Two-stage attack-resistant coupled memristive neural network finite-time bipartite synchronization control method based on t-s fuzzy model

Abstract

The application discloses a two-stage anti-attack coupled memristive neural network finite time bisecting synchronization control method based on a T-S fuzzy model, which comprises the following steps: establishing a memristive neural network model and a symbolic topological structure; converting the memristive neural network model into a fuzzy coupled memristive neural network model, defining a synchronization error state variable, and establishing an error system of the memristive neural network; converting the error system into a form based on differential inclusion; designing a two-stage finite time synchronization controller; in the first stage, when the error system state satisfies a condition, designing a pulse controller based on a mixed trigger mechanism to resist a deception attack; and in the second stage, designing a controller combining a finite time control mechanism and a fixed time control mechanism to resist a DoS attack. The two-stage controller is designed, the controller is fused with pulse safety control, feedback control, a finite time control mechanism and a fixed time control mechanism, and can resist a deception attack with energy constraint and a DoS attack with a random burst feature at the same time.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent control and network security, and is suitable for a complex scene with network attacks, uncertain disturbances and multiple time delays, and particularly relates to a two-stage attack-resistant coupled memristive neural network finite-time bisection synchronization control method based on a T-S fuzzy model. BACKGROUND

[0002] In recent years, the dynamic modeling technology based on neural networks has shown significant advantages in the fields of artificial intelligence, pattern recognition and optimization calculation, etc. By simulating the nonlinear characteristics of the biological neural system, it provides an efficient solution framework for linear / nonlinear programming, image processing and associative memory tasks in complex scenarios. In particular, the physical characteristics of the memristor are highly similar to those of the biological synapse, making the memristive neural network a core carrier for realizing the integration of storage and calculation and low-power brain-like chips. Through the memory effect and nonlinear conductance characteristics of the memristor, the memristive neural network can more accurately depict the dynamic behavior of the biological neural network, laying a physical foundation for neuromorphic computing and intelligent hardware development.

[0003] The synchronization research of fuzzy coupled memristive neural networks is a frontier direction in the fields of intelligent systems and complex networks, and its core lies in solving the synchronization performance degradation problem caused by the nonlinear switching of memristive weights, the uncertainty of network topology and external disturbances in multi-node dynamic collaboration. The existing technology introduces a T-S fuzzy model to model the memristive dynamics and topological uncertainty, and constructs a double-channel non-fragile control mechanism (such as a mixed time delay compensation channel based on an improved Jensen inequality and a memory-type sampling control channel driven by a Bernoulli sequence), making progress in robust synchronization control under parameter disturbance and partially solving the problems of finite-time / asymptotic synchronization, time delay compensation and parameter uncertainty handling. However, the current method still has significant limitations: first, the controller design is mostly based on ideal communication assumptions, lacking a security control mechanism for network security threats such as spoofing attacks and denial-of-service attacks; second, the existing framework is difficult to handle multiple time delays, uncertain disturbances and finite-time bisection synchronization requirements simultaneously, resulting in limited applicability in dynamic complex scenarios such as industrial Internet of Things and multi-agent antagonistic cooperation. The above defects restrict the engineering application of memristive neural networks in high-security and real-time scenarios, and an integrated solution that combines attack-resistant cooperative control, time delay-disturbance joint suppression and fast bisection synchronization is urgently needed.

[0004] The core challenge of secure communication in networked control systems is to resist hybrid attacks (e.g., channel blocking of DoS attacks and data forgery of deception attacks) and maintain system synchronization stability. For coupled memristive neural networks, the memory effect and non-smooth nonlinear characteristics make the synchronization process have a conduction amplification effect on multi-modal attacks: hybrid attacks on the sensor-controller and controller-actuator double channels can destroy the charge-magnetic balance through synaptic weight space-time mismatch, trigger error cascade diffusion through coupling structure disturbance, and cause activation function distortion through memristive threshold shift, forming a multi-dimensional threat chain. Although existing secure control methods can cope with single attack patterns, they lack a coordinated defense mechanism for multi-modal conduction effects and nonlinear dynamic coupling in hybrid attack scenarios, leading to the risk of synchronization instability in high-security demand scenarios such as industrial Internet of Things and distributed collaborative computing. It is urgent to build an integrated anti-attack synchronization control framework that takes into account channel attack blocking, topology disturbance suppression, and parameter distortion compensation.

[0005] To address the continuous attack threat caused by false data injection in the communication channel, existing research uses discontinuous pulse safety control strategies to effectively suppress the attack effectiveness probability by reducing the attack window frequency, and has made progress in multi-agent network deception attack suppression, DoS attack under pulse consensus control, and random double attack scenarios of neural network almost sure synchronization. However, existing pulse safety control methods still have significant limitations: first, they are not deeply combined with T-S fuzzy rules, making it difficult to model the synchronization compensation of parameter perturbations, time delay disturbances, and other uncertain factors through the coordination of fuzzy logic and the dynamic characteristics of neural network synaptic weights; second, existing research focuses on asymptotic synchronization, lacking theoretical support for pulse control law design and stability analysis in strong constraint scenarios with dynamic performance indicators such as finite time and fixed time, leading to insufficient adaptability in real-time decision-making and high-precision collaboration in industrial scenarios. The above defects restrict the universality of pulse safety control in hybrid driving and fault diagnosis of intelligent systems, and it is urgent to build a new pulse cooperative control framework that integrates fuzzy dynamic compensation, multi-modal attack suppression, and strong time synchronization goals. SUMMARY

[0006] The present application aims to at least partially solve one of the technical problems existing in the related art.

[0007] The present application aims to at least partially solve one of the technical problems existing in the related art.

[0008] In order to achieve the above object, the application provides a two-stage attack-resistant coupled memristive neural network finite time bisection synchronization control method based on a T-S fuzzy model, comprising the following steps:

[0009] S100, a memristive neural network model and a symbolic topology structure oriented to multiple time delays and T-S fuzzy rules are established;

[0010] S200, symbolic topology structure conversion is performed, a structure balance graph definition specification transformation matrix is defined, and the memristive neural network model is converted;

[0011] S300, fuzzy logic rules are defined, the memristive neural network model is converted into a fuzzy coupled memristive neural network model, a synchronization error state variable between the ith node and a target node is defined, and an error system of the memristive neural network is established;

[0012] S400, the error system is converted into a form based on differential inclusion based on set value mapping and differential inclusion theory estimation of the memristive function;

[0013] S500, a two-stage finite time synchronization controller is designed, comprising:

[0014] The first stage: when the error system state satisfies the condition, a pulse safety controller based on a mixed trigger mechanism is designed to resist deception attacks;

[0015] The second stage: according to the active-sleep alternation characteristics of DoS attacks, an attack feature driven dynamic switching strategy is constructed, a controller combining finite time control and fixed time control mechanisms is designed to resist DoS attacks, efficient information interaction is performed during the attack interval, and safe state maintenance is performed during the attack duration.

[0016] The further preferred technical solution of the application is that in step S100, the memristive neural network model and the symbolic topology structure oriented to multiple time delays and T-S fuzzy rules are established, specifically:

[0017] S110, a memristive neural network coupled with N node neural networks is constructed, and the dynamic model of the ith node of the memristive neural network is represented as:

[0018]

[0019] wherein, , denotes a node set, and N denotes the number of nodes; denotes the state vector of the ith node at time t, and n denotes the dimension of the state vector of each node; denotes a positive definite diagonal matrix; , , ​and both represent uncertain disturbances; and represents an activation function;

[0020] Assume that the memristive neural network has a heavy time delay, represents the first heavy time delay, and ; represents the coupling strength; represents a set of weights; represents a sign function; represents a constant, when the first node has a cooperative relationship with the first node , an antagonistic relationship 0, no connection relationship ;

[0021] and represents the memristive weight of the first node, respectively:

[0022]

[0023]

[0024] wherein represents a switching jump coefficient, , , and are all real constants, represents the first element of an -dimensional vector , ;

[0025] S120, the dynamics model of the target node of the memristive neural network is represented as:

[0026]

[0027] wherein represents the state vector of the target node at the time , and and represent the memristive weights of the target node, respectively:

[0028]

[0029]

[0030] S130, representing the N-node neural network as a symbolic topology structure wherein represents a vertex set, whose index set is denoted as , represents an edge set, represents an adjacency matrix; if there is information interaction between nodes and , then , otherwise, ; it is assumed that the graph does not have self-loop, when represents that the vertex and are in a cooperative relationship, when represents that the vertex and are in a competitive relationship;

[0031] The Laplacian matrix is defined as , the degree matrix , wherein ; the element of the Laplacian matrix is represented as:

[0032] .

[0033] As preferred, the symbolic topology structure conversion in step S200 is performed, a canonical transformation matrix is defined based on the structure balanced graph definition, and the memristor neural network model is converted; specifically:

[0034] S210, defining the structure balance of the graph ; if the set is divided into two subsets and , and , ; that is, for , is established; for , is established;

[0035] S220, assuming that the graph is a structure balanced graph, there is a canonical transformation matrix whose elements are , so that is established, wherein ; let the matrix be , then is established, the matrix is a semi-positive definite matrix and satisfies the row sum of zero, and is represented as:

[0036]

[0037] Let , is the structural balance graph determination equation is established, then ;

[0038] S230, the i-th node dynamics model of the memristive neural network is converted into the following form:

[0039] .

[0040] As a preferred, the definition of fuzzy logic rules in step S300 converts the memristive neural network model into a fuzzy coupled memristive neural network model, and defines the synchronization error state variable between the i-th node and the target node, and establishes the error system of the memristive neural network; including:

[0041] S310, a T-S fuzzy logic rule base is constructed , set as , as , , as , combined with the fuzzy rule, the i-th node dynamics model of the memristive neural network converted in step S230 is converted into a fuzzy memristive neural network i-th node dynamics model again, represented as:

[0042]

[0043] wherein, is a known constant matrix of node , is a memristive matrix of node ; is a measurable premise variable, is a fuzzy set, is a fuzzy set; , , is the i-th membership function of the i-th rule, and ;

[0044] S320, the dynamics model of the target node in step S120 is converted into a fuzzy memristive neural network target node dynamics model, represented as:

[0045]

[0046] ​​S330, define the synchronization error state variable between the ith node and the target node as:

[0047]

[0048] The error system of the memristive neural network is established, denoted as:

[0049]

[0050] wherein, , .

[0051] As a preferred, the step S400 based on the set value mapping and the differential inclusion theory estimates the memristive function, and converts the error system into a form based on differential inclusion; Specifically:

[0052] Based on the fuzzy rule of the memristive coefficient of the ith node dynamics model of the memristive neural network, the fuzzy memristive matrix , , and are constructed; wherein The element , The element , The element , The element ;

[0053] According to the differential inclusion theory and the set value mapping, there are matrices and , the error system of the memristive neural network established in step S330 is converted into the following form:

[0054]

[0055] wherein, , .

[0056] As a preferred, in the first stage of step S500, when the error system state satisfies the condition, a pulse safety controller based on a hybrid trigger mechanism is designed to resist deception attacks, specifically including:

[0057] S511, when the state of the error system , a pulse controller based on a hybrid trigger mechanism is designed, denoted as:

[0058]

[0059] wherein, denotes the controller, denotes the pulse control gain, Indicates the pulse time, is a set of pulse control sequences that satisfies , represents a Dirac pulse;

[0060] S512, for the coexistence of deception attacks and DoS attacks on the controller-actuator communication channel, a composite attack model of leader-follower neural network topology is constructed.

[0061] when When, Control instructions for each node A spoofing attack occurs in the controller-actuator transmission channel, causing the actuator receiving signal to be injected with tampered data, namely:

[0062]

[0063] in As an attack signal; construct the Bernoulli distributed random variables associated with network nodes To characterize the probability of attack success, assume Independent of each other, their distribution satisfies:

[0064]

[0065] in, is a constant;

[0066] S513: Based on the control instruction after the received signal is tampered with, the controller of the first stage is rewritten as follows:

[0067]

[0068] Under the first stage control, that is When , the error system of the memristor neural network is expressed as:

[0069]

[0070] in, ,set up exist Left continuous, that is , ; After the first stage pulse safety control, ,At this time, the second stage of security control is started.

[0071] Preferably, in the second stage of step S500, a controller combining finite time control and fixed time control mechanisms is designed to resist DoS attacks; specifically, the controller includes:

[0072] S521, the second stage considers the influence of the DoS attack in the communication channel on the system finite time synchronization, based on the active-sleep alternation characteristics of the DoS attack, the active time and the sleep time of the DoS attack are represented as and respectively, wherein the time sequence is the control time redefined on the second stage of the controller, in the sleep time period, the communication channel works normally, and in the attack time period, the control input is 0, and accordingly, the second stage controller is represented as

[0073]

[0074] , are respectively

[0075]

[0076] wherein, , , , are control gains, , ;

[0077] S522, under the control of the second stage, that is , the error system of the memristive neural network is represented as

[0078]

[0079] The error system of the memristive neural network under the influence of the hybrid attack is stably fixed in time and mean square, and the dynamic network and the target network are safely and stably synchronized in mean square in fixed time.

[0080] Another aspect of the present application provides a non-transitory computer readable storage medium, which stores computer instructions, the computer instructions enable a computer to execute the two-stage attack-resistant coupled memristive neural network finite time bisection synchronization control method based on the T-S fuzzy model.

[0081] Still another aspect of the present application provides an electronic device, comprising: a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete mutual communication through the communication bus, the processor calls logical instructions in the memory to execute the two-stage attack-resistant coupled memristive neural network finite time bisection synchronization control method based on the T-S fuzzy model.

[0082] In still another aspect, the present application provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program, when executed by a processor, causing a computer to execute the two-stage attack-resistant coupled memristive neural network finite-time bisection synchronization control method based on T-S fuzzy model described above.

[0083] Beneficial effects: the two-stage attack-resistant coupled memristive neural network finite-time bisection synchronization control method based on T-S fuzzy model of the present application, aiming at the synchronization control demand of fuzzy coupled memristive neural network in complex environment, first, by introducing an improved fuzzy membership function and the characteristics of the memristor, a new fuzzy coupled memristive neural network model is established, which effectively solves the limitations of traditional neural network model in processing asymmetric activation function and external disturbance, and provides a new paradigm for the collaborative optimization of complex systems; secondly, in view of the deception attack and DoS attack faced by the controller to the actuator communication channel, a two-stage controller is designed, which combines pulse safety control, feedback control and finite-time and fixed-time control mechanism, and can resist deception attack with energy constraint and DoS attack with random burst characteristics at the same time; this research breaks through the paradigm that existing pulse safety control research is mostly limited to asymptotic synchronization, constructs a finite-time fixed-time bisection synchronization analysis framework, constructs a new time-varying segmented Lyapunov-Krasovskii functional, and derives a finite fixed-time synchronization criterion with lower conservativeness, and establishes a calculation model of the upper bound of synchronization convergence time. BRIEF DESCRIPTION OF DRAWINGS

[0084] Figure 1 It is a schematic diagram of the memristive neural network of the present application suffering from deception attack and DoS attack;

[0085] Figure 2 It is a schematic diagram of the safety control method of the present application against mixed attack in different stages;

[0086] Figure 3 It is a topological graph of the fuzzy memristive coupled dynamic network in embodiment 2;

[0087] Figure 4 It is a schematic diagram of the follower and target synchronization error state under the two-stage safety control of the present application schematic diagram;

[0088] Figure 5 It is a schematic diagram of the follower and target synchronization error state under the two-stage safety control of the present application schematic diagram. DETAILED DESCRIPTION

[0089] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below in combination with the drawings in the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments, and they should not be understood as a limitation on the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application. In the description of the present application, it should be understood that the terms used are only for the purpose of description and should not be understood as indicating or implying relative importance.

[0090] The problems faced by the present application mainly include the following points:

[0091] 1. Insufficient adaptability of existing models: The traditional memristor neural network model is limited by single time delay assumption and deterministic coupling topology, and cannot analyze the heterogeneous attack scene under dynamic coupling topology, multiple time delays and the synergistic effect of mixed attacks (deception attacks and DoS attacks), resulting in the decline of synchronization control precision and robustness;

[0092] 2. Lack of mixed attack defense mechanism: The existing controller does not design a dynamic defense strategy for the time domain switching characteristics of deception attacks and DoS attacks, and the attack mode and controller parameters are mismatched, making it difficult to achieve suppression during the attack window period;

[0093] 3. Difficulty in quantifying the binary synchronization error: The binary synchronization error under the coupling effect of multiple time delays, pulse disturbance and fuzzy logic lacks effective quantification tools, and the existing stability criterion cannot be compatible with nonlinear memory effect and attack transmission mechanism; In particular, the traditional synchronization time calculation method ignores the interactive influence of saturation constraint and fuzzy differential inclusion, resulting in deviation of the estimated time threshold from the actual engineering requirements.

[0094] The following will be described in combination with Figures 1-5 The present application provides a two-stage anti-attack coupled memristor neural network finite-time binary synchronization control method based on T-S fuzzy model, non-transient computer readable storage medium, electronic device and computer program product.

[0095] Embodiment 1: The present embodiment provides a two-stage anti-attack coupled memristor neural network finite-time binary synchronization control method based on T-S fuzzy model. The overall idea of the method is:

[0096] A memristor-coupled neural network model integrating multiple time delays and fuzzy rules is constructed, and the time-varying characteristics of the dynamic coupling topology and the nonlinear behavior of the memristor weight switching are approximated by TS fuzzy rules. A heterogeneous attack scenario analysis framework is introduced to model the synergistic mechanism of deception attacks and DoS attacks in the sensor-controller and controller-actuator dual channels, and to characterize the multi-dimensional destructive path of attacks on synaptic weights and activation functions. A two-stage dynamic anti-attack controller is designed, and combined with the differential inclusion theory under fuzzy rules, the influence of multiple time delays and fuzzy logic coupling on the synchronization error dynamics is uniformly analyzed, and the sufficient conditions for finite-time binary synchronization are derived. Integral inequalities and scaling techniques are used to quantify the coupling relationship between attack intensity, delay upper bound and fuzzy membership function, and calculate the upper bound threshold of synchronization time to ensure that the estimated results meet the actual engineering fault tolerance requirements.

[0097] The specific steps are as follows:

[0098] S100. Establish a memristive neural network model and symbolic topology structure for multiple time delays and TS fuzzy rules.

[0099] S110, Consider Finite-time binary synchronization control of a memristor neural network coupled with neural networks (nodes), where each neural network model is a nonlinear system containing deterministic disturbances and multiple time delays. The dynamic model of the i-th node of the memristor neural network is expressed as:

[0100]

[0101] in, , Represents a node set, N represents the number of nodes; Indicates the Nodes in The state vector at the moment, n represents the dimension of the state vector of each node; represents a positive definite diagonal matrix; 、 and Both represent uncertain disturbances; and represents the activation function;

[0102] Assume that the memristive neural network has Heavy delay, Indicates the Heavy delay, and ; represents the coupling strength; represents a multiplicity set; represents a symbolic function; Represents a constant, when Node and When the nodes have a cooperative relationship , when the relationship is adversarial 0, when there is no connection ;

[0103] and Indicates the The memristor weights of the nodes are:

[0104]

[0105]

[0106] in Indicates the switching jump coefficient, 、 、 and are all real constants, express dimensional vector No. elements, ;

[0107] S120, the dynamic model of the target node of the memristive neural network is expressed as:

[0108]

[0109] in Indicates that the target node is The state vector at time t, and Represents the memristor weight of the target node, which are:

[0110]

[0111]

[0112] S130, representing the N-node neural network as a symbolic topological structure ,in Represents a vertex set, and its index set is recorded as , represents the edge set, Represents the adjacency matrix; if the node and If there is information interaction between , otherwise, ; Assume that the graph There is no self-loop when Represents a vertex and There is a cooperative relationship between Represents a vertex and There is a competitive relationship between them;

[0113] The Laplacian matrix Defined as , degree matrix ,in ; Laplacian matrix Elements Expressed as:

[0114] .

[0115] S2. Perform symbolic topology transformation, define the canonical transformation matrix based on the structural balance diagram, and transform the memristor neural network model.

[0116] S210, Definition Diagram The structural balance of Divide into two subsets and ,and 、 ; That is, for , established; for , Established;

[0117] S220, Design is a structural equilibrium diagram, then there exists is the canonical transformation matrix of the element , making Established, of which ; Let the matrix ,but Established, Matrix is a semi-positive definite matrix with zero row sum, expressed as:

[0118]

[0119] make ,Depend on The structural equilibrium diagram determines the equation If established, ;

[0120] S230, converting the dynamic model of the i-th node of the memristor neural network into the following form:

[0121] .

[0122] S3, define fuzzy logic rules, convert the memristive neural network model into a fuzzy coupled memristive neural network model, and define the synchronization error state variable between the ith node and the target node, and establish the error system of the memristive neural network.

[0123] S310, construct a T-S fuzzy logic rule base , set as , as , , as , combine the fuzzy rules with the memristive neural network ith node dynamics model converted in step S230 to convert the memristive neural network ith node dynamics model into a fuzzy memristive neural network ith node dynamics model again, which is represented as:

[0124]

[0125] wherein, is a known constant matrix of the node , is a memristive matrix of the node ; is a measurable premise variable, is a fuzzy set, is a fuzzy set; , , is the ith membership function of the ith rule, , ; ;

[0126] S320, convert the dynamics model of the target node in step S120 into a fuzzy memristive neural network target node dynamics model, which is represented as:

[0127]

[0128] S330, define the synchronization error state variable between the ith node and the target node as:

[0129]

[0130] Establish the error system of the memristive neural network, which is represented as:

[0131]

[0132] wherein, , .

[0133] ​S4, estimate the memristor function based on the set-valued mapping and differential inclusion theory, and convert the error system into a differential inclusion-based form.

[0134] Based on the memristor coefficient of the i-th node dynamics model of the memristor neural network and the fuzzy rule, a fuzzy memristor matrix is constructed 、 、 and ; wherein the element , the element , the element , the element ;

[0135] According to the differential inclusion theory and set-valued mapping, there exist matrices and , the error system of the memristor neural network established in step S330 is converted into the following form:

[0136]

[0137] wherein, , .

[0138] S5, design a two-stage finite-time synchronization controller, including:

[0139] S510, the first stage: when the error system state satisfies the condition, design a pulse safety controller based on the mixed trigger mechanism to resist deception attacks;

[0140] S511, when the state of the error system , design a pulse controller based on the mixed trigger mechanism, denoted as:

[0141]

[0142] wherein, denotes the controller, denotes the pulse control gain, denotes the pulse time, denoted as the pulse control sequence set, and satisfies , denotes the Dirac pulse;

[0143] Next, for the coexistence scenario of deception attacks and DoS attacks on the controller-actuator communication channel, a composite attack model is constructed Figure 1 as shown in the leader-follower neural network topology.

[0144] S512, for the controller-actuator communication channel, the coexistence of deception attack and DoS attack scene, build leader-following neural network topology of composite attack model,

[0145] When , the first node control instruction In the controller-actuator transmission channel suffers from deception attack, resulting in the actuator receiving signal is tampered with data injection, namely:

[0146]

[0147] Where is the attack signal; the first network node related Bernoulli distribution random variable To characterize the success probability of attack, assuming independent of each other, its distribution satisfies:

[0148]

[0149] Where, is a constant;

[0150] S513, based on the control instruction after receiving signal tampered with data injection, the first stage of the controller is rewritten as:

[0151]

[0152] Under the control of the first stage, that is , the error system of memristor neural network is represented as:

[0153]

[0154] Where, , set In left continuous, that is , ; after the first stage of pulse safety control, so that , at this time, the second stage of safety control is started.

[0155] S520, the second stage: according to the active-sleep alternation characteristics of DoS attack, build attack feature driven dynamic switching strategy, design combined with finite time control and fixed time control mechanism of controller to resist DoS attack, in attack interval period for efficient information interaction, and in attack duration period for safe state retention.

[0156] Because network synchronization relies on the dynamic information exchange between neurons in the follower and leader networks, attackers can trigger a double-destruction effect by periodically blocking communication channels. This causes the network topology to exhibit discontinuous time-varying characteristics, leading to dynamic parameter perturbations in node coupling relationships. Therefore, the second phase focuses on the impact of DoS attacks in the communication channel on the system's finite-time synchronization. By constructing a time-varying coupled topology model that is aware of the attack cycle, efficient information exchange between attacks and maintenance of a secure state during the attack duration are achieved.

[0157] S521, the second stage considers the impact of DoS attacks in the communication channel on the limited time synchronization of the system, based on the active-dormant alternation characteristics of DoS attacks, and They represent the time period of DoS attack and the dormant time period of attack respectively, such as Figure 2 As shown, the time series is the control moment redefined in the second stage of the controller. During the sleep period, the communication channel works normally; during the attack period, the control input is 0. Based on this, the controller of the second stage is expressed as:

[0158]

[0159] 、 They are:

[0160]

[0161] in, , , , are control gains, , ;

[0162] When a periodic DoS attack occurs, the time The information transmission from the controller to the actuator is intercepted, that is, , and during the dormant period The internal signal is restored. The second stage controller The first part consists of three items. Ensure that the network reaches asymptotic or exponential synchronization, which is consistent with The combination can ensure that the network reaches a finite time synchronization and The combination of terms ensures that the network achieves fixed-time synchronization during this phase, and a superlinear design eliminates initial state dependency, ensuring an upper bound on the synchronization time. Asymptotic convergence ensures robustness, finite-time improves transient performance, and fixed-time strengthens attack resistance, ultimately achieving fixed-time bounded synchronization under DoS attacks.

[0163] S522、in the second stage control, that is , the error system of the memristive neural network is expressed as:

[0164]

[0165] The error system of the memristive neural network under the influence of a hybrid attack is stably bounded in the fixed time mean square, and the dynamic network and the target network are stably synchronized in the fixed time mean square.

[0166] The two-stage anti-attack coupled memristive neural network finite time bisection synchronization control method based on the T-S fuzzy model provided in this embodiment can achieve:

[0167] 1. A memristive neural network model is proposed, which breaks through the dual limitations of single time delay constraint and deterministic coupling relationship in traditional bisection synchronization theory. By establishing a mathematical representation that combines dynamic coupling topology and memory characteristics, a new computing framework is constructed that can analyze complex heterogeneous attack scenarios, and dynamic evolution modeling of multi-modal network security threats is achieved.

[0168] 2. In view of the time domain alternating threats of spoofing attacks and DoS attacks faced by the controller-actuator communication channel, a two-stage anti-attack control method is proposed based on pulse control, finite time control and fixed time control mechanism. By constructing an attack feature driven dynamic switching mechanism, the technical problem of dynamic reconstruction of security control strategy in a hybrid attack scenario is solved, and the flexibility of the networked system is significantly improved.

[0169] 3. By constructing Lyapunov functional, the sufficient algebraic criterion for finite time bisection synchronization is strictly derived, which breaks through the traditional single time delay hypothesis and deterministic disturbance constraint from the theoretical level, establishes the stability analysis framework of time delay-disturbance coupled system, and gives the analytical expression of the upper bound of synchronization time, which provides a quantitative evaluation benchmark for the robustness analysis and security enhancement of neuromorphic computing system in complex adversarial environment.

[0170] Embodiment 2: This embodiment provides a specific example to illustrate the two-stage anti-attack coupled memristive neural network finite time bisection synchronization control method based on the T-S fuzzy model.

[0171] First step, establish a fuzzy memristive neural network model with uncertain disturbance and multiple time delays

[0172] In this embodiment, the finite time mean square safe bounded synchronization control of the fuzzy memristive neural network is considered, which includes 5 follower neural networks and a target network. The topology of the fuzzy memristive neural network is as shown in Figure 3 The dynamic model of the i-th node of the memristive neural network is expressed as:

[0173]

[0174] in , Indicates the The state of the neural network, , , the weighted fitness of the fuzzy rule is:

[0175]

[0176] Time memristive coefficient ;

[0177] , ,

[0178] , .

[0179] Assume that the uncertain disturbance is:

[0180] ;

[0181] Assume that the activation function is , the delay is , , , the coupling strength is .

[0182] The target neural network dynamics model given in this embodiment is:

[0183]

[0184] In the formula represents the state of the target neural network, , , , , and nonlinear functions , Same value as following neural network.

[0185] In this embodiment, the symbolic topology is given for 5 neural networks. ,in Represents a vertex set, and its index set is recorded as , represents the edge set, Represents the adjacency matrix. If the node and If there is information interaction between , otherwise, then ; assume graph There is no self-loop, when represents a cooperative relationship between vertices and , when represents a competitive relationship between vertices and . In this embodiment, the internal coupling weight matrix of the five neural network interfaces given is as follows:

[0186]

[0187] Second step, introduce hybrid attack modeling

[0188] In this embodiment, the first stage considers that the controller-to-actuator channel is subjected to a deception attack. Define the deception attack signal , introduce Bernoulli distribution variable to describe the probability of attack success, and assume that random variables are mutually independent, is a positive integer, and:

[0189]

[0190] where is a constant, represents the probability that the random variable takes the value 1 at time t, and is equal to the constant , represents the probability that the random variable takes the value 0 at time t, and is equal to the constant .

[0191] In the second stage, define the DoS attack: consider the attack period , where the time of the DoS attack is .

[0192] Third step, design a two-stage controller:

[0193] The first stage controller is: , where ;

[0194] The second stage controller is:

[0195] where ,

[0196] In this embodiment, , , , , .

[0197] Under the action of the two-stage attack-resistant coupled memristive neural network finite time bisection synchronization control method based on the T-S fuzzy model of the embodiment, when the complex coupled memristive neural network is subjected to a mixed attack, the method combines Figure 4 and Figure 5 It can be seen that the state between each follower neural network and the target neural network ultimately realizes finite time mean square safe bounded synchronization control.

[0198] Embodiment 3: The embodiment provides a non-transitory computer readable storage medium, which stores computer instructions, and the computer instructions enable a computer to execute a two-stage attack-resistant coupled memristive neural network finite time bisection synchronization control method based on a T-S fuzzy model. The method includes the following steps:

[0199] S100, a memristive neural network model and a symbolic topology structure oriented to multiple time delays and T-S fuzzy rules are established;

[0200] S200, symbolic topology structure conversion is performed, a norm transformation matrix is defined based on a structure balance graph, and the memristive neural network model is converted;

[0201] S300, fuzzy logic rules are defined, the memristive neural network model is converted into a fuzzy coupled memristive neural network model, a synchronization error state variable between the i th node and the target node is defined, and an error system of the memristive neural network is established;

[0202] S400, the error system is converted into a form based on differential inclusion based on set value mapping and differential inclusion theory estimation of a memristive function;

[0203] S500, a two-stage finite time synchronization controller is designed, including:

[0204] First stage: when the error system state satisfies the condition, a pulse safe controller based on a mixed trigger mechanism is designed to resist deception attacks;

[0205] Second stage: according to the active-sleep alternation characteristics of DoS attacks, an attack feature driven dynamic switching strategy is constructed, a controller combining finite time control and fixed time control mechanisms is designed to resist DoS attacks, efficient information interaction is performed during the attack interval, and safe state maintenance is performed during the attack duration.

[0206] Embodiment 4: The electronic device can include a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other through the communications bus. The processor can invoke a logic instruction in the memory to execute a two-stage attack-resistant coupled memristive neural network finite-time bisection synchronization control method based on a T-S fuzzy model, which includes the following steps:

[0207] S100, establishing a memristive neural network model and a symbolic topology structure oriented to multiple time delays and T-S fuzzy rules;

[0208] S200, performing symbolic topology structure conversion, defining a canonical transformation matrix based on a structure balance graph, and converting the memristive neural network model;

[0209] S300, defining fuzzy logic rules, converting the memristive neural network model into a fuzzy coupled memristive neural network model, defining a synchronization error state variable between the ith node and the target node, and establishing an error system of the memristive neural network;

[0210] S400, estimating a memristive function based on set-valued mapping and differential inclusion theory, and converting the error system into a form based on differential inclusion;

[0211] S500, designing a two-stage finite-time synchronization controller, including:

[0212] First stage: when the error system state satisfies the condition, a pulse safety controller based on a hybrid trigger mechanism is designed to resist deception attacks;

[0213] Second stage: according to the active-sleep alternation characteristics of DoS attacks, an attack feature-driven dynamic switching strategy is constructed, and a controller combining finite-time control and fixed-time control mechanisms is designed to resist DoS attacks, which can perform efficient information interaction during the attack interval and maintain a safe state during the attack duration.

[0214] In addition, the logic instructions in the above-mentioned memory can be realized in the form of a software function unit and sold or used as a stand-alone product, and can be stored in a computer-readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that contribute to the prior art or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0215] Embodiment 5: The present embodiment provides a computer program product, the computer program product comprising a computer program, the computer program being storable on a non-transitory computer-readable storage medium, and the computer program being executable by a processor to enable a computer to execute a two-stage attack-resistant coupled memristive neural network finite-time bisection synchronization control method based on a T-S fuzzy model, the method comprising the following steps:

[0216] S100, establishing a memristive neural network model and a symbolic topology structure oriented to multiple time delays and T-S fuzzy rules;

[0217] S200, performing symbolic topology structure conversion, defining a canonical transformation matrix based on a structure balance graph, and converting the memristive neural network model;

[0218] S300, defining fuzzy logic rules, converting the memristive neural network model into a fuzzy coupled memristive neural network model, defining a synchronization error state variable between the i-th node and the target node, and establishing an error system of the memristive neural network;

[0219] S400, estimating a memristive function based on set-valued mapping and differential inclusion theory, and converting the error system into a form based on differential inclusion;

[0220] S500, designing a two-stage finite-time synchronization controller, comprising:

[0221] First stage: when the error system state satisfies the condition, designing a pulse safety controller based on a hybrid trigger mechanism to resist deception attacks;

[0222] Second stage: according to the active-dormant alternation characteristics of DoS attack, a dynamic switching strategy driven by attack characteristics is constructed, a controller combining finite time control and fixed time control mechanism is designed to resist DoS attack, efficient information interaction is carried out in attack interval period, and safe state is maintained in attack duration period.

[0223] The device embodiments described above are only illustrative, wherein the units described as separate components can or can not be physically separated, and the components displayed as units can or can not be physical units, i.e., can be located in one place or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the embodiment scheme according to actual needs. Those skilled in the art can understand and implement without creative labor.

[0224] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be realized by means of software and the necessary general hardware platform, and of course, it can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of software products, which can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and include a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0225] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A two-stage anti-attack coupled memristor neural network finite time binary synchronization control method based on TS fuzzy model, characterized by: The steps include: S100: Establish a memristive neural network model and symbolic topology structure for multiple time delays and TS fuzzy rules; specifically: S110, constructing a memristive neural network comprising N node neural network couplings, and expressing the dynamic model of the i-th node of the memristive neural network as: ； in, , Represents a node set, N represents the number of nodes; Indicates the Nodes in The state vector at the moment, n represents the dimension of the state vector of each node; represents a positive definite diagonal matrix; 、 and Both represent uncertain disturbances; and represents the activation function; Assume that the memristive neural network has Heavy delay, Indicates the Heavy delay, and ; represents the coupling strength; represents a multiplicity set; represents a symbolic function; Represents a constant, when Node and When the nodes have a cooperative relationship , when the relationship is adversarial 0, when there is no connection ; in, and Indicates the The memristor weights of the nodes are: ； ； in Indicates the switching jump coefficient, 、 、 and are all real constants, express dimensional vector No. elements, ; S120, the dynamic model of the target node of the memristive neural network is expressed as: ； in Indicates that the target node is The state vector at time t, and Represents the memristor weight of the target node, which are: ； ； S130, representing the N-node neural network as a symbolic topological structure ,in Represents a vertex set, and its index set is recorded as , represents the edge set, Represents the adjacency matrix; if the node and If there is information interaction between , otherwise, ; Assume that the graph There is no self-loop when Represents a vertex and There is a cooperative relationship between Represents a vertex and There is a competitive relationship between them; The Laplacian matrix Defined as , degree matrix ,in ; Laplacian matrix Elements Expressed as: ； S200, performing symbolic topology conversion, defining a canonical transformation matrix based on the structural balance diagram, and converting the memristor neural network model; specifically: S210, Definition Diagram The structural balance of Divide into two subsets and ,and 、 ; That is, for , established; for , Established; S220, Design is a structural equilibrium diagram, then there exists is the canonical transformation matrix of the element , making Established, of which ; Let the matrix ,but Established, Matrix is a semi-positive definite matrix with zero row sum, expressed as: ； make ,Depend on The structural equilibrium diagram determines the equation If established, ; S230, converting the dynamic model of the i-th node of the memristor neural network into the following form: ； S300, defining fuzzy logic rules, converting the memristor neural network model into a fuzzy coupled memristor neural network model, defining a synchronization error state variable between the i-th node and the target node, and establishing an error system of the memristor neural network; S400, estimating the memristor function based on set-valued mapping and differential inclusion theory, and converting the error system into a form based on differential inclusion; S500, design a two-stage finite-time synchronous controller, including: Phase 1: When the error system state meets the conditions, a pulse security controller based on a hybrid trigger mechanism is designed to resist spoofing attacks; Phase 2: Based on the active-dormant alternation characteristics of DoS attacks, a dynamic switching strategy driven by attack characteristics is constructed. A controller that combines finite time control and fixed time control mechanisms is designed to resist DoS attacks, conduct efficient information exchange during the attack intervals, and maintain a safe state during the attack period.

2. The two-stage anti-attack coupled memristor neural network finite time binary synchronization control method based on the TS fuzzy model according to claim 1 is characterized in that: Step S300 defines fuzzy logic rules, transforms the memristor neural network model into a fuzzy coupled memristor neural network model, defines the synchronization error state variable between the i-th node and the target node, and establishes the error system of the memristor neural network; including: S310, build TS fuzzy logic rule base ,set up for , for , , for , combined with fuzzy rules, the dynamic model of the i-th node of the memristor neural network converted in step S230 is again converted into the fuzzy dynamic model of the i-th node of the memristor neural network, which is expressed as: ； in, is a node The known constant matrix of is a node The memristor matrix; is a measurable premise variable, is a fuzzy set, is a fuzzy set; , , It is Rule No. membership functions, and ; S320, converting the dynamic model of the target node in step S120 into a fuzzy memristor neural network target node dynamic model, expressed as: ； S330, define the synchronization error state variable between the i-th node and the target node as: ； The error system of the memristor neural network is established and expressed as: ； in, , .

3. The two-stage anti-attack coupled memristor neural network finite time binary synchronization control method based on the TS fuzzy model according to claim 2 is characterized in that: Step S400 estimates the memristor function based on set-valued mapping and differential inclusion theory, and converts the error system into a form based on differential inclusion; specifically: Based on the memristor coefficient and fuzzy rules of the dynamic model of the i-th node of the memristor neural network, a fuzzy memristor matrix is ​​constructed. 、 、 and ;in Elements , Elements , Elements , Elements ; According to differential inclusion theory and set-valued mapping, there exists a matrix and , convert the error system of the memristor neural network established in step S330 into the following form: ； in, , .

4. The two-stage anti-attack coupled memristor neural network finite time binary synchronization control method based on the TS fuzzy model according to claim 3 is characterized in that: In the first stage of step S500, when the error system state meets the conditions, a pulse security controller based on a hybrid trigger mechanism is designed to resist spoofing attacks, specifically including: S511, when the state of the error system When , a pulse controller based on a hybrid trigger mechanism is designed, which can be expressed as: ； in, Represents the controller, represents the pulse control gain, Indicates the pulse time, is a set of pulse control sequences that satisfies , represents a Dirac pulse; S512, for the coexistence of deception attacks and DoS attacks on the controller-actuator communication channel, a composite attack model of leader-follower neural network topology is constructed. when When, Control instructions for each node A spoofing attack occurs in the controller-actuator transmission channel, causing the actuator receiving signal to be injected with tampered data, namely: ； in As an attack signal; construct the Bernoulli distributed random variables associated with network nodes To characterize the probability of attack success, assume Independent of each other, their distribution satisfies: ； in, is a constant; S513: Based on the control instruction after the received signal is tampered with, the controller of the first stage is rewritten as follows: ； Under the first stage control, that is When , the error system of the memristor neural network is expressed as: ； in, ,set up exist Left continuous, that is , ; After the first stage pulse safety control, ,At this time, the second stage of security control is started.

5. The two-stage anti-attack coupled memristor neural network finite time binary synchronization control method based on the TS fuzzy model according to claim 4 is characterized in that: In the second phase of step S500 , a controller combining finite time control and fixed time control mechanisms is designed to resist DoS attacks; Specifically include: S521, the second stage considers the impact of DoS attacks in the communication channel on the limited time synchronization of the system, based on the active-dormant alternation characteristics of DoS attacks, and Represent the DoS attack time period and the attack sleep time period respectively, where the time series is the control moment redefined in the second stage of the controller. During the sleep period, the communication channel works normally; during the attack period, the control input is 0. Based on this, the controller of the second stage is expressed as: ； 、 They are: ； in, , , , are control gains, , ; S522, under the second stage control, i.e. When , the error system of the memristor neural network is expressed as: ； The error system of the memristor neural network under the influence of hybrid attacks is boundedly stable in fixed time mean square, realizing secure fixed time mean square synchronization control of the dynamic network and the target network.

6. A non-transitory computer-readable storage medium, characterized in that Computer instructions are stored thereon, which enable the computer to execute the two-stage anti-attack coupled memristor neural network finite time binary synchronization control method based on the TS fuzzy model as described in any one of claims 1 to 5.

7. An electronic device, characterized in that: include: A processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus, and the processor calls logic instructions in the memory to execute the two-stage anti-attack coupled memristor neural network finite-time binary synchronization control method based on the TS fuzzy model described in any one of claims 1 to 5.

8. A computer program product, characterized in that The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer executes the two-stage anti-attack coupled memristor neural network finite-time binary synchronization control method based on the TS fuzzy model according to any one of claims 1 to 5.

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