A security control method for a double-layer hidden Markov jump power system

Abstract

The application discloses a safety control method of a double-layer hidden Markov jump power system and belongs to the technical field of Markov system control. The application considers the asynchronous behavior between the power system and the controller and the difficulty in obtaining system state information, establishes a hidden Markov power system model, and then, based on the random process (transmission success, transmission failure and DoS attack) of communication transmission and the difficulty in obtaining the mode information of the communication process, establishes an HMM for describing the communication process, and further establishes a novel double-layer hidden Markov jump power system.

Description

Technical Field

[0001] This invention relates to the field of Markov system control technology, and specifically to a safety control method for a two-layer hidden Markov jump power system. Background Technology

[0002] As complex nonlinear systems, power systems frequently experience low-frequency oscillations during operation. These persistent oscillations severely impact system stability, causing significant economic losses. Power system stabilizers (PSS) can provide supplementary damping for synchronous machine rotor oscillations, thereby suppressing them, and have therefore received widespread research and application. Considering the changing operating conditions of power systems, there are currently two main methods for stabilizing large-scale power systems: robust PSS and adaptive PSS. Compared to adaptive PSS, which requires relatively strict continuous excitation conditions, robust PSS has attracted more attention because it maintains good dynamic performance even under large load variations and system nonlinearity. For example, experts have discussed the control problem of nonlinear robust coordinated PSS automatic voltage regulators. However, these studies have not considered the impact of random topological mutations on system stability. Studying the impact of random topological mutations in power systems on system stability is both significant and challenging.

[0003] The faults and external disturbances experienced by power systems are unpredictable. Therefore, Markov theory can be used to model abrupt changes in system structure and parameters; for example, some scholars have used Markov models to describe the stochastic changes in power systems. However, most existing Markov power system controller designs are mode-independent or mode-dependent. Due to potential data loss or delays during data transmission from sensors to the controller, partial loss of system mode information can occur, potentially leading to controller desynchronization with the system. Furthermore, obtaining power system state information is a significant challenge in practical applications. Considering these factors, Hidden Markov Models (HMMs) are undoubtedly a better choice. HMMs can not only characterize desynchronization phenomena but also solve the problem of difficult system mode information acquisition; therefore, research on power systems based on HMMs is essential.

[0004] On the other hand, data in power systems may be subject to malicious cyberattacks during transmission, the most common of which is DoS attacks leading to packet loss. Furthermore, transmission failures are prone to occur due to the unreliability of transmission channels. Faced with these challenges, some scholars have used discrete hidden Markov chains to model the probability of transmission failures. However, most current research on communication transmission neglects the possibility of DoS attacks and transmission failures occurring simultaneously. It is worth noting that network failures leading to packet loss are different from energy-limited DoS attacks. Transmission failures are usually unintentional and random, while DoS attacks are intentional and may persist for a period of time. Based on the above discussion, how to handle these random processes in Hidden Markov Jump power systems is the main motivation of this invention.

[0005] Similar to obtaining pattern information in Markov power system models, obtaining model information for communication transmission is also challenging. Fortunately, research shows that Hidden Markov Models (HMMs) offer a feasible solution to this challenge. Therefore, the communication transmission process can be modeled as a Hidden Markov Jump Communication Model. In some studies, HMMs have been effectively used to characterize channel dynamics. In other studies, finite-state HMMs have been used to study state estimation problems in unreliable communication channels, but these studies are limited by the assumption of complete knowledge of the transition probability matrix or observation probability matrix, resulting in significant theoretical limitations. To address this issue, some researchers consider using partially known transition probability matrices when using HMMs to describe stochastic processes of packet loss and time delay. Furthermore, some researchers have studied Markov jump systems based on sliding modes, considering partially known observation probability matrices. Based on the above research, this invention explores a more general scenario where both the transition probability matrix and the observation probability matrix may be partially known, or one of them may be partially unknown. Based on the above discussion, overcoming the asynchronous behavior of the controller and system patterns, as well as the asynchronous behavior of data, in unreliable network transmission, especially under conditions of unknown probabilities, is a highly challenging problem. Summary of the Invention

[0006] The technical problem this invention aims to solve is: how to overcome the asynchronous behavior of controllers and system modes, as well as data, in unreliable network transmission. It provides a safety control method for a two-layer Hidden Markov jump power system, based on controller control and H... ∞ By combining performance indicator control with other methods, it is possible to achieve secure control of the system under DoS attacks.

[0007] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0008] S1: Considering the circuit breaker switching action caused by line faults in the power system and the asynchronous behavior between the power system and the controller, a hidden Markov jump power system model is introduced.

[0009] S2: In order to handle the packet loss and DoS attack that may be encountered when data is transmitted in unreliable network channels, another independent Hidden Markov Model is used to describe this situation. The transition probability matrix and observation probability matrix in this Hidden Markov Model may both be unknown.

[0010] S3: Construct the controller model to obtain the closed-loop system model of the system under a DoS attack;

[0011] S4: Determine whether the system obtained in step S3 is stochastically stable under perturbation and satisfies H ∞ Linear matrix inequality conditions for performance index σ;

[0012] S5: Use the Lyapunov function and the performance index function to prove that the inequality conditions in step S4 are valid;

[0013] S6: Solve for the gain matrix of the controller;

[0014] S7: Implement safe control of the two-layer hidden Markov power system based on the controller gain matrix and given system parameters in step S6.

[0015] Furthermore, in step S1, the specific processing procedure is as follows:

[0016] S11: The dynamic model of the power system is established as follows:

[0017]

[0018] Where δ is the rotor angle, x d It is the synchronous reactance along the d-axis, x' d It is the transient reactance along the d-axis, T e It is the electric torque, V is the infinite bus voltage, and E fd It is the generator field voltage, u is the stable signal, and T do ' is the d-axis open-circuit transient time constant, V t It is the terminal voltage, E q ' is the q-axis voltage after transient reactance, x e It is the external line reactance, M is the inertia coefficient, and k is the external line reactance. E ,T E It is the exciter gain and time constant, T m It is mechanical torque;

[0019] S12: The fourth-order state-space model of the power system in step S11 is represented as:

[0020]

[0021] in:

[0022] x T (υ)=[Δδ Δω ΔE′ q ΔE fd ];

[0023]

[0024] x(υ) and u(υ) represent the state variable and control input of the υ-th node, respectively, and y(υ) is the measurement output. It is the internal coupling matrix between nodes, and w(υ) is the interval [interval]. Additional interference on It is the sensor's measurement matrix. is the system's output matrix, k1, k2...k6 are the linearization model constants of the synchronous motor, and Δω is the speed deviation;

[0025] S13: Introducing a partially unknown Hidden Markov Process (HMM) to establish the following Hidden Markov Jumping Electric System:

[0026]

[0027] in, It is a discrete-time Markov chain;

[0028] The transition probability matrix R = {η} in the hidden Markov jump power system ψj}as follows:

[0029]

[0030] Where, η ψj ∈[0,1],

[0031] The observation probability matrix of this hidden Markov jump power system as follows:

[0032]

[0033] in,

[0034] Furthermore, in step S2, the energy of a DoS attack is limited and may continue until the Nth time point. The pattern of a DoS attack is as follows:

[0035] Mode 1: Indicates successful data transmission (λ(μ) = 1); in this mode, the probability of the system continuing to succeed in the next time step is τ. 11The probability of a transmission channel failure is τ. 12 The probability of suffering a DoS attack is τ. 13 ;

[0036] Mode 2: Indicates communication transmission failure (λ(μ) = 2); in this mode, the probability of successful transmission in the next time step is τ. 21 The probability of a transmission channel failure is τ. 22 The probability of suffering a DoS attack is τ. 23 ;

[0037] Mode 3: Represents transmission under a DoS attack (λ(μ) = 3); the probability of the system transmitting normally in the next time step is τ. 31 The probability of a transmission channel failure is τ. 32 The probability of continuing to be subjected to DoS attacks is τ. 34 ;

[0038] Following the same principle, this is extended to the pattern λ(μ)=N+1; since the attack energy is finite when the attack reaches λ(μ)=N+2, the system may, in the next time step, proceed with the attack with probability τ. (N+2)1 and τ (N+2)2 Return to mode 1 or mode 2.

[0039] Furthermore, in step S2, the specific processing procedure is as follows:

[0040] S21: Consider using Markov variables q(μ) to simulate the switching of a DoS attack and determine the transition probability matrix. as follows:

[0041]

[0042] in,

[0043] S22: The variable λ(μ) is observed through q(μ), and... The values ​​are selected from the middle, and the observation probability matrix is ​​determined. as follows:

[0044]

[0045] in,

[0046] S23: Analyze the case where the transition probability matrix and observation probability matrix are partially unknown: in:

[0047]

[0048] The specific situations can be divided into the following three categories:

[0049]

[0050] Furthermore, in step S3, the specific processing procedure is as follows:

[0051] S31: Construct the following asynchronous state feedback controller based on a hidden Markov model:

[0052]

[0053] in, Represents the controller gain matrix. variable θ ζ belong Indicates the transmission status. When ζ = 1, it indicates that the data transmission was successful; when ζ ≠ 1, it indicates that the current status information cannot be obtained, and the data from the last successful transmission is used.

[0054] S32: This leads to the following two-layer hidden Markov jump power system:

[0055]

[0056] Where x(t+1) represents the state variable of the (t+1)th node, and y(t) is the measurement output. Given the system parameter matrix, w(t) is a parameter belonging to the interval [0, 1]. Additional interference on It is the sensor's measurement matrix. It is the system's output matrix;

[0057] S33: Augment the two-layer hidden Markov skip power system in step S32 to obtain the closed-loop system model as follows:

[0058]

[0059] in,

[0060] Furthermore, in step S4, given a scalar σ > 0, if there exists a matrix K i , ρ = a, b; and symmetric matrix Then, when the following inequality condition is true, the system in step S32 can achieve the given H. ∞ Achieving stochastic stability under performance metric σ:

[0061]

[0062] in:

[0063]

[0064] Furthermore, in step S5, the specific processing procedure is as follows:

[0065] S51: For w(t) ≡ 0 and any initial value, when the condition... When established, the system in step S32 is stochastically stable; when all non-zero values ​​are true, the system is stochastically stable. Furthermore, when the zero initial state satisfies the following inequality, the system in step S32 can achieve the specified H. ∞ Performance index σ:

[0066]

[0067] S52: Consider selecting the following Lyapunov functionals:

[0068]

[0069] in,

[0070] make get:

[0071]

[0072] in,

[0073] We obtain the following from the inequality below and the above equation in step S51:

[0074]

[0075] in:

[0076] S53: Using the inequality above the inequality condition in step S4, we obtain:

[0077]

[0078] in,

[0079] S54: Substitute the inequality from step S53 into the inequality below the inequality condition in step S4, and we get:

[0080]

[0081] S55: Then, based on the inequality By combining Schur's complement, we can obtain the inequality below the inequality condition in step S4;

[0082] S56: Based on the inequality in step S54, we get:

[0083]

[0084] If w(t)≡0, then The system is stochastically stable;

[0085] Given zero initial conditions, w(t) ≠ 0, we know that

[0086] The system is stochastically stable and satisfies the specified H. ∞ Performance index σ.

[0087] Furthermore, in step S6, the specific processing procedure is as follows:

[0088] S61: Let K i =T i -1 U i ;

[0089] S62: The inequality at the bottom of the inequality conditions in step S4 is equivalently transformed as follows:

[0090]

[0091] in:

[0092]

[0093] S63: Then, using simulation software, the value of the controller gain matrix is ​​calculated using the given matrix parameters.

[0094] The present invention has the following advantages over the prior art:

[0095] 1. Considering the asynchronous behavior between the power system and the controller, and the difficulty in obtaining system state information, a Hidden Markov Power System Model was established. 2. Based on the stochastic process of communication transmission (transmission success, transmission failure, and DoS attack), and the difficulty in obtaining information on these communication process patterns, an HMM describing the communication process was established. Furthermore, a novel two-layer Hidden Markov Jump Power System was established.

[0096] 2. For stochastic processes in communication, Hidden Markov Models (HMMs) with limited information are used for description. Specifically, this limited information may exist in the transition probability matrix, the observation probability matrix, or both. Attached Figure Description

[0097] Figure 1 This is a flowchart illustrating the safety control method for a two-layer hidden Markov jump power system in an embodiment of the present invention.

[0098] Figure 2 These are the system modal and controller modal diagrams in this embodiment of the invention;

[0099] Figure 3 This is a sequence diagram of different attacks considering the impact of hybrid network attacks on power system stability in an embodiment of the present invention;

[0100] Figure 4 This is the trajectory diagram of the controller under the gain matrix of the controller obtained in the embodiment of the present invention;

[0101] Figure 5 This is a system state trajectory diagram without a controller in this embodiment of the invention;

[0102] Figure 6 This is a system state trajectory diagram in an embodiment of the present invention when a controller is included;

[0103] Figure 7 This is a state trajectory diagram of x1(t) in an embodiment of the present invention;

[0104] Figure 8 This is a top view of x4(t) in the open-loop system of this embodiment of the invention;

[0105] Figure 9 This is a three-dimensional diagram of x4(t) in the open-loop system of this embodiment of the invention;

[0106] Figure 10 This is a top view of x4(t) in the closed-loop system of this embodiment of the invention;

[0107] Figure 11 This is a top view of x4(t) in the closed-loop system of this embodiment of the invention;

[0108] Figure 12 This is a schematic diagram of the information transmission construction structure in an embodiment of the present invention. Detailed Implementation

[0109] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0110] This embodiment provides a technical solution: a safety control method for a two-layer Hidden Markov Jumping Power System. First, considering the circuit breaker switching actions caused by line faults in the power system and the asynchronous behavior between the power system and the controller, a Hidden Markov Jumping Power System model is introduced. To handle potential packet loss and Denial-of-Service (DoS) attacks during data transmission over unreliable network channels, another independent Hidden Markov Model (HMM) is used to describe this situation, where the transition probability matrix (TPM) and observation probability matrix (OPM) may be unknown. Second, based on the power system with a two-layer Hidden Markov Jumping Structure, several sufficient conditions are established to ensure the closed-loop system achieves stochastic stability during asynchronous and unreliable data network transmission. Finally, simulation examples verify the correctness of the theory of the two-layer Hidden Markov Jumping Structure power system.

[0111] like Figure 1 As shown, the above-mentioned safety control method for a two-layer hidden Markov jump power system specifically includes the following steps:

[0112] Step S1: Considering the circuit breaker switching action caused by line faults in the power system and the asynchronous behavior between the power system and the controller, a hidden Markov jump power system model is introduced.

[0113] The dynamic model of the power system is established as follows:

[0114]

[0115] Where δ is the rotor angle, x d It is the synchronous reactance along the d-axis, x' d It is the transient reactance along the d-axis, T e It is the electric torque, V is the infinite bus voltage, and E fd It is the generator field voltage, u is the stable signal, and T do ' is the d-axis open-circuit transient time constant, V t It is the terminal voltage, E q ' is the q-axis voltage after transient reactance, x e It is the external line reactance, M is the inertia coefficient, and k is the external line reactance. E ,T E It is the exciter gain and time constant, T m It is mechanical torque;

[0116] The fourth-order state-space model of the above power system (1) can be represented as:

[0117]

[0118] in:

[0119] xT (υ)=[Δδ Δω ΔE′ q ΔE fd ];

[0120]

[0121] x(υ) and u(υ) represent the state variable and control input of the υ-th node, respectively, and y(υ) is the measurement output. It is the internal coupling matrix between nodes, and w(υ) is the interval [interval]. Additional interference on It is the sensor's measurement matrix. is the system's output matrix, k1, k2...k6 are the linearization model constants of the synchronous motor, and Δω is the speed deviation.

[0122] By introducing a partially unknown Hidden Markov Process (HMM), the following Hidden Markov Jumping Electric System is established:

[0123]

[0124] in, It is a discrete-time Markov chain;

[0125] The transition probability matrix R = {η} ψj}:

[0126]

[0127] Where, η ψj ∈[0,1],

[0128] Considering the asynchronous behavior and the difficulty in obtaining system state information, a Hidden Markov Jumping Power System Model is established in this embodiment. The probability matrix s(t) associated with r(t) follows the following observation probability matrix.

[0129]

[0130] in,

[0131] Step S2: In order to handle the packet loss and denial-of-service attacks that may be encountered when data is transmitted in unreliable network channels, another independent Hidden Markov Model is used to describe this situation, and the transition probability matrix and observation probability matrix in the Hidden Markov Model may be unknown.

[0132] In power system research, communication channels may encounter transmission failures and denial-of-service (DoS) attacks during transmission. These situations can damage or even lose data packets, severely impacting system stability. While DoS attacks have limited energy, they may persist until a specific point in time. The patterns of DoS attacks are as follows:

[0133] Mode 1: Indicates successful data transmission (λ(μ) = 1); in this mode, the probability of the system continuing to succeed in the next time step is τ. 11 The probability of a transmission channel failure is τ. 12 The probability of suffering a DoS attack is τ. 13 ;

[0134] Mode 2: Indicates communication transmission failure (λ(μ) = 2); in this mode, the probability of successful transmission in the next time step is τ. 21 The probability of a transmission channel failure is τ. 22 The probability of suffering a DoS attack is τ. 23 ;

[0135] Mode 3: Represents transmission under a DoS attack (λ(μ) = 3); the probability of the system transmitting normally in the next time step is τ. 31 The probability of a transmission channel failure is τ. 32 The probability of continuing to be subjected to DoS attacks is τ. 34 ;

[0136] Following the same principle, this is extended to the mode λ(μ)=N+1. Since the attack energy is finite when the attack reaches λ(μ)=N+2, the system may, in the next time step, proceed with the attack with probability τ. (N+2)1 and τ (N+2)2 Return to mode 1 or mode 2.

[0137] Consider using a Markov variable q(μ) to simulate the switching of a DoS attack, and the transition probability matrix.

[0138]

[0139] in,

[0140] The variable λ(μ) is observed through q(μ), and... The values ​​are taken from the middle, and the observation probability matrix is...

[0141]

[0142] in,

[0143] Analyze cases where the transition probability matrix and observation probability matrix are partially unknown.

[0144]

[0145] in,

[0146] Step S3: Construct the controller model to obtain the closed-loop system model of the system under a DoS attack.

[0147] Construct the following asynchronous state feedback controller based on a hidden Markov model:

[0148]

[0149] in, K represents the controller gain matrix, where the two subscripts of K represent the system mode and the observation mode, respectively.

[0150] A structural diagram can be constructed based on modeling information such as successful transmission, failed transmission, and DoS attack, for example. Figure 12 As shown. Variable θ ζ belong Indicates the transmission status.

[0151]

[0152] When ζ = 1, it indicates that the data transmission was successful; conversely, when ζ ≠ 1, it indicates that the current status information cannot be obtained, so the data from the last successful transmission is used. The specific expression is as follows:

[0153]

[0154] In summary, the following two-layer hidden Markov jump power system can be obtained:

[0155]

[0156] Where x(t+1) represents the state variable of the (t+1)th node, and y(t) is the measurement output. Given the system parameter matrix, w(t) is a parameter belonging to the interval [0, 1]. Additional interference on It is the sensor's measurement matrix. It is the system's output matrix.

[0157] By augmenting equation (6), the closed-loop system model is obtained as follows:

[0158]

[0159] in,

[0160] Step S4: Determine whether the system in step S3 is stochastically stable under disturbance and satisfies H ∞ Linear matrix inequality conditions for performance index σ.

[0161] Given a scalar σ > 0, if there exists a matrix K i , ρ = a, b, and the symmetric matrix Then, when the following inequality holds, system (7) can be used in a given H. ∞ Achieving stochastic stability under performance metric σ:

[0162]

[0163] in:

[0164]

[0165] Step S5: Use the Lyapunov function and the performance index function to prove that the inequality conditions in step S4 are valid.

[0166] When system (7) holds under given conditions, it not only exhibits stochastic stability but also satisfies H ∞ Performance index σ.

[0167] For w(t)≡0 and any initial value, system (7) is stochastically stable when the condition is met. At the time of its establishment:

[0168] When all non-zero Furthermore, when the zero initial state satisfies the following inequality, system (7) can achieve the specified H. ∞ Performance index σ.

[0169]

[0170] Consider selecting the following Lyapunov functional:

[0171]

[0172] in,

[0173] make We can obtain:

[0174]

[0175] in,

[0176] From equation (10) and the above equation, we can obtain:

[0177]

[0178] in: We obtain the following from equation (8):

[0179]

[0180] in, Substituting the above inequality into equation (9), we get:

[0181]

[0182] Then, based on the inequality By combining Schur and the complement, we can obtain equation (9);

[0183] According to equation (12), we can obtain:

[0184]

[0185] If w(t)≡0, then we know The system is stochastically stable.

[0186] Under zero initial conditions, w(t)≠0, we can obtain The system is stochastically stable and satisfies the specified H. ∞ Performance index σ.

[0187] Step S6: Solve for the gain matrix of the controller.

[0188] Let K i =T i -1 U i .

[0189] The following is an equivalent transformation of some of the inequality conditions in step S4:

[0190]

[0191] in:

[0192]

[0193] At this point, simulation software can be used to calculate the controller gain matrix K using the given matrix parameters. i The value of .

[0194] Step S7: Implement safe control of the two-layer hidden Markov power system based on the controller gain matrix and given system parameters from step S6.

[0195] When a line fault occurs, the hidden Markov switching power system according to equation (3) has two modes of change based on the on / off state of the circuit breaker, with the specific parameters as follows:

[0196] Mode 1:

[0197]

[0198] Mode 2:

[0199]

[0200] The remaining parameters in this embodiment are assumed to be as follows:

[0201] σ = 20, w(t) = 0.3 * cos(0.3t)e -0.56t S1 = [0.6 0.6 0.45 0.3] T S2 = [1.2 0.45 0.45 0.45] T ;

[0202] Therefore, the controller gain matrix is ​​as follows:

[0203] K1=[-0.0076 -0.048 0.0393 0.0043];

[0204] K2=[-0.0239 -0.2067 0.0107 -0.0021].

[0205] Based on the above parameters, the following simulation diagram can be obtained. Figure 4 The output response u(t) is displayed on the 10 sampling paths. Figure 2 This shows the evolution of system and controller patterns over time. Similarly, Figure 3 Three transmission modes under HMM are described. Figure 5 This indicates that without a controller, the system state trajectory is unstable across the 10 sampling paths. Figure 7 In the process of applying the controller, the state trajectory x1(t) clearly shows that the system eventually stabilizes. Figure 6 This indicates that all state trajectories have reached stability. Furthermore, Figures 8-11 A three-dimensional plot of x4(t) for a single sampling path is shown. Figure 8 and Figure 9 The system state in the diagram diverges from a three-dimensional perspective (without a controller), and then, with the intervention of the controller, the system state tends to stabilize, such as... Figure 10 and Figure 11 As shown.

[0206] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A safety control method for a two-layer hidden Markov jump power system, characterized in that, Includes the following steps: S1: Considering the circuit breaker switching action caused by line faults in the power system and the asynchronous behavior between the power system and the controller, a hidden Markov jump power system model is introduced. S2: In order to handle the packet loss and DoS attack that may be encountered when data is transmitted in unreliable network channels, another independent Hidden Markov Model is used to describe this situation. The transition probability matrix and observation probability matrix in this Hidden Markov Model may both be unknown. S3: Construct the controller model to obtain the closed-loop system model of the system under a DoS attack; In step S3, the specific processing procedure is as follows: S31: Construct the following asynchronous state feedback controller based on a hidden Markov model: in, Represents the controller gain matrix. variable θ ζ belong Indicates the transmission status. When ζ = 1, it indicates that the data transmission was successful; when ζ ≠ 1, it indicates that the current status information cannot be obtained, and the data from the last successful transmission is used. S32: This leads to the following two-layer hidden Markov jump power system: Where x(t+1) represents the state variable of the (t+1)th node, and y(t) is the measurement output. Given the system parameter matrix, w(t) is a parameter belonging to the interval [0, 1]. Additional interference on It is the sensor's measurement matrix. It is the system's output matrix; S33: Augment the two-layer hidden Markov skip power system in step S32 to obtain the closed-loop system model as follows: in, S4: Determine whether the system obtained in step S3 is stochastically stable under perturbation and satisfies H ∞ Linear matrix inequality conditions for performance index σ; S5: Use the Lyapunov function and the performance index function to prove that the inequality conditions in step S4 are valid; S6: Solve for the gain matrix of the controller; S7: Implement safe control of the two-layer hidden Markov power system based on the controller gain matrix and given system parameters in step S6.

2. The safety control method for a two-layer hidden Markov jump power system according to claim 1, characterized in that, In step S1, the specific processing procedure is as follows: S11: The dynamic model of the power system is established as follows: Where δ is the rotor angle, x d It is the synchronous reactance along the d-axis, x' d It is the transient reactance along the d-axis, T e It is the electric torque, V is the infinite bus voltage, and E fd It is the generator field voltage, u is the stable signal, and T do ' is the d-axis open-circuit transient time constant, V t It is the terminal voltage, E q ' is the q-axis voltage after transient reactance, x e It is the external line reactance, M is the inertia coefficient, and k is the external line reactance. E ,T E It is the exciter gain and time constant, T m It is mechanical torque; S12: The fourth-order state-space model of the power system in step S11 is represented as: in: x T (υ)=[Δδ Δω ΔE′ q DE fd ]; x(υ) and u(υ) represent the state variable and control input of the υ-th node, respectively, and y(υ) is the measurement output. It is the internal coupling matrix between nodes, and w(υ) is the interval [interval]. Additional interference on It is the sensor's measurement matrix. is the system's output matrix, k1, k2...k6 are the linearization model constants of the synchronous motor, and Δω is the speed deviation; S13: Introducing a partially unknown Hidden Markov Process (HMM) to establish the following Hidden Markov Jumping Electric System: in, It is a discrete-time Markov chain; The transition probability matrix R = {η} in the hidden Markov jump power system ψj }as follows: Where, η ψj ∈[0,1], The observation probability matrix of this hidden Markov jump power system as follows: in, ξ ψi ∈[0,1], 3. A safety control method for a two-layer hidden Markov jump power system according to claim 2, characterized in that, In step S2, the energy of a DoS attack is limited and may continue until the Nth time point. The pattern of a DoS attack is as follows: Mode 1: Indicates successful data transmission (λ(μ) = 1); in this mode, the probability of the system continuing to succeed in the next time step is τ. 11 The probability of a transmission channel failure is τ. 12 The probability of suffering a DoS attack is τ. 13 ; Mode 2: Indicates communication transmission failure (λ(μ) = 2); in this mode, the probability of successful transmission in the next time step is τ. 21 The probability of a transmission channel failure is τ. 22 The probability of suffering a DoS attack is τ. 23 ; Mode 3: Represents transmission under a DoS attack (λ(μ) = 3); the probability of the system transmitting normally in the next time step is τ. 31 The probability of a transmission channel failure is τ. 32 The probability of continuing to be subjected to DoS attacks is τ. 34 ; Following the same principle, this is extended to the pattern λ(μ)=N+1; since the attack energy is finite when the attack reaches λ(μ)=N+2, the system may, in the next time step, proceed with the attack with probability τ. (N+2)1 and τ (N+2)2 Return to mode 1 or mode 2.

4. A safety control method for a two-layer hidden Markov jump power system according to claim 3, characterized in that, In step S2, the specific processing procedure is as follows: S21: Consider using Markov variables q(μ) to simulate the switching of a DoS attack and determine the transition probability matrix. as follows: in, S22: The variable λ(μ) is observed through q(μ), and... The values ​​are selected from the middle, and the observation probability matrix is ​​determined. as follows: in, S23: Analyze the case where the transition probability matrix and observation probability matrix are partially unknown: in: The specific situations can be divided into the following three categories: Case1: Case2: Case3:

5. A safety control method for a two-layer hidden Markov jump power system according to claim 4, characterized in that, In step S4, given a scalar σ > 0, if there exists a matrix K i , ρ = a, b; and symmetric matrix Then, when the following inequality condition is true, the system in step S32 can achieve the given H. ∞ Achieving stochastic stability under performance metric σ: in:

6. A safety control method for a two-layer hidden Markov jump power system according to claim 5, characterized in that, In step S5, the specific processing procedure is as follows: S51: For w(t) ≡ 0 and any initial value, when the condition... When established, the system in step S32 is stochastically stable; when all non-zero values ​​are true, the system is stochastically stable. Furthermore, when the zero initial state satisfies the following inequality, the system in step S32 can achieve the specified H. ∞ Performance index σ: S52: Consider selecting the following Lyapunov functionals: in, make get: in, We obtain the following from the inequality below and the above equation in step S51: in: S53: Using the inequality above the inequality condition in step S4, we obtain: in, S54: Substitute the inequality from step S53 into the inequality below the inequality condition in step S4, and we get: S55: Then, based on the inequality By combining Schur's complement, we can obtain the inequality below the inequality condition in step S4; S56: Based on the inequality in step S54, we get: If w(t)≡0, then The system is stochastically stable; Given zero initial conditions, w(t) ≠ 0, we know that The system is stochastically stable and satisfies the specified H. ∞ Performance index σ.

7. A safety control method for a two-layer hidden Markov jump power system according to claim 6, characterized in that, In step S6, the specific processing procedure is as follows: S61: Let K i =T i -1 U i ; S62: The inequality at the bottom of the inequality conditions in step S4 is equivalently transformed as follows: in: S63: Then, using simulation software, the value of the controller gain matrix is ​​calculated using the given matrix parameters.

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