estimator model according to the sufficient conditions, and finally substitute the calculated estimated gain parameters into equation (4) to obtain the final non-fragile neural network state estimator model.

[0124] Step 107: Use the final non-fragile state estimator model to obtain the neuron states of the time-delay memristive neural network system.

[0125] In summary, in order to better reflect the real environment, a class of time-delay memristive neural network circuit systems affected by time delay and disturbance is established in this application. Through the analysis and exploration of the memristive weights, combined with the physical characteristics of the memristor, the time-delay neural network system is transformed into a class of traditional neural network systems with parameter uncertainties. By introducing an adaptive saturation function, a new type of non-fragile state estimator model is constructed. Through the augmentation of the time-delay neural network system and the error system, and by combining the upper and lower bounds of the time delay to construct an appropriate energy function (i.e., Lyapunov function), the corresponding sufficient conditions are derived. Finally, by solving the gain parameters required for the non-fragile state estimator model, the final non-fragile state estimator model is obtained to complete the estimation of the state of the time-delay neural network system. Compared with the existing neural network estimation methods, this application selects memristors to replace the weights constructed by resistors, which is more in line with the characteristics of neural networks. In addition, it solves the problem of interference with the estimator performance after singular values appear in network measurements in the actual production environment, and at the same time considers the influence of the existence of randomly distributed time delays, and can be applied to traditional neural networks and Chua's circuit systems, etc., expanding the scope of application and conforming to the actual environment.

[0126] To verify the effectiveness of the estimation method provided in this application. Here, a three-dimensional memristive neural network is selected as the research object:

[0127]

[0128] The system parameters are selected as follows:

[0129]

[0130]

[0131] The measurement output and the controlled regulation matrix are:

[0132]

[0133] The activation function of the time-delay neural network system is:

[0134]

[0135] Using linear matrix inequality technology to solve the relevant expectations and estimate its gain matrix, some of the results are as follows: (1) Case one:

[0136]

[0137]

[0138] To verify the effectiveness of the proposed estimation method, the initial values of the neural network in this embodiment are selected as: v(0) = [1.9 -1.8 -1.2] T , The disturbance attenuation index μ = 1.2, and the upper and lower bounds of the time-varying time delay are selected as: h 1 = 0.6, h 2 = 1.2, h 3 = 1.8. To verify the non-fragile effectiveness of the design of this application, the Dirac function δ(.) is selected to describe the pulse / anomaly disturbance, and there is:

[0139] ζ(t) = 60δ(t - 8) + 80δ(t - 15) + 100δ(t - 24) + 45δ(t - 32) + 150δ(t - 40) + 48δ(t - 122).

[0140] The effect of the non-fragile state estimator model designed in this application is shown in Figures 2 - 9 : Figures 2 - 4 It shows the estimation effect of the non-fragile state estimator model designed in this application in the scenario of abnormal interference. Figures 5 - 7 It describes the trajectory of the neuron state ν(t) and its estimated value under the action of the traditional Luenberger state estimator when affected by measurement outliers. Figure 8 It shows the introduced singular value perturbation. Based on Figure 9 it can be obtained that when there is no interference from measurement abnormal perturbation, the non-fragile state estimator model proposed in this application still has a good estimation effect. From Figures 2 - 9 it can be clearly seen that the method proposed in this application can effectively estimate the state of the research object and has a wider application range. Figures 2 - 9 In, time represents time.

[0141] In summary, this application ensures the stability of the augmented error system by introducing a class of saturation functions with innovation constraints, which is different from the conventional static saturation function and can avoid the situation of deteriorated estimation performance caused by singular value interference during measurement.

[0142] In addition, the introduction of memristors successfully solves the problem that synapses composed of resistors cannot effectively simulate the dynamic behavior of synapses between biological neurons, and promotes the research and application of the dynamic behavior analysis of neural network models. This application can be applied to Chua circuits (Chua circuits) and four-tank process control systems, etc., which has important practical significance.

[0143] In an exemplary embodiment, a computer device is provided. The computer device can be a server or a terminal, and its internal structure diagram can be as Figure 10As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store the data for determining the non-fragile state of the time-delay neural network. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals through a network connection. When the computer program is executed by the processor, it implements a method for estimating the non-fragile state of a time-delay neural network.

[0144] Those skilled in the art can understand that Figure 10 the structure shown in is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0145] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by the processor, the steps in the above method embodiments are implemented.

[0146] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by the processor, the steps in the above method embodiments are implemented. It should be noted that the data involved in this application (including but not limited to the data for analysis, storage, and display) are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of the relevant data need to comply with the relevant regulations.

[0147] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memories. Non-volatile memories can include read-only memory (ROM), magnetic tapes, floppy disks, flash memories, etc. Volatile memories can include random access memory (RAM) or external cache memories, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0148] The databases involved in the embodiments provided in the present application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in the present application can be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logics, data processing logics based on quantum computing, etc., without limitation.

[0149] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0150] In this article, specific examples are used to elaborate on the principles and implementation manners of the present application. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A non-fragile state estimation method for a time-delay neural network, characterized in that: The non-fragile state estimation method of a time-delay neural network comprises: A time-delay memristor neural network system is established by replacing the resistance weights in the artificial neural network circuit system with a memristor; the time-delay memristor neural network system includes: a neural network dynamic model and a measurement output model; According to the switching characteristics of the memristor, a time-delay neural network system with parameter uncertainty is obtained by analyzing and processing the weights of the time-delay memristor neural network system; Based on a time-delay neural network system with parameter uncertainty, a non-fragile state estimator model with saturation constraints is established. Determine the estimation error using a time-delay neural network system with parameter uncertainty and a non-fragile state estimator model, and construct the error system; Performing augmentation processing based on the error system and the time-delay neural network system with parameter uncertainty to obtain an estimated error augmentation system model; Set constraints on the estimation error; Based on the constraint conditions of the estimation error, an energy function containing time-delay boundary information is constructed, and sufficient conditions for satisfying the set performance requirements are derived using matrix analysis technology and linear matrix inequality methods; Determine a gain parameter of a non-fragile state estimator model according to the sufficient condition to obtain a final non-fragile state estimator model; The final non-fragile state estimator model is used to obtain the neuron states of the time-delay memristor neural network system.

2. The non-fragile state estimation method of a time-delay neural network according to claim 1, characterized in that: The neural network dynamic model is expressed as: In the formula, v i (t) is the state of the i-th neuron at time t, is the first-order derivative of the neuron state, a ij (v j (t)) and b ij (v j (t)) is the state v of the jth neuron at time t j (t) memristor weight, d i is the self-feedback coefficient of the i-th neuron state, is the activation function of the jth neuron, h(t) is the time-varying lag at time t, ω(t) is the external disturbance at time t, ζ(t) is the impulse disturbance or singular value disturbance at time t, and are dimension coefficients, y j (t) is the measured output of the jth neuron at time t, v j (*) is the jth neuron state at time *, is the disturbance coefficient.

3. The non-fragile state estimation method of a time-delay neural network according to claim 2, characterized in that: According to the physical characteristics of memristors, the weights of memristor neural networks are analyzed and processed; According to the state-dependent characteristics of the memristor weight coefficient, the memristor weight coefficient a ij (·),b ij (·) is expressed as: In the formula, is the switching threshold, are all constants; definition: roll out definition Based on this, the matrix It is expressed as: Satisfying norm bounded uncertainty, we have: In the formula, is an unknown matrix that satisfies are all known constant matrices, and are all memristor synaptic connection weights, and is the uncertainty term after the transformation of memristor weight, I is the unit vector, and is the vector form to which the maximum memristor switches.

4. The non-fragile state estimation method of a time-delay neural network according to claim 3, characterized in that: The neural network with switching characteristics is expressed as: In the formula, is the first-order derivative of the neuron state In vector form, is the neuron inhibition rate, ν(t) is the neuron state at time t, is the activation function, γ(t) is the estimated error of the neuron state at time t, h1(t) is the first time-varying lag at time t, h2(t) is the second time-varying lag at time t, H is a coefficient matrix of known dimension, and ω(t) is the external disturbance at time t.

5. The non-fragile state estimation method of a time-delay neural network according to claim 4, characterized in that: The non-fragile state estimator model is expressed as: In the formula, is the estimated value of the neuron state The derivative of is the estimated value of the non-fragile state estimator model at time t, and are all memristor synaptic connection weights, is the neuronal inhibition rate, is the activation function, γ is the expectation of the random variable γ(t), is the estimated gain matrix, is the estimated value of the measured output y(t) at time t, is the estimator gain change matrix, is the saturation function, and E1 is the matrix coefficient of known dimension.

6. The non-fragile state estimation method of a time-delay neural network according to claim 5, characterized in that: The error is defined as: The error system is expressed as: In the formula, is the derivative form of the error r(t), r(t) is the estimated error of the neuron state at time t, and are all memristor synaptic connection weights, is the neuronal inhibition rate, is a known scalar, h1(t) is the first time-varying lag at time t, h2(t) is the second time-varying lag at time t, v(*) is the neuron state at time *, γ(t) is a random variable, E1, H and M are all real matrices of known dimensions, φ(·) is a nonlinear function, is the estimated error of the neuron state at time t, and ω(t) is the external disturbance at time t.

7. The non-fragile state estimation method of a time-delay neural network according to claim 6, characterized in that: definition The augmented system model is expressed as: in, In the formula, are the coefficient matrices of the augmented system, is a nonlinear term containing random variables, v(t) is the augmented form of the neuron state error, is a nonlinear function, g(v(t)) and are the activation function and the corresponding error form respectively, and T is the transpose of the matrix.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the non-fragile state estimation method for a time-delay neural network according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the non-fragile state estimation method of a time-delay neural network described in any one of claims 1 to 7 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the non-fragile state estimation method of a time-delay neural network described in any one of claims 1 to 7 is implemented.

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