Iterative learning security control method for discrete time system under composite attack

Abstract

The invention provides an iterative learning security control method for a discrete time system under composite attack, and belongs to the field of communication information processing. The method comprises the following steps: S1, constructing a discrete time system subjected to random spoofing attack and DoS attack; the system comprises a discrete time system model and a hybrid network attack model in which random spoofing attack and DoS attack coexist. S2, designing an output estimation compensation mechanism, and constructing estimation output to compensate actual output, which cannot be directly obtained, of the discrete time system, so as to obtain the estimation output; and S3, designing an iterative learning control strategy based on the estimated output, so that the tracking error of the discrete time system after the spoofing attack and the DoS attack is converged within a preset security level. According to the method, the boundaries of system trajectories can be guaranteed, the convergence condition is simpler than that in the prior art, the method is easy to check in practical application, and the system safety control target is finally and effectively achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of communication information processing, and particularly relates to an iterative learning security control method for a discrete-time system under composite attacks. BACKGROUND

[0002] With the development of network technology, networked systems are ubiquitous in real life. However, signals are extremely vulnerable to malicious network attacks in network space and signal transmission processes, leading to data loss and system failure, such as deception attacks and denial of service (DoS) attacks. How to keep the system stable and secure from various malicious attacks has attracted people's attention to security control, and some security control protocols have been proposed. However, some sufficient conditions in existing researches are slightly complex, and it is difficult to verify them in practical applications when the model dimension is large. In addition, the combination of multiple network attacks increases the difficulty of theoretical analysis.

[0003] Iterative learning control (ILC) technology is widely considered as an effective control method due to its simple design and strong adaptability. This control method has applications in bionic robotic fish, large-scale urban road networks, batch processes, network systems, etc. Iterative learning control technology uses error information in previous iterations to correct the current control input, thereby achieving high-precision trajectory tracking without relying too much on the accurate mathematical model of the system, providing an effective way to solve high-precision tracking control problems.

[0004] Through the iterative learning control method, some reasonable control algorithms are designed to solve security problems. For example, two criteria are proposed to analyze the security of discrete nonlinear systems under injection attacks, and data-driven control is used to consider security problems under deception and false data injection attacks. However, due to the different forms of DoS attacks, the above methods are not effective in dealing with DoS attacks, and when the system is subjected to random deception attacks and DoS attacks at the same time, the real output and tracking error become unavailable, which brings great difficulty to the design of effective iterative learning control strategies. Therefore, it is very meaningful to propose an iterative learning control algorithm with simple conditions to consider the security problems of the system under random deception and DoS attacks. SUMMARY

[0005] The present application aims to provide an iterative learning security control method for a discrete-time system under composite attacks, which introduces an output compensation mechanism to evaluate the actual output, designs and applies an iterative learning strategy according to an estimation formula to achieve the security of the system, thereby solving the technical problem of the existing iterative learning control method which is not effective in dealing with the system subjected to random deception attacks and DoS attacks at the same time.

[0006] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0007] An iterative learning security control method for a discrete-time system subjected to composite attacks, the method comprising the following steps:

[0008] Step S1: Construct a discrete-time system subjected to random spoofing attacks and DoS attacks; the discrete-time system subjected to random spoofing attacks and DoS attacks includes a discrete-time system model and a hybrid network attack model in which random spoofing attacks and DoS attacks coexist.

[0009] Step S2: Design an output estimation compensation mechanism to construct an estimated output to compensate for the actual output of the discrete-time system that cannot be directly obtained, and obtain the estimated output;

[0010] Step S3: Based on the estimated output, design an iterative learning control strategy to bring the tracking error of the discrete-time system after being subjected to deception attacks and DoS attacks to converge within a preset security level.

[0011] Further, step S1 includes the following steps:

[0012] Step S11: Construct a discrete-time system model;

[0013] The discrete-time system model is defined as follows:

[0014]

[0015] in, It is the state vector at time t in the k-th iteration process. Let n represent the set of real numbers, and n represent the dimension of the state vector. It is the state vector at time t+1 of the k-th iteration process; It is the input vector at time t in the k-th iteration process, where p represents the dimension of the input vector; is the output vector at time t of the k-th iteration process, where m represents the dimension of the output vector; A, B, C, and D represent the first, second, third, and fourth coefficient matrices, respectively. Represents a set of time indices; This represents the set of time indices after removing the endpoint;

[0016] Step S12: Construct a hybrid network attack model that combines random spoofing attacks and DoS attacks. The hybrid network attack model includes a spoofing attack model and a DoS attack model.

[0017] The deception attack model is represented as:

[0018] μ k (t)=-y k (t)+ξ k(t) (8)

[0019] Where, μ k (t) represents a deception attack, ξ k (t) is a bounded signal;

[0020] The DoS attack model is represented as follows:

[0021] v k (t)=-y k (t) (9)

[0022] in, Indicates a DoS attack;

[0023] The output of a discrete-time system subjected to deception and DoS attacks can be expressed as:

[0024]

[0025] in, This represents the output of a discrete-time system after being subjected to a combined attack. and Let α represent the spoofing attack and the DoS attack that occur at time t in the k-th iteration, respectively; k,t β represents the probability of an attack occurring. k,t 1-β represents the probability of a deception attack occurring. k,t This indicates the probability of a DoS attack occurring.

[0026] Furthermore, the output estimation compensation mechanism in step S2 is implemented in the following way:

[0027]

[0028] in, This represents the estimated output, y d (t) represents the target output.

[0029] Furthermore, the iterative learning control strategy designed in step S3 is as follows:

[0030]

[0031] Among them, u k+1 (t) represents the input at time t in the (k+1)th iteration, u k (t) represents the input at time t in the k-th iteration; and Let y represent the first gain matrix and the second gain matrix, respectively. d (t), y d (t+1) represents the target output at time t and time t+1, respectively. These represent the estimated outputs at time t and time t+1, respectively.

[0032] Compared with existing technologies, the present invention has the following beneficial technical effects: The present invention proposes a new output estimation method to assess the unmeasurability of the actual output; it adopts an iterative learning strategy to achieve system security and ensure that the system trajectory is bounded; compared with existing methods, the iterative learning control method of the present invention is simple, can guarantee the boundedness of the system trajectory, and its convergence condition is simpler than that of existing technologies, making it easier to verify in practical applications, and ultimately effectively achieving the system security control goal. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart of the iterative learning control method for discrete-time systems subjected to composite attacks according to the present invention.

[0035] Figure 2 This is a schematic diagram of the tracking trajectory under deception and DoS attack conditions according to the present invention.

[0036] Figure 3 This is a schematic diagram illustrating the tracking error under deception and DoS attacks according to the present invention.

[0037] Figure 4 This is a schematic diagram of the system trajectory according to Theorem 1 of this invention.

[0038] Figure 5 This is a schematic diagram of the system trajectory for Theorem 3 of this invention.

[0039] Figure 6 This is a schematic diagram showing the distribution of DoS attack occurrence times according to the present invention.

[0040] Figure 7 This is a schematic diagram of the tracking error under a DoS attack according to the present invention.

[0041] Figure 8 This is a schematic diagram showing the distribution of the timing of the deception attack according to the present invention.

[0042] Figure 9 This is a schematic diagram of the tracking error under the deception attack of the present invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0044] This invention proposes an iterative learning security control method for discrete-time systems subjected to composite attacks, such as... Figure 1 As shown, the method includes the following steps:

[0045] Step S1: Construct a discrete-time system subjected to random spoofing attacks and DoS (Denial of Service) attacks; the discrete-time system subjected to random spoofing attacks and DoS attacks includes a discrete-time system model and a hybrid network attack model in which random spoofing attacks and DoS attacks coexist.

[0046] Step S11: Construct a discrete-time system model.

[0047] A discrete-time system model can be defined as:

[0048]

[0049] Where k represents the kth iteration process; It is the state vector at time t in the k-th iteration process. Let n represent the set of real numbers, and let x represent the dimension of the state vector. k (0) is the initial state of the k-th iteration; It is the state vector at time t+1 of the k-th iteration process; It is the input vector at time t in the k-th iteration process, where p represents the dimension of the input vector; This is the output vector at time t in the k-th iteration, where m represents the dimension of the output vector. a, B, C, and D represent the first, second, third, and fourth coefficient matrices, respectively; the dimensions of the coefficient matrices A, B, C, and D should be set appropriately as needed. T represents the time index set. This represents the set of time indices after removing the endpoint. l is a fixed end time.

[0050] Step S12: Construct a hybrid network attack model that combines random spoofing attacks and DoS attacks. The hybrid network attack model includes a spoofing attack model and a DoS attack model.

[0051] The deception attack model is represented as:

[0052] μk (t)=-y k (t)+ξ k (t) (14)

[0053] Where, μ k (t) represents a deception attack, ξ k (t) is any bounded signal, i.e., ||ξ k (t)||≤ξ b ξ b >0, ξ b Indicates signal ξ k The upper bound of (t) is a constant.

[0054] The DoS attack model is represented as follows:

[0055] v k (t)=-y k (t) (15)

[0056] in, This indicates a DoS attack.

[0057] The output of a discrete-time system subjected to deception and DoS attacks can be expressed as:

[0058]

[0059] in, This represents the output of a discrete-time system after being subjected to a combined attack. and Let α represent the spoofing attack and the DoS attack that occur at time t in the k-th iteration, respectively. k,t Let β be the first Bernoulli random variable, representing the probability of the attack occurring; k,t Let denote the second Bernoulli random variable, representing the probability of a deception attack occurring, 1-β. k,t This represents the probability of a DoS attack occurring. α k,t With β k,t The two are unrelated and satisfy the following conditions:

[0060]

[0061] Where Prob{·} denotes calculating the probability; This indicates a demand for expectation; This represents the expected value of the first Bernoulli random variable; Let k1 and k2 be the expected value of the second Bernoulli random variable; and let t1 and t2 be the expected value of the first Bernoulli random variable for any two iterations. and and the second Bernoulli random variable and They are independent, where k1≠k2 and

[0062] Then, from equations (2), (3), and (4), we can write:

[0063]

[0064] Step S2: Design an output estimation compensation mechanism to construct an available estimated output to compensate for the actual output of the discrete-time system (1) that cannot be directly obtained, and obtain the estimated output.

[0065] Furthermore, in step S2, the output estimation compensation mechanism is designed as follows:

[0066] When studying trajectory tracking problems, the tracking error e is usually used as a reference. k (t)=y d (t)-y k (t) is used to adjust the control input; where, This is the target output. However, due to cyberattacks, the actual output y may not be directly obtainable and usable. k (t), which could lead to incorrect measurement signals being used to adjust the control strategy, making it difficult to achieve the tracking target. Therefore, the designed estimated output is... Substituting equation (6) into the equation, we obtain the final estimated output as follows:

[0067]

[0068] Accordingly, the tracking error of the system's estimated output is

[0069] Step S3: Based on the estimated output, design an iterative learning control strategy. By adjusting the gain matrix, the tracking error of the discrete-time system after being subjected to deception attacks and DoS attacks converges to a preset security level.

[0070] Furthermore, in step S3, for discrete-time systems susceptible to random spoofing attacks and DoS attacks, a security definition is introduced, and the iterative controller is designed as follows:

[0071] Define security:

[0072] This step proposes a security concept from an iterative perspective, applicable to repetitive systems, and reflects the impact of random network attacks. It can clearly describe the security level through the parameter σ, as specifically described in Definition 1.

[0073] Definition 1: Specify the required security level as σ > 0. When for When established, the discrete-time system is σ-safe.

[0074] Design an iterative learning control strategy:

[0075] For a repetitive linear discrete-time system, the iterative learning control strategy is constructed as follows:

[0076]

[0077] Among them, u k+1 (t) represents the input at time t in the (k+1)th iteration, u k (t) represents the input at time t in the k-th iteration; and Let y represent the first gain matrix and the second gain matrix, respectively. d (t), y d (t+1) represents the target output at time t and time t+1, respectively. Let represent the estimated outputs at time t and time t+1, respectively. In (8), the estimated outputs are used. Instead of the actual output y k (t) Design an iterative learning strategy that can fully take into account the impact of network attacks.

[0078] Design the first gain matrix. Second gain matrix

[0079] Based on the above security definition and iterative learning scheme, considering the design of the gain matrix in the output equation of different discrete-time systems, the following assumptions need to be made first:

[0080] Assumption 1: The initial state does not change in each iteration, i.e.

[0081] Where, x k (0) is the initial state of the k-th iteration; x k+1 (0) is the initial state of the (k+1)th iteration; x d (0) indicates the initial target state.

[0082] Assumption 2: For any target output y d The discrete-time system (1) with (t) and the fourth coefficient matrix D≠0 has a target state x. d (t) and target input u d (t), such that:

[0083]

[0084] Where, x d (t+1) represents the target state at time t+1, x d (t) represents the target state at time t, u d(t) represents the target input at time t.

[0085] Next, this step will discuss the design of the gain matrix for different output modes of discrete-time systems.

[0086] 1) Case A: In the discrete-time system (1), the fourth coefficient matrix in the output equation is not zero, i.e., D≠0. At this time, the controller output (input vector u) k When (t) can directly affect the output of the discrete-time system at the current moment, the second gain matrix will be used. The iterative learning strategy (8) is applied to discrete-time systems (1).

[0087] To analyze the convergence of the discrete-time system (1), let the input error at time t in the k-th iteration be δu. k (t)=u d (t)-u k (t), the state error at time t in the k-th iteration is δx k (t)=x d (t)-x k (t), then according to assumptions 1 and 2, we have

[0088]

[0089] The tracking error at time t in the k-th iteration

[0090] e k (t)=Cδx k (t)+Dδu k (t) (23)

[0091] It is established. Wherein, δx k (t-1) represents the state error at time t-1 of the k-th iteration, δu k (t-1) represents the input error at time t-1 of the k-th iteration, δu k (t-1-i) represents the input error at time t-1-i of the k-th iteration. The first coefficient matrix A, the second coefficient matrix B, the third coefficient matrix C, and the fourth coefficient matrix D have appropriate dimensions, determined by the specific application system. t is time. Combining the control strategy (8), we can obtain:

[0092]

[0093] Where, δu k+1 (t) represents the input error at time t in the (k+1)th iteration.

[0094] Substituting equations (7), (10), and (11) into equation (12), the input error can be further expressed as:

[0095]

[0096] in, Let α represent the identity matrix. k，t Let β represent the probability of an attack occurring at time t in the k-th iteration. k，t It is the probability of a deception attack occurring at time t in the k-th iteration.

[0097] Taking the norm and expectation of both sides of equation (13), we have

[0098]

[0099] Where ||·|| represents the norm. Analyzing equation (14), it is not difficult to find that its convergence is related to the terms. Related. Due to α k，t It is a Bernoulli random variable, so α k，t It can only take the value 0 or 1. When α k，t When = 1, When α k，t When = 0, Let the first expected convergence factor but And from ||ξ k (t)||≤ξ b Equation (14) can be rewritten as

[0100]

[0101] Furthermore, writing equation (15) in matrix form, we have

[0102]

[0103] That is, E k+1 <Ψ1E k +M ξ E k and E k+1 Let M be a vector representing the expected input error at all times from t=0 to t=l in the k-th and (k+1)-th iterations, respectively, where l represents the time when the iteration ends. ξ The first attack strength vector is represented by the following specific form: T denotes transpose, and Ψ1 is the first lower triangular matrix.

[0104]

[0105] Through induction, we can know This represents the (k+1)th power of the first lower triangular matrix Ψ1. Let represent the i-th power of the first lower triangular matrix Ψ1, and E0 represent the expected value of the input error at all times before the iteration begins. When ψ < 1, the spectral radius ρ(Ψ1) of the lower triangular matrix Ψ1 is < 1. According to matrix theory, we have and It is absolutely convergent. in Let be the convergence constant matrix of the series. Therefore, we can conclude that... Therefore, there is yes The maximum value element in. Combining with equation (10), we can obtain

[0106]

[0107] in, This represents the summation of matrix norm powers, when ||A|| ≠ 1. When ||A||=1, Therefore, combining equation (11), we have

[0108]

[0109] Security level By definition 1, the system is σ-safe, meaning the proposed iterative learning control strategy can make the system σ-safe. Therefore, we can derive Theorem 1.

[0110] Theorem 1: Let Assumption 1 and Assumption 2 hold, then The iterative learning strategy (8) is applied to discrete-time systems with D ≠ (1). If the inequality If this condition is met, the system achieves σ-security.

[0111] Furthermore, when inequalities When this holds true, all trajectories of the system are bounded in the expected sense, i.e., Theorem 2.

[0112] Theorem 2: Let Assumption 1 and Assumption 2 hold, then The iterative learning strategy (8) is applied to the discrete-time system (1) where D≠0. If the inequality... If true, then state x k (t) and input u k (t) is bounded in the sense of expectation, that is

[0113]

[0114] Among them, Z + Represents positive integers. and It is finitely bounded. Furthermore, output y. k (t) and actual tracking error e k (t) is also bounded in the sense of expectation, that is

[0115]

[0116] in, and It is finitely bounded.

[0117] 2) Case B: In the discrete-time system (1), the fourth coefficient matrix D in the output equation is a zero matrix, i.e., D = 0. This means that the controller output does not directly affect the output of the discrete-time system at the current moment. The iterative learning strategy (8) is applied to discrete-time systems (1).

[0118] From the discrete-time system equation (1), we can obtain

[0119] e k+1 (t)=y d (t)-y k+1 (t)

[0120] =e k (t)-C[x k+1 (t)-x k (t)] (34)

[0121] Among them, e k (t) and e k+1 (t) represent the tracking errors of the k-th and (k+1)-th iterations, respectively. d (t) is the target output, y k+1 (t) is the system output at time t in the (k+1)th iteration, x k (t) and x k+1 (t) are the state vectors at time t for the k-th and (k+1)-th iterations, respectively. Δx k (t-1) represents the difference between the state vector at time t-1 of the (k+1)th iteration and the state vector at time t-1 of the kth iteration. Combining equation (7), and through inductive analysis, equation (22) can be rewritten as follows:

[0122]

[0123] Among them, e k+1 (t) represents the tracking error at time t in the (k+1)th iteration, α k，t-1-i Let e ​​represent the probability of an attack occurring at time t-1-i in the k-th iteration. k (t-1-i) represents the tracking error at time t-1-i in the k-th iteration, α k，t-i β represents the probability of an attack occurring at time ti in the k-th iteration. k，t-i Let ξ represent the probability of a deception attack occurring at time ti in the k-th iteration. k(ti) represents the signal of the deception attack at time ti in the k-th iteration.

[0124] Similar to case A, taking the norm and expectation of both sides of equation (23) respectively, we can write it in matrix form, i.e.

[0125] E′ k+1 <Ψ2E′ k +M′ ξ (36)

[0126] Among them, E′ k+1 Let E′ be a vector representing the expected tracking error at all times during the (k+1)th iteration. k M′ represents the vector of expected tracking errors at all times during the k-th iteration. ξ This represents the second attack strength vector. Ψ2 is the second lower triangular matrix

[0127]

[0128] And φ represents the second expected convergence factor. Similarly, to ensure convergence, φ < 1 ​​must be satisfied, that is, it must satisfy... Furthermore, we can determine from Definition 1 that the system achieves σ-security, thus leading to Theorem 3.

[0129] Theorem 3: Let Assumptions 1 and 2 hold, then The iterative learning strategy (8) is applied to the discrete-time system (1) where D = 0. If the inequality... If true, then the discrete system (1) achieves σ-security.

[0130] Similar to case A, when the inequality When the condition is met, the trajectory of the discrete system (1) is bounded in the sense of expectation, i.e., Theorem 4.

[0131] Theorem 4: Let Assumptions 1 and 2 hold, then The iterative learning strategy (8) is applied to the discrete system (1) where D≠0. If the inequality... If true, then state x k (t) and input u k (t) is bounded in the sense of expectation, that is

[0132]

[0133] in, and It is finitely bounded. Furthermore, output y. k (t) and actual tracking error e k (t) is also bounded in the sense of expectation, that is

[0134]

[0135] in, and It is finitely bounded.

[0136] The following detailed description, in conjunction with the accompanying drawings and embodiments, provides a method for designing an iterative learning controller for discrete-time systems subjected to complex attacks, as proposed in this invention.

[0137] In step S1, the discrete-time system model is as follows:

[0138]

[0139] Where time t∈[0,10], initial state The first coefficient matrix, the second coefficient matrix, and the third coefficient matrix are set as follows: C = [0.5 0.5]. The values ​​of the fourth coefficient matrix D will be discussed in detail in the example.

[0140] In step S2, the estimated output design is as follows:

[0141]

[0142] The probability of an attack occurring is... The probability of a deception attack occurring is and They are α k,t and β k,t The mathematical expectation, ||ξ k (t)||≤ξ b =1, the target output is y d (t) = 2sin(0.2πt).

[0143] In step S3, the following two examples are discussed.

[0144] Example 1: Spoofing and DoS attacks occur randomly.

[0145] In this example, we will discuss two system output modes: D≠0 and D=0.

[0146] 1) For the above system, take D = 0.5. And design the learning gain matrix. The initial input u0(t) = 0. Calculations show that... Then Theorem 1 and Theorem 2 hold, meaning that the system can achieve σ-safety and all trajectories are bounded in the desired sense.

[0147] 2) For the above system, take D = 0. And design the learning gain matrix. The initial input u0(t) = 0. Calculations show that... Satisfying inequalities Then Theorem 3 and Theorem 4 hold, meaning that the system can achieve σ-safety and the system trajectory is bounded in the desired sense.

[0148] The tracking trajectory and error in Example 1 are as follows: Figure 2 and Figure 3 As shown. Figure 2 The tracking trajectory at the 100th iteration is shown. Figure 3 The tracking error is shown from the first iteration to the 150th iteration. According to... Figure 2 and Figure 3 It can be seen that, for both system output scenarios, the iterative control strategy tracks trajectories that almost perfectly overlap with the target trajectory, and the amplitude of the tracking error is very small, indicating that the algorithm yields good results. Furthermore, from... Figure 3 It can be seen that the purple line has the smallest fluctuation, which means that Theorem 1 has a better convergence effect, and by Figure 4 and Figure 5 It can be seen that the trajectories of all variables are bounded in both cases.

[0149] Example 2: Spoofing and DoS attacks occurring separately

[0150] In this example, we will discuss the scenario where the two attack modes occur separately.

[0151] 1) Only DoS attacks, i.e., β k，t ≡0 or ζ k (t)≡0. The distribution of attacks under this condition is shown in the diagram below. Figure 6 As shown. From Figure 7 It can be seen that the tracking error e k It can asymptotically approach zero, and the iterative learning control algorithm in Theorem 1 has a faster convergence speed than the iterative learning control method in Theorem 3, which shows that the controller helps to resist the effects of DoS attacks.

[0152] 2) Only deception attacks, i.e., β k，t ≡1. The distribution of attacks in this case is shown in the diagram below. Figure 8 As shown. From Figure 9 The tracking error trajectory shown indicates that the tracking error jitter range is greater than that of a DoS attack alone. It is easy to conclude that deception attacks have a greater negative impact on system security. However, the iterative learning control method in this step still has a good tracking effect.

[0153] In summary, the iterative learning controller design method for discrete-time systems subjected to composite attacks proposed in this invention can effectively achieve σ-security, reduce the impact of network attacks, and make the tracking error of the system gradually decrease with each iteration, approaching 0 in a finite time, thus achieving accurate tracking of the system. Furthermore, this invention can guarantee the boundedness of the trajectory of each variable in the system.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An iterative learning security control method for discrete-time systems subjected to composite attacks, characterized in that, The method includes the following steps: Step S1: Construct a discrete-time system subjected to random spoofing attacks and DoS attacks; the discrete-time system subjected to random spoofing attacks and DoS attacks includes a discrete-time system model and a hybrid network attack model in which random spoofing attacks and DoS attacks coexist. Step S2: Design an output estimation compensation mechanism to construct an estimated output to compensate for the actual output of the discrete-time system that cannot be directly obtained, and obtain the estimated output; Step S3: Based on the estimated output, design an iterative learning control strategy to bring the tracking error of the discrete-time system after being subjected to deception attacks and DoS attacks to converge within a preset security level.

2. The iterative learning security control method for discrete-time systems subjected to composite attacks according to claim 1, characterized in that, Step S1 includes the following steps: Step S11: Construct a discrete-time system model; The discrete-time system model is defined as follows: in, It is the state vector at time t in the k-th iteration process. Let n represent the set of real numbers, and n represent the dimension of the state vector. It is the state vector at time t+1 of the k-th iteration process; It is the input vector at time t in the k-th iteration process, where p represents the dimension of the input vector; is the output vector at time t of the k-th iteration process, where m represents the dimension of the output vector; A, B, C, and D represent the first, second, third, and fourth coefficient matrices, respectively. Represents a set of time indices; This represents the set of time indices after removing the endpoint; Step S12: Construct a hybrid network attack model that combines random spoofing attacks and DoS attacks. The hybrid network attack model includes a spoofing attack model and a DoS attack model. The deception attack model is represented as: μ k (t)=-y k (t)+ξ k (t) (2) Where, μ k (t) represents a deception attack, ξ k (t) is a bounded signal; The DoS attack model is represented as follows: v k (t)=-y k (t) (3) where, Indicates a DoS attack; The output of a discrete-time system subjected to deception and DoS attacks can be expressed as: in, This represents the output of a discrete-time system after being subjected to a combined attack. and Let α represent the spoofing attack and the DoS attack that occur at time t in the k-th iteration, respectively; k,t β represents the probability of an attack occurring. k,t 1-β represents the probability of a deception attack occurring. k,t This indicates the probability of a DoS attack occurring.

3. The iterative learning security control method for discrete-time systems subjected to composite attacks according to claim 2, characterized in that, The output estimation compensation mechanism in step S2 is implemented in the following way: in, This represents the estimated output, y d (t) represents the target output.

4. The iterative learning security control method for discrete-time systems subjected to composite attacks according to claim 3, characterized in that, The iterative learning control strategy designed in step S3 is as follows: Among them, u k+1 (t) represents the input at time t in the (k+1)th iteration, u k (t) represents the input at time t in the k-th iteration; and Let y represent the first gain matrix and the second gain matrix, respectively. d (t), y d (t+1) represents the target output at time t and time t+1, respectively. These represent the estimated outputs at time t and time t+1, respectively.

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