Quantized iterative control method for event-triggered deception attack discrete singular time-delay systems

Abstract

The application discloses an event-triggered deception attack discrete singular time-delay system quantization iterative control method and belongs to the technical field of information physical system safety control. The method comprises the following steps: a general system model of an information physical system under deception attack is established, and the system model is a discrete time singular nonlinear system with time delay; an event-triggered communication mechanism with a dynamic threshold is designed, the event-triggered communication mechanism is combined with a quantizer, and an iterative learning control protocol is constructed; based on the compression mapping principle, a sufficient condition for error convergence of the general system model is derived; the iterative learning control protocol is switched to a communication topology scene, and the system stability under the switched communication topology is analyzed. The application proposes an iterative learning control scheme of event-triggered communication and quantization cooperation, which can greatly reduce data transmission and calculation amount while ensuring tracking accuracy, and effectively improves resource utilization efficiency.

Description

Technical Field

[0001] This invention relates to the field of cyber-physical system security control technology, and in particular to a quantitative iterative control method for discrete singular time-delay systems subjected to event-triggered deception attacks. Background Technology

[0002] With the rapid development of fields such as the Industrial Internet, smart grids, and intelligent manufacturing, Cyber-Physical Systems (CPS) have become a core support for modern engineering systems through the deep integration of computing, communication, and physical processes. Due to the algebraic constraints and dynamic coupling inherent in these systems, singular nonlinear models can more accurately describe their intrinsic characteristics, while network transmission inevitably introduces problems such as time delays, bandwidth limitations, and strained communication resources. Furthermore, the open communication environment makes CPS highly vulnerable to malicious network attacks, with spoofing attacks, which tamper with sensor data or control commands, seriously threatening the stable operation of the system.

[0003] In recent years, Iterative Learning Control (ILC) has been widely applied to the cooperative control of cyber-physical systems due to its advantages in repetitive tasks and high-precision tracking. To reduce communication burden, event-triggered mechanisms and signal quantization have become key technologies for efficient resource utilization, effectively reducing data transmission and controller update frequency. However, most existing technologies only consider quantization, event triggering, or attack defense individually, making it difficult to simultaneously accommodate complex engineering elements such as singular dynamics, nonlinearity, time delay, spoofing attacks, and iterative correlation switching topologies.

[0004] Furthermore, traditional control methods often pursue asymptotic stability along the time axis, making it difficult to achieve precise tracking along the iteration axis; most schemes are only applicable to fixed communication topologies and cannot adapt to scenarios with dynamic switching of communication links; and they lack strict convergence guarantees and security control mechanisms when spoofing attacks exist. Therefore, how to design a secure iterative learning control scheme that combines high accuracy, low communication overhead, and strong robustness under the conditions of resource constraints and network attacks has become a critical problem that urgently needs to be solved. Summary of the Invention

[0005] Purpose of the invention: To address the above problems, the purpose of this invention is to provide a quantitative iterative control method for discrete singular time-delay systems subjected to event-triggered deception attacks.

[0006] Technical solution: The present invention provides a method for quantized iterative control of discrete singular time-delay systems using event-triggered deception attacks, comprising the following steps:

[0007] Step 1: Establish a general system model for cyber-physical systems under deception attacks, wherein the system model is a discrete-time singular nonlinear system with time delay;

[0008] Step 2: Design an event-triggered communication mechanism with dynamic thresholds, and combine the event-triggered communication mechanism with a logarithmizer to construct an iterative learning control protocol;

[0009] Step 3: Based on the principle of compression mapping, derive the sufficient condition for the convergence of the error of the general system model;

[0010] Step 4: Switch the iterative learning control protocol to the communication topology scenario and analyze the system stability under the switched communication topology.

[0011] Preferably, step 1 includes:

[0012] Step 11: Based on graph theory, describe the communication topology of agents in a cyber-physical system, and denote the weighted directed graph describing the relationships between agents as follows: The directed graph and the navigating agent constitute an extended graph. ,Right now , This represents the root node of the leading intelligent agent; where A set of intelligent agent nodes. For the number of agents, For edge sets, ordered pairs Represents intelligent agents To intelligent agents Transmitting information, adjacency matrix Defined as follows: If Then the intelligent agent Can be used with intelligent agents Communication is necessary; otherwise, information cannot be received.

[0013] The Laplace matrix of a directed graph is defined as ,in For degree matrix, , ;

[0014] Step 12: Establish a discrete singular nonlinear cyber-physical system model with constant time delay, defining the iterative index, discrete-time variables, agent state, input, and output parameters. The mathematical expression of the constructed system model is as follows:

[0015] ,

[0016] In the formula, the matrix For a singular matrix, satisfying ; Indicates the first The agent in the th... Next iteration, time step state, Let the coefficient matrix be denoted as . , For the first The connection weights between the following agent and the leading agent, if , indicating the first A following agent can receive information from the leading agent; otherwise... ; Indicates the first The agent in the th... Next iteration, time step Input; Indicates the first The agent in the th... Next iteration, time step The output, For a constant time delay, let be... For the initial state function, when When the state satisfies , Represents the coefficient matrix; For any nonlinear function, The following global Lipschitz conditions must be met:

[0017] ,

[0018] In the formula, For positive integers,

[0019] Step 13, construct a deception attack model based on Bernoulli distribution, represented as:

[0020] ,

[0021] In the formula, the success rate of injecting fake data follows a Bernoulli distribution. Indicates whether the fake data was successfully injected into the first... An intelligent agent, when This indicates that the injection failed, but the data was transmitted normally and there was no false information. This indicates the injection of false data; For the first in the system The success rate of false information injection in each iteration of the intelligent agent satisfies ;

[0022] Step 14: Combining the connection weights of the following agent and the leading agent, calculate the consistency safety control error using the following formula:

[0023] ,

[0024] In the formula, To output the tracking error, For any given reference trajectory, For attackers at any time To the False signals injected by an intelligent agent At the same time, the signal meets the conditions , It is a bounded constant.

[0025] Preferably, step 2 includes:

[0026] Step 21, for a given quantization density Define the set of quantized logarithms as follows:

[0027] ,

[0028] in, The initial value for the quantizer;

[0029] Step 22, define the quantizer, expressed as:

[0030] ,

[0031] In the formula, This represents the object that needs to be quantified; ;

[0032] Step 23: The system safety control error is quantified using a quantitative method. The quantized error is represented as the product of the original error and a bounded scalar.

[0033] Step 24: The event triggering mechanism is designed based on Lyapunov stability theory or performance indicators to determine the triggering conditions, expressed as follows:

[0034] ,

[0035] In the formula, The event triggers the iteration time. ; For trigger threshold parameters, This is represented as an event triggering condition function. , Indicates error;

[0036] Step 25: Combining quasi-adjacency topology, dynamic event triggering, and logarithmic quantization, construct an iterative learning security control protocol under event-triggered conditions, expressed as:

[0037]

[0038] In the formula, To learn the gain matrix.

[0039] Preferably, step 3 includes:

[0040] Step 31, define each parameter as a vector pattern, expressed as follows:

[0041]

[0042] Step 32, then the consistency security control error is expressed in compact form:

[0043] ,

[0044] In the formula, express An identity matrix of order 1;

[0045] Step 33: Based on the principle of compression mapping, a sufficient condition for the global uniform convergence of the error is obtained, expressed as:

[0046] ,

[0047] In the formula, Extracted for dimensional expansion An identity matrix of order 1.

[0048] Represented as:

[0049] .

[0050] Preferably, step 4 includes:

[0051] Step 41, construct a time-varying topological model, represented as:

[0052] ,

[0053] In the formula, For the first The time-varying Laplace matrix of the directed graph G at the next iteration. For the first The connection weight matrix at the next iteration;

[0054] Step 42, the consistency error under the iterative switching topology is rewritten as follows:

[0055] ,

[0056] Step 43, consider a time-delayed discrete singular nonlinear cyber-physical system under an event-triggered quantization iterative learning control protocol. If... , denoted as:

[0057] ,

[0058] Under the sufficient condition that the error converges globally uniformly, the learning gain matrix is... The goal of consistency security control is achieved when the following inequality is satisfied:

[0059] ,

[0060] in, This represents a singular matrix, that is, a matrix with a determinant of 0. express An identity matrix of order 1.

[0061] Beneficial effects: Compared with the prior art, the significant advantages of this invention are:

[0062] 1. This invention constructs a unified cyber-physical system model that integrates deception attacks, time delays, singular dynamics, and nonlinearity. It can more realistically reflect the complex dynamics and security threats in the actual network environment and has stronger applicability than existing models.

[0063] 2. This invention proposes an event-triggered communication and iterative learning control scheme for quantitative collaboration, which significantly reduces data transmission and computation while ensuring tracking accuracy, effectively improving resource utilization efficiency.

[0064] 3. Achieve precise convergence along the iteration axis. Compared with traditional asymptotic control methods, this invention has higher tracking accuracy and more reliable convergence, making it more suitable for engineering scenarios involving repetitive tasks.

[0065] 4. This invention is compatible with iterative correlation switching topologies and can still guarantee bounded convergence of errors under conditions of dynamic changes in communication structure and coexistence of spoofing attacks, thus possessing stronger robustness and security. Attached Figure Description

[0066] Figure 1 This invention presents a security control model for a discrete singular time-delay cyber-physical system based on ET-QILC under deception attacks.

[0067] Figure 2 This is a fixed topology diagram of the discrete singular nonlinear cyber-physical system in this invention;

[0068] Figure 3 This invention demonstrates the tracking performance of agent 1 and agent 2 on desired output 1 and desired output 2 under different iterations in a cyber-physical system subjected to a deception attack.

[0069] Figure 4 This invention demonstrates the tracking performance of agents 3 and 4 in a cyber-physical system under deception attack conditions for different iterations of desired output 1 and desired output 2.

[0070] Figure 5 The quantization output of agent 1 and agent 2 under different iterations in a discrete singular nonlinear cyber-physical system under time delay and spoofing attacks;

[0071] Figure 6The quantization output of agent 3 and agent 4 under different iterations in a discrete singular nonlinear cyber-physical system under time delay and deception attacks;

[0072] Figure 7 To assess the convergence effect of consistency security control error in discrete singular nonlinear cyber-physical systems under deception attacks;

[0073] Figure 8 This shows the trend of the number of events triggered by the four agents in Example 1 as the number of iterations changes;

[0074] Figure 9 This invention demonstrates the tracking performance of agent 1 and agent 2 on desired output 1 and desired output 2 at different iterations in a cyber-physical system without being subjected to a deception attack.

[0075] Figure 10 This invention demonstrates the tracking performance of agents 3 and 4 in a cyber-physical system under different iteration numbers for desired output 1 and desired output 2 in the absence of a deception attack.

[0076] Figure 11 This is the quantization output of agent 1 and agent 2 under different iterations in a discrete singular nonlinear cyber-physical system with only time delays;

[0077] Figure 12 The quantization outputs of agents 3 and 4 under different iterations in a discrete singular nonlinear cyber-physical system with only time delays;

[0078] Figure 13 The convergence effect of consistency security control error in discrete singular nonlinear cyber-physical systems without deception attacks;

[0079] Figure 14 This shows the trend of the number of events triggered by the four agents in Example 2 as the number of iterations changes;

[0080] Figure 15 The communication topology changes with iteration;

[0081] Figure 16 To illustrate the output tracking of the desired reference signal by Agent 1 and Agent 2 in a communication topology switching scenario under a deception attack;

[0082] Figure 17 To illustrate the output tracking of the desired reference signal by agents 3 and 4 in a communication topology switching scenario under a deception attack;

[0083] Figure 18 The quantized outputs of Agent 1 and Agent 2 after processing by the designed quantizer for a communication topology switching scenario involving spoofing attacks.

[0084] Figure 19 The quantized outputs of agents 3 and 4 after processing by the designed quantizer for a communication topology switching scenario involving spoofing attacks.

[0085] Figure 20 The convergence effect of consistency security control error in discrete singular nonlinear switching cyber-physical systems under the ET-QILC scheme of this invention;

[0086] Figure 21 To determine the trend of the number of events triggered by the four agents in the switching system as a function of the number of iterations. Detailed Implementation

[0087] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the embodiments of the present invention, and not all structures.

[0088] In the following description, specific details such as target system architecture and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0089] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0090] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0091] Furthermore, in the description of this application and the appended claims, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0092] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include the target features, structures, or characteristics described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0093] The event-triggered deception attack method for quantized iterative control of discrete singular time-delay systems described in this embodiment includes the following steps:

[0094] Step 1: Establish a general system model for cyber-physical systems under deception attacks, wherein the system model is a discrete-time singular nonlinear system with time delay.

[0095] Further, step 1 includes:

[0096] Step 11: Based on graph theory, describe the communication topology of agents in a cyber-physical system, and denote the weighted directed graph describing the relationships between agents as follows: The directed graph and the navigating agent constitute an extended graph. ,Right now , This represents the root node of the leading intelligent agent; where A set of intelligent agent nodes. For the number of agents, For edge sets, ordered pairs Represents intelligent agents To intelligent agents Transmitting information, adjacency matrix Defined as follows: If Then the intelligent agent Can be used with intelligent agents Communication is necessary; otherwise, information cannot be received.

[0097] The Laplace matrix of a directed graph is defined as ,in For degree matrix, , ;

[0098] Step 12: Establish a discrete singular nonlinear cyber-physical system model with constant time delay, defining the iterative index, discrete-time variables, agent state, input, and output parameters. The mathematical expression of the constructed system model is as follows:

[0099] (1)

[0100] In the formula, the matrix For a singular matrix, satisfying ; Indicates the first The agent in the th... Next iteration, time step state, Let the coefficient matrix be denoted as . , For the first The connection weights between the following agent and the leading agent, if , indicating the first A following agent can receive information from the leading agent; otherwise... ; Indicates the first The agent in the th... Next iteration, time step Input; Indicates the first The agent in the th... Next iteration, time step The output, For a constant time delay, let be... For the initial state function, when When the state satisfies , Represents the coefficient matrix; For any nonlinear function, The following global Lipschitz conditions must be met:

[0101] ,

[0102] In the formula, For positive integers,

[0103] Step 13, construct a deception attack model based on Bernoulli distribution, represented as:

[0104] (2)

[0105] The success rate of injecting fake data follows a Bernoulli distribution. Indicates whether the fake data was successfully injected into the first... An intelligent agent, when This indicates that the injection failed, but the data was transmitted normally and there was no false information. This indicates the injection of false data; For the first in the system The success rate of false information injection in each iteration of the intelligent agent satisfies ;

[0106] Step 14: Combine the connection weights of the following agent and the leading agent to calculate the consistency safety control error, using the following formula:

[0107] ,

[0108] In the formula, To output the tracking error, For any given reference trajectory, For attackers at any time To the False signals injected by an intelligent agent At the same time, the signal meets the conditions , It is a bounded constant.

[0109] Step 2: Design an event-triggered communication mechanism with dynamic thresholds, and combine the event-triggered communication mechanism with a logarithmizer to construct an iterative learning control protocol.

[0110] Further, step 2 includes:

[0111] Step 21, for a given quantization density Define the set of quantized logarithms as follows:

[0112] ,

[0113] in, The initial value for the quantizer;

[0114] Step 22, define the quantizer, expressed as:

[0115] ,

[0116] In the formula, This indicates the object that needs to be quantified; ;

[0117] Step 23: Quantify the system safety control error using a quantitative method. The quantized error is represented as the product of the original error and a bounded scalar. The event triggering condition function expression is as follows:

[0118] ,

[0119] In the formula, It is a scalar and satisfies ;

[0120] The event-triggered communication mechanism is represented as follows:

[0121] (3)

[0122] In the formula, Describe distributed error. To learn the gain matrix;

[0123] Step 24: In order to combine the event-triggered quantization control scheme with the iterative learning method, a quasi-adjacency matrix was constructed. Combining this quasi-adjacency matrix, the event-triggered quantization iterative learning control is represented as a boosting matrix. The event-triggered mechanism is based on Lyapunov stability theory or performance index to design trigger conditions, expressed as:

[0124] ,

[0125] In the formula, The event triggers the iteration time. ; For trigger threshold parameters, This is represented as an event triggering condition function. , Indicates error;

[0126] Step 25: Combining quasi-adjacency topology, dynamic event triggering, and logarithmic quantization, construct an iterative learning security control protocol under event-triggered conditions, expressed as:

[0127] (4)

[0128] In the formula, To learn the gain matrix;

[0129] Regarding the first At the next trigger moment, the event-triggered quantization iterative learning control protocol can be written as:

[0130] (5)

[0131] Step 3: Based on the principle of compression mapping, derive the sufficient condition for the convergence of the error of the general system model.

[0132] Furthermore, step 3 includes:

[0133] Step 31, define each parameter as a vector pattern, expressed as follows:

[0134]

[0135] Step 32, then the consistency security control error is expressed in compact form:

[0136] ,

[0137] Step 33: Based on the principle of compression mapping, a sufficient condition for the global uniform convergence of the error is obtained, expressed as:

[0138] ,

[0139] In the formula, Extracted for dimensional expansion An identity matrix of order 1.

[0140] Represented as:

[0141] .

[0142] The proof of error convergence includes:

[0143] Theorem 1: For a time-delayed singular nonlinear cyber-physical system under an event-triggered quantization iterative learning control protocol, if the learning gain... Satisfy the following formula:

[0144] ,

[0145] When the system is subjected to a deception attack, the following can be obtained:

[0146] ,

[0147] in, , , , , ;

[0148] Combining the convergence condition given in Theorem 1, we can choose a sufficiently large... , making Thus ensuring When the number of iterations approaches infinity, that is... At that time, we can obtain:

[0149] ,

[0150] For any given bounded expected output If the product of the system coefficient matrix To achieve full rank, for any given reference trajectory Then there exists an expected state. and expected input Satisfy system dynamics:

[0151] (6)

[0152] in, , These represent the desired state and input vector of the navigating agent, respectively; when hour, .

[0153] Subtracting equation (1) from equation (6) yields:

[0154] (7)

[0155] Based on the definition of quantification, we can obtain from equation (6):

[0156] ,

[0157] in, , , , ;

[0158] Substituting the above equation into equation (7), we get:

[0159] (8)

[0160] Will Subtracting equation (6), we get:

[0161] ;

[0162] Combining equation (8) with the above equation, we get:

[0163] (9)

[0164] in, , ;

[0165] Taking the norm of both sides of equation (9), we get:

[0166] (10)

[0167] in,

[0168] Taking the norm of both sides of equation (8), we get:

[0169] (11)

[0170] in, , , ;

[0171] According to Lemma 1, we can obtain from equation (11):

[0172] (12)

[0173] Substituting equation (12) into equation (10), we get:

[0174] (13)

[0175] Multiply both sides of equation (13) ,have to:

[0176] ,

[0177] Using the time delay condition, we can further derive:

[0178] ;

[0179] Therefore, we can conclude that:

[0180] (14)

[0181] Multiply both sides of equation (12) ,have to:

[0182] ,

[0183] Taking the supremum of the above inequality and relating it to the time variable... After further scaling transformation, we get:

[0184] ,

[0185] according to From the properties of norms, we can obtain:

[0186] (15)

[0187] Substituting equation (15) into equation (14), we get:

[0188] (16)

[0189] Applying the expectation operation to both sides of equation (16), we get:

[0190] (17)

[0191] Therefore, the cyber-physical system asymptotically converges along the iteration axis, controlling the input error. The upper bound is related to the attack factor coefficient. Next, we analyze the security control error. The expression is:

[0192] ,

[0193] Taking the norm of the above equation and substituting equation (12) into it, we get:

[0194] ,

[0195] Multiply both sides of the above equation by We can obtain:

[0196] ,

[0197] Taking the supremum of the right-hand side of the above equation, and considering the time variable... After further scaling and simplification, we get:

[0198] ,

[0199] Further simplification yields

[0200] (18)

[0201] From equation (15), we can obtain:

[0202] ,

[0203] Substituting the above formula into equation (18), we get:

[0204] (19)

[0205] Applying the expectation operation to equation (19), we get:

[0206] ,

[0207] in:

[0208] , ,

[0209] Therefore, the following conclusions can be drawn:

[0210] ,

[0211] Combining discrete From the definition of norm, we can obtain:

[0212] ,

[0213] Therefore, it can be deduced that:

[0214] ,

[0215] Consistency safety control error can be expressed as:

[0216] ,

[0217] Consider the first At the next trigger moment, the control law can be written as:

[0218] ,

[0219] Using a method similar to the derivation above, we can derive:

[0220] ,

[0221] Because a sufficiently large value can be selected ,make , Thus ensuring When the number of iterations approaches infinity, we obtain:

[0222] ,

[0223] Therefore, we can conclude that:

[0224] ,

[0225] According to discrete The norm is defined as follows:

[0226] ,

[0227] It is obvious that we can obtain:

[0228] .

[0229] Therefore, it can be seen that the systematic error decreases with the number of iterations. As it approaches infinity, it converges to zero, thus completing the proof of Theorem 1.

[0230] In practical cyber-physical systems, the constraints of fixed communication topologies are difficult to satisfy, and switching topologies are widespread. Therefore, it is necessary to extend the research results under fixed topologies to switching topology scenarios that depend on iteration, in order to verify the effectiveness of the controller in dynamic environments with topological uncertainties such as link creation and failure.

[0231] Step 4: Switch the iterative learning control protocol to the communication topology scenario and analyze the system stability under the switched communication topology.

[0232] Furthermore, step 4 includes:

[0233] Step 41, construct a time-varying topological model, represented as:

[0234] ,

[0235] In the formula, For the first The time-varying Laplace matrix of the directed graph G at the next iteration. For the first The connection weight matrix at the next iteration;

[0236] Step 42, the consistency error under the iterative switching topology is rewritten as follows:

[0237] ,

[0238] Step 43, consider a time-delayed discrete singular nonlinear cyber-physical system under an event-triggered quantization iterative learning control protocol. If... , denoted as:

[0239] ,

[0240] Under the sufficient condition that the error converges globally uniformly, the learning gain matrix is... The goal of consistency security control is achieved when the following inequality is satisfied:

[0241] ,

[0242] in, This represents a singular matrix, that is, a matrix with a determinant of 0. express An identity matrix of order 1.

[0243] Example 1

[0244] In this embodiment, the control method described in this invention (denoted as ET-QILC) is verified using numerical simulation in the Matlab environment. The specific steps are as follows:

[0245] This embodiment considers the secure tracking problem of a discrete singular time-delay nonlinear cyber-physical system under deception attacks. The system comprises four agents, with a time range of... Time Delay The system matrix is ​​set as follows:

[0246] , , ,

[0247] The initial state is denoted as:

[0248] ,

[0249] Learning gain is denoted as:

[0250] ,

[0251] Nonlinear terms are denoted as:

[0252] .

[0253] Deceptive attacks follow a Bernoulli distribution, and the attack probability is... Attack signal limit The threshold for triggering events for each agent is 0.1. .

[0254] The fixed leader trajectory is recorded as follows:

[0255] .

[0256] Figure 1 This is a security control model for a discrete singular time-delay cyber-physical system based on ET-QILC under deception attacks, as shown in the figure. CPS N represents N intelligent agents in the cyber-physical system. Figure 2 This is a fixed topology diagram of the discrete singular nonlinear cyber-physical system in this invention. 0 represents the root node composed of the leading agent, nodes 1-4 are the following agents, and the edges between the nodes represent the flow of transmitted information.

[0257] Figure 3 This paper demonstrates the tracking performance of agents 1 and 2 in a cyber-physical system under different iterations during a deception attack, showcasing the tracking performance of desired output 1 and desired output 2. A comparison with traditional iterative learning control protocols reveals that the controller constructed in this invention exhibits a faster convergence speed.

[0258] Figure 4 This figure shows the tracking performance of agents 3 and 4 in a cyber-physical system under a deception attack scenario, at different iteration counts, for desired output 1 and desired output 2. As can be seen from the figure, when the number of iterations is 10, a good tracking performance for desired output 1 is achieved; when the number of iterations is 20, a good tracking performance for desired output 2 is achieved.

[0259] Figure 5 and Figure 6 The figure shows the quantized output of an agent in a discrete singular nonlinear cyber-physical system under time delay and spoofing attacks at different iteration numbers. As can be seen from the figure, even after adding error quantization, the present invention can still achieve output tracking well.

[0260] Figure 7 The convergence effect of consistency security control error in discrete singular nonlinear cyber-physical systems under deception attacks shows that the error can be effectively converged under the algorithm proposed in this invention.

[0261] Figure 8 The figure illustrates the trend of event trigger counts for the four agents in Example 1 as the number of iterations changes. As can be seen from the figure, the ET-QILC protocol of this invention can effectively save resources and improve efficiency.

[0262] Example 2

[0263] In this embodiment, numerical simulation is used in the Matlab environment to verify the tracking performance of the system under no-attack conditions. The system structure, number of agents, matrix parameters, time delay, learning gain, nonlinear term, and event triggering threshold are completely consistent with those in Embodiment 1. Only the deception attack is not applied, and the expected trajectory is the same as that in Embodiment 1.

[0264] Figure 9 and Figure 10 The tracking performance of four agents in a cyber-physical system at different iteration numbers under conditions of no deception attack shows that they can keep up with the target expectation after about twenty iterations.

[0265] Figure 11 and Figure 12 This represents the quantization output of an agent in a discrete singular nonlinear cyber-physical system with only time delays, under different iteration numbers.

[0266] Figure 13 The variation of the maximum consistency security control error without deception attacks is shown. Simulation results show that the error is large and the tracking performance is poor in the early stage of iteration. As the number of iterations increases, the maximum error gradually converges, thereby improving the tracking performance.

[0267] Figure 14 The figure shows the trend of the number of events triggered by the four agents as the number of iterations changes. As can be seen from the figure, the ET-QILC protocol of the present invention can effectively save resources and improve efficiency.

[0268] Example 3

[0269] This embodiment uses Matlab to simulate and verify a scenario where switching topology and spoofing attacks coexist. The system parameters, time delay, learning gain, nonlinear terms, attack probability, and amplitude are all consistent with those in Embodiment 1. The communication topology adopts an iteratively dependent switching topology structure, which consists of the following four sets of matrices that alternately switch with each iteration:

[0270] , ,

[0271]

[0272] The fixed leader trajectory is as follows:

[0273]

[0274] Figure 15 The diagram illustrates the communication topology that changes with iteration, consisting of four graphs that are connected via functions. The selection is made such that the first topology graph is used when the number of iterations is 1, the second topology graph is used when the number of iterations is 2, and so on.

[0275] Figure 16 and Figure 17 This paper demonstrates the output tracking of four agents to a desired reference signal in a communication topology switching scenario under a spoofing attack. For state 1, the output converges to the reference value after 20 iterations. For state 2, the convergence speeds of the four agents differ slightly, but the security control error decreases significantly after 20 iterations and gradually approaches the desired trajectory.

[0276] Figure 18 and Figure 19 The diagram shows the quantized output of the agents after processing by the designed quantizer. Specifically, the two diagrams show the quantized output of the four agents in state 1 at the 5th, 10th and 20th iterations, and the quantized output in state 2 at the 3rd, 20th and 100th iterations.

[0277] Figure 20 The maximum consistency security control error convergence process in the switching communication topology scenario of Example 3 under the proposed ET-QILC scheme is shown. It can be seen that the algorithm proposed in this invention can make the error have good convergence.

[0278] Figure 21 The event triggering time in the scenario of switching communication topology is shown, demonstrating that the proposed ET-QILC protocol can improve efficiency and save resources, thus verifying its effectiveness.

Claims

1. A quantitative iterative control method for discrete singular time-delay systems subjected to event-triggered deception attacks, characterized in that, Includes the following steps: Step 1: Establish a general system model for cyber-physical systems under deception attacks, wherein the system model is a discrete-time singular nonlinear system with time delay; Step 2: Design an event-triggered communication mechanism with dynamic thresholds, and combine the event-triggered communication mechanism with a logarithmizer to construct an iterative learning control protocol; Step 3: Based on the principle of compression mapping, derive the sufficient condition for the convergence of the error of the general system model; Step 4: Switch the iterative learning control protocol to the communication topology scenario and analyze the system stability under the switched communication topology.

2. The method for quantized iterative control of discrete singular time-delay systems subjected to event-triggered deception attacks according to claim 1, characterized in that, Step 1 includes: Step 11: Based on graph theory, describe the communication topology of agents in a cyber-physical system, and denote the weighted directed graph describing the relationships between agents as follows: The directed graph and the navigating agent constitute an extended graph. ,Right now , This represents the root node of the leading intelligent agent; where A set of intelligent agent nodes. For the number of agents, For edge sets, ordered pairs Represents intelligent agents To intelligent agents Transmitting information, adjacency matrix Defined as follows: If Then the intelligent agent Can be used with intelligent agents Communication is necessary; otherwise, information cannot be received. The Laplace matrix of a directed graph is defined as ,in For degree matrix, , ; Step 12: Establish a discrete singular nonlinear cyber-physical system model with constant time delay, defining the iterative index, discrete-time variables, agent state, input, and output parameters. The mathematical expression of the constructed system model is as follows: ， In the formula, the matrix For a singular matrix, satisfying ; Indicates the first The agent in the th... Next iteration, time step state, Let the coefficient matrix be denoted as . , For the first The connection weights between the following agent and the leading agent, if , indicating the first A following agent can receive information from the leading agent; otherwise... ; Indicates the first The agent in the th... Next iteration, time step Input; Indicates the first The agent in the th... Next iteration, time step The output, For a constant time delay, let be... For the initial state function, when When the state satisfies , Represents the coefficient matrix; For any nonlinear function, The following global Lipschitz conditions must be met: ， In the formula, For positive integers, Step 13, construct a deception attack model based on Bernoulli distribution, represented as: ， In the formula, the success rate of injecting fake data follows a Bernoulli distribution. Indicates whether the fake data was successfully injected into the first... An intelligent agent, when This indicates that the injection failed, but the data was transmitted normally and there was no false information. This indicates the injection of false data; For the first in the system The success rate of false information injection in each iteration of the intelligent agent satisfies ; Step 14: Combine the connection weights of the following agent and the leading agent to calculate the consistency safety control error, using the following formula: ， In the formula, To output the tracking error, For any given reference trajectory, For attackers at any time To the False signals injected by an intelligent agent At the same time, the signal meets the conditions , It is a bounded constant.

3. The method for quantized iterative control of discrete singular time-delay systems subjected to event-triggered deception attacks according to claim 2, characterized in that, Step 2 includes: Step 21, for a given quantization density Define the set of quantized logarithms as follows: ， in, The initial value for the quantizer; Step 22, define the quantizer, expressed as: ， In the formula, This represents the object that needs to be quantified; ; Step 23: The system safety control error is quantified using a quantitative method. The quantized error is represented as the product of the original error and a bounded scalar. Step 24: The event triggering mechanism is designed based on Lyapunov stability theory or performance indicators to determine the triggering conditions, expressed as follows: ， In the formula, The event triggers the iteration time. ; For trigger threshold parameters, This is represented as an event triggering condition function. , Indicates error; Step 25: Combining quasi-adjacency topology, dynamic event triggering, and logarithmic quantization, construct an iterative learning security control protocol under event-triggered conditions, expressed as: ， In the formula, To learn the gain matrix.

4. The method for quantized iterative control of discrete singular time-delay systems subjected to event-triggered deception attacks according to claim 3, characterized in that, Step 3 includes: Step 31, define each parameter as a vector pattern, expressed as follows: ， Step 32, then the consistency security control error is expressed in compact form: ， In the formula, express An identity matrix of order 1; Step 33: Based on the principle of compression mapping, a sufficient condition for the global uniform convergence of the error is obtained, expressed as: ， In the formula, Extracted for dimensional expansion An identity matrix of order 1. Represented as: 。 5. The method for quantized iterative control of discrete singular time-delay systems subjected to event-triggered deception attacks according to claim 1, characterized in that, Step 4 includes: Step 41, construct a time-varying topological model, represented as: ， In the formula, For the first The time-varying Laplace matrix of the directed graph G at the next iteration. For the first The connection weight matrix at the next iteration; Step 42, the consistency error under the iterative switching topology is rewritten as follows: ， Step 43, consider a time-delayed discrete singular nonlinear cyber-physical system under an event-triggered quantization iterative learning control protocol. If... , denoted as: ， Under the sufficient condition that the error converges globally uniformly, the learning gain matrix is... The goal of consistency security control is achieved when the following inequality is satisfied: ， in, This represents a singular matrix, that is, a matrix with a determinant of 0. express An identity matrix of order 1.

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