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CN119276566B - Safety control method for double-layer hidden Markov jump power system - Google Patents

Safety control method for double-layer hidden Markov jump power system

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Publication number
CN119276566B
CN119276566B CN202411382126.XA CN202411382126A CN119276566B CN 119276566 B CN119276566 B CN 119276566B CN 202411382126 A CN202411382126 A CN 202411382126A CN 119276566 B CN119276566 B CN 119276566B
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power system
matrix
hidden markov
inequality
probability
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CN119276566A (en
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苏磊
樊成
费习宏
李峰
方田
汪婧
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Anhui University of Technology AHUT
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Anhui University of Technology AHUT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
    • H04L63/1441—Countermeasures against malicious traffic
    • H04L63/1458—Denial of Service
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/20—Network architectures or network communication protocols for network security for managing network security; network security policies in general
    • H04L63/205—Network architectures or network communication protocols for network security for managing network security; network security policies in general involving negotiation or determination of the one or more network security mechanisms to be used, e.g. by negotiation between the client and the server or between peers or by selection according to the capabilities of the entities involved
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/40—Network security protocols

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computer Hardware Design (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Feedback Control In General (AREA)

Abstract

本发明公开了一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，属于马尔科夫系统控制技术领域。本发明考虑到电力系统与控制器之间的异步行为，以及系统状态信息获取的困难性，建立了隐马尔科夫电力系统模型；其次，基于通信传输的随机过程(传输成功、传输失败和DoS攻击)，以及获取这些通信过程模式信息的困难性，建立了描述通信过程的HMM；进而建立了一种新型的双层隐马尔科夫跳跃电力系统。

This invention discloses a safety control method for a two-layer Hidden Markov Power System (HMM) with skip-stepping, belonging to the field of Markov system control technology. Considering the asynchronous behavior between the power system and the controller, and the difficulty in obtaining system state information, this invention establishes a Hidden Markov Power System model. Secondly, based on the stochastic processes of communication transmission (transmission success, transmission failure, and DoS attacks), and the difficulty in obtaining information on these communication process patterns, an HMM describing the communication process is established. Furthermore, a novel two-layer Hidden Markov Power System with skip-stepping is established.

Description

Safety control method for double-layer hidden Markov jump power system
Technical Field
The invention relates to the technical field of control of Markov systems, in particular to a safety control method of a double-layer hidden Markov jump power system.
Background
As a complex nonlinear system, the power system often suffers from low frequency oscillations during operation. These continuous oscillations can seriously affect the stability of the system, resulting in significant economic losses. Power System Stabilizers (PSS) can provide supplementary damping for synchronous machine rotor oscillations, thus suppressing the oscillations, and thus have been widely studied and applied. Considering the change of the operation condition of the power system, the current method for stabilizing the power system on a large scale mainly comprises two methods, namely robust PSS and self-adaptive PSS. Robust PSS has received more attention than adaptive PSS which require relatively stringent continuous excitation conditions, since it can maintain good dynamic performance under conditions of large load variation and system nonlinearity. For example, experts discuss the control problem of nonlinear robust coordination PSS automatic voltage regulators. However, these studies did not consider the effect of random topological mutations on system stability. The research of the influence of the topological random mutation of the power system on the system stability is significant and challenging.
Faults and external disturbances experienced by the power system are unpredictable, and thus, abrupt changes in system structure and parameters may be modeled using markov theory, for example, some students have employed markov models to describe random abrupt changes in the power system. However, existing markov power system controller designs are mostly mode independent or mode dependent, and partial loss of system mode information may occur due to data loss or delay in the data transmission from the sensor to the controller, thereby possibly causing the controller to be out of sync with the system. Second, the acquisition of power system state information in actual operation is also a difficult challenge. In view of these factors, hidden Markov Models (HMMs) are certainly a better choice, and HMMs can not only characterize the phenomenon of dyssynchrony, but also solve the difficult problem of system mode information acquisition, so that it is necessary to study a power system based on HMMs.
On the other hand, data in a power system may be subjected to malicious network attacks during transmission, most often DoS attacks that lead to packet loss, and in addition, transmission failures are liable to occur due to unreliability of transmission channels. Faced with such challenges, some students employ discrete hidden Markov chains to model the probability of transmission failure. However, most of the current communication transmission studies ignore the possibility of DoS attacks and transmission failures occurring simultaneously. Notably, network failures that result in packet loss and energy-limited DoS attacks are different. Transmission failures are typically unintentional and random, while DoS attacks are intentional and may last for a period of time. Based on the above discussion, how to handle these stochastic processes in a hidden markov jump power system is the primary motivation for the present invention.
Similar to the acquisition of pattern information in a markov power system model, it is also challenging to acquire model information for communication transmissions. Fortunately, studies have shown that HMMs provide a viable solution to this challenge. Thus, the communication transmission process can be modeled as a hidden markov jump communication model. HMMs are effectively used in some studies to characterize channel dynamics. In other studies finite state HMMs have been used to study the problem of state estimation in unreliable communication channels, but these studies are limited by the assumption that the transition probability matrix or observation probability matrix is fully understood, and have great limitations in theory. To address this problem, some students consider using a partial information transition probability matrix when describing the random process of packet loss and time delay using HMMs. In addition, some scholars have studied markov jump systems based on sliding patterns, taking into account partly known observation probability matrices. Based on the above study, the present invention discusses a more general scenario in which 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, it is a very challenging problem to overcome the asynchronous behavior of controllers and system modes and asynchronous behavior of data in unreliable network transmissions, especially under unknown probability conditions.
Disclosure of Invention
The technical problem to be solved by the invention is how to overcome the asynchronous behavior problems of a controller and a system mode and data in unreliable network transmission, and provide a safety control method of a double-layer hidden Markov jump power system, which can realize the safety control of the system under the DoS attack by combining the control of the controller and the control of an H ∞ performance index.
The invention solves the technical problems through the following technical proposal, and the invention comprises the following steps:
S1, taking into consideration the action of a breaker switch caused by line faults in a power system and the asynchronous behavior between the power system and a controller, introducing a hidden Markov jump power system model;
s2, in order to deal with data packet loss and DoS attack which can be encountered when data is transmitted in an unreliable network channel, another independent hidden Markov model is adopted to describe the situation, and a transition probability matrix and an observation probability matrix in the hidden Markov model can be unknown;
s3, constructing a controller model to obtain a closed-loop system model of the system under the DoS attack;
s4, giving a linear matrix inequality condition that the system obtained in the step S3 is randomly stable under disturbance and meets the performance index sigma of H ∞;
s5, proving that the inequality condition of the step S4 is effective by utilizing a Lyapunov function and a performance index function;
S6, solving a gain matrix of the controller;
And S7, realizing the safety control of the double-layer hidden Markov power system according to the gain matrix of the controller and the given system parameters in the step S6.
Further, in the step S1, the specific processing procedure is as follows:
s11, establishing a dynamic model of the power system as follows:
where δ is the rotor angle, x d is the synchronous reactance along the d-axis, x ' d is the transient reactance along the d-axis, T e is the electric torque, V is the infinite bus voltage, E fd is the generator field voltage, u is the stationary signal, T do ' is the d-axis open-circuit transient time constant, V t is the terminal voltage, E q ' is the q-axis voltage after transient reactance, x e is the external line reactance, M is the inertia coefficient, k E,TE is the exciter gain and time constant, T m is the mechanical torque;
s12, representing the fourth-order state space model of the power system in the step S11 as:
Wherein:
xT(υ)＝[Δδ Δω ΔE′q ΔEfd];
x (v) and u (v) respectively represent the state variable and the control input of the v-th node, y (v) is the measurement output, Is an internal coupling matrix between nodes, w (v) is a segmentAn additional disturbance on the surface of the substrate,Is the measurement matrix of the sensor and,Is the output matrix of the system, k 1,k2...k6 is the linearization model constant of the synchronous motor, and Δω is the speed deviation;
s13, introducing a hidden Markov process with unknown part of information, and establishing a hidden Markov jump power system as follows:
Wherein, the Is a discrete-time markov chain;
The transition probability matrix r= { η ψj } in the hidden markov jump power system is as follows:
wherein eta ψj epsilon [0,1],
Observation probability matrix in hidden Markov jump power systemThe following are provided:
Wherein, the
Further, in the step S2, the DoS attack has limited energy, and may last until the nth time point, and the DoS attack mode is as follows:
Mode 1, which shows that data transmission is successful (lambda (mu) =1), wherein in the mode, the probability of the system continuing to succeed in the next time step is τ 11, the probability of occurrence of transmission channel faults is τ 12, and the probability of DoS attack is τ 13;
Mode 2, which represents communication transmission failure (lambda (mu) =2), wherein in the mode, the probability of successful transmission of the system in the next time step is τ 21, the probability of occurrence of transmission channel failure is τ 22, and the probability of DoS attack is τ 23;
mode 3, representing transmission under DoS attack (λ (μ) =3), wherein the probability of normal transmission of the system in the next time step is τ 31, the probability of occurrence of transmission channel failure is τ 32, and the probability of possible continued DoS attack is τ 34;
According to the same principle, the system is extended to the mode λ (μ) =n+1, and the system may return to the mode 1 or the mode 2 with probabilities τ (N+2)1 and τ (N+2)2, respectively, in the next time step, due to the limited attack energy when the attack reaches λ (μ) =n+2.
Further, in the step S2, the specific processing procedure is as follows:
S21, considering the use of Markov variable q (mu) to simulate the switching of a DoS attack, determining a transition probability matrix The following are provided:
Wherein, the
S22. variable lambda (μ) is observed through q (μ) and is shown inTakes the value of the middle, and determines the observation probability matrixThe following are provided:
Wherein, the
S23, analyzing the situation that the transition probability matrix and the observation probability matrix are partially unknown: Wherein:
The specific cases are divided into the following three types:
Further, in the step S3, the specific processing procedure is as follows:
s31, constructing the following asynchronous state feedback controller based on the hidden Markov model:
Wherein, the Representing the gain matrix of the controller,The variable theta ζ belongs toIndicating the state of transmission,When ζ=1, it indicates that the data transmission was successful, and when ζ+.1, it indicates that the current state information cannot be obtained, and the last successfully transmitted data is used
And S32, further obtaining the following double-layer hidden Markov jump power system:
where x (t+1) represents the state variable of the (t+1) th node, y (t) is the measurement output, Is given as a system parameter matrix, w (t) is the belonging intervalAn additional disturbance on the surface of the substrate,Is the measurement matrix of the sensor and,Is the output matrix of the system;
S33, performing augmentation processing on the double-layer hidden Markov jump power system in the step S32 to obtain a closed-loop system model as follows:
Wherein, the
Further, in said step S4, given a scalar σ >0, if a matrix K i is present,Ρ=a, b; and symmetric matrixThe system in step S32 is able to achieve random stabilization at a given H ∞ performance index σ when the following inequality condition holds:
Wherein:
further, in the step S5, the specific processing procedure is as follows:
S51 for w (t) ≡0 and any initial value, when the condition is When established, the system in step S32 is randomly stable, when all non-zeroAnd the zero initial state satisfies the following inequality, the system in step S32 can reach the specified performance index σ of H ∞:
S52, considering selecting the following Lyapunov functional:
Wherein, the
Order theThe method comprises the following steps:
Wherein, the
The following inequality and the above equation in step S51 are used to obtain:
Wherein:
s53, obtaining by the upper inequality in the inequality condition in the step S4:
Wherein, the
S54, substituting the inequality in step S53 into the inequality below the inequality condition in step S4, yields:
S55, then, based on inequality And Schur complement, capable of obtaining the lower inequality of the inequality condition in the step S4;
S56, according to the inequality in step S54, obtaining:
If w (t) ≡0, then The system is randomly stable;
Under zero initial conditions, w (t) +.0, knowing
The system is randomly stable and meets the specified H ∞ performance index σ.
Further, in the step S6, the specific processing procedure is as follows:
S61, enabling K i＝Ti -1Ui to be the same as that of the original;
S62, performing equivalent transformation on the inequality below the inequality condition of the step S4 as follows:
Wherein:
and S63, using simulation software, calculating the values of the gain matrix of the controller through given matrix parameters.
Compared with the prior art, the invention has the following advantages:
1. Secondly, based on the random process of communication transmission (transmission success, transmission failure and DoS attack) and the difficulty of acquiring the mode information of the communication process, an HMM describing the communication process is established, and a novel double-layer hidden Markov jump power system is further established;
2. for random processes in communication HMMs are described that employ limited information, which may be present in the transition probability matrix, the observation probability matrix, or both.
Drawings
FIG. 1 is a flow diagram of a method of security control with a dual layer hidden Markov jump power system in an embodiment of the invention;
FIG. 2 is a diagram of system modalities and controller modalities in an embodiment of the invention;
FIG. 3 is a sequence diagram of different attacks in an embodiment of the present invention that take into account the impact of a hybrid network attack on the stability of the power system;
FIG. 4 is a graph of the trajectory of the controller under the gain matrix of the controller solved in an embodiment of the present invention;
FIG. 5 is a diagram of a system state trace without a controller in an embodiment of the invention;
FIG. 6 is a diagram of a system state trace with a controller according to an embodiment of the present invention;
FIG. 7 is a state trace diagram of x 1 (t) in an embodiment of the present invention;
FIG. 8 is a top view of x 4 (t) under an open loop system in an embodiment of the present invention;
FIG. 9 is a three-dimensional view of x 4 (t) under an open loop system in an embodiment of the present invention;
FIG. 10 is a top view of x 4 (t) under a closed loop system in an embodiment of the present invention;
FIG. 11 is a top view of x 4 (t) under a closed loop system in an embodiment of the present invention;
fig. 12 is a schematic diagram of a transmission information construction structure in an embodiment of the present invention.
Detailed Description
The following describes in detail the examples of the present invention, which are implemented on the premise of the technical solution of the present invention, and detailed embodiments and specific operation procedures are given, but the scope of protection of the present invention is not limited to the following examples.
The embodiment provides a technical scheme that a safety control method of a double-layer hidden Markov jump power system is provided, firstly, a hidden Markov jump power system model is introduced in consideration of the switching action of a circuit breaker caused by line faults in the power system and the asynchronous behavior between the power system and a controller. To address packet loss and denial of service attacks (DoS attacks) that may be encountered when data is transmitted in an unreliable network channel, another separate Hidden Markov Model (HMM) is used to describe this situation, and the Transition Probability Matrix (TPM) and Observation Probability Matrix (OPM) in the HMM may be unknown. Secondly, based on the electric power system with the double-layer hidden Markov jump structure, some sufficient conditions are established to ensure that the closed-loop system realizes random stability in the mode asynchronous and unreliable data network transmission process. And finally, verifying the correctness of the double-layer hidden Markov jump structure power system theory through a simulation example.
As shown in fig. 1, the safety control method with the double-layer hidden markov jump power system specifically includes the following steps:
step S1, a hidden Markov jump power system model is introduced in consideration of the switching action of a circuit breaker caused by line faults in a power system and the asynchronous behavior between the power system and a controller;
the dynamic model of the power system is built as follows:
where δ is the rotor angle, x d is the synchronous reactance along the d-axis, x ' d is the transient reactance along the d-axis, T e is the electric torque, V is the infinite bus voltage, E fd is the generator field voltage, u is the stationary signal, T do ' is the d-axis open-circuit transient time constant, V t is the terminal voltage, E q ' is the q-axis voltage after transient reactance, x e is the external line reactance, M is the inertia coefficient, k E,TE is the exciter gain and time constant, T m is the mechanical torque;
the fourth-order state space model of the power system (1) is expressed as:
Wherein:
xT(υ)＝[Δδ Δω ΔE′q ΔEfd];
x (v) and u (v) respectively represent the state variable and the control input of the v-th node, y (v) is the measurement output, Is an internal coupling matrix between nodes, w (v) is a segmentAn additional disturbance on the surface of the substrate,Is the measurement matrix of the sensor and,Is the output matrix of the system, k 1,k2...k6 is the linearization model constant of the synchronous motor, Δω is the speed deviation.
And (3) introducing a hidden Markov process with unknown part information, and establishing a hidden Markov jump power system as follows:
Wherein, the Is a discrete-time markov chain;
transition probability matrix r= { η ψj }:
wherein eta ψj epsilon [0,1],
In view of the asynchronous behavior and the difficulty in acquiring system state information, a hidden markov jump power system model is built in this embodiment. S (t) related to r (t) follows the following observation probability matrix
Wherein, the
In order to handle packet loss and denial of service attacks that may be encountered when data is transmitted in an unreliable network channel, another separate hidden markov model is used to describe this situation, where both the transition probability matrix and the observation probability matrix may be unknown.
In power system research, communication channels may experience transmission failures and denial of service attacks (DoS attacks) during transmission. These conditions can damage or even lose data packets, severely affecting system stability. Where the DoS attack has limited energy, it may last until the nth time point, the DoS attack mode is as follows:
Mode 1, which shows that the data transmission is successful (lambda (mu) =1), in which the probability of the system continuing to succeed in the next time step is τ 11, and the probability of being subjected to DoS attack is τ 13 because the probability of the transmission channel failure is τ 12;
Mode 2, which represents communication transmission failure (lambda (mu) =2), wherein in the mode, the probability of successful transmission of the system in the next time step is τ 21, the probability of occurrence of transmission channel failure is τ 22, and the probability of DoS attack is τ 23;
mode 3, representing transmission under DoS attack (λ (μ) =3), wherein the probability of normal transmission of the system in the next time step is τ 31, the probability of occurrence of transmission channel failure is τ 32, and the probability of possible continued DoS attack is τ 34;
according to the same principle, it is extended to the pattern λ (μ) =n+1. Since the attack energy is limited when the attack reaches λ (μ) =n+2, the system may return to either mode 1 or mode 2 with probabilities τ (N+2)1 and τ (N+2)2, respectively, in the next time step.
Considering the use of a Markov variable q (μ) to simulate the switching of a DoS attack, a transition probability matrix
Wherein, the
The variable lambda (mu) is observed through q (mu) and is shown inTakes the value of the middle, and observes the probability matrix
Wherein, the
Analyzing the cases where the transition probability matrix and the observation probability matrix are partially unknown,
Wherein, the
And step S3, constructing a controller model to obtain a closed-loop system model of the system under the DoS attack.
The following asynchronous state feedback controller based on the hidden Markov model is constructed:
Wherein, the The two subscripts representing the controller gain matrix, K, represent the system mode and the observed mode, respectively.
The block diagram may be constructed from the modeling information of transmission success, transmission failure, and DoS attack, as shown in fig. 12. The variable theta ζ belongs toRepresenting the transmission status.
When ζ=1, it indicates that the data transmission was successful, on the contrary, when ζ+.1, it indicates that the current state information cannot be acquired, so that the last successfully transmitted data is usedThe specific expression is as follows:
in summary, the following two-layer hidden markov jump power system can be obtained:
where x (t+1) represents the state variable of the (t+1) th node, y (t) is the measurement output, Is given as a system parameter matrix, w (t) is the belonging intervalAn additional disturbance on the surface of the substrate,Is the measurement matrix of the sensor and,Is the output matrix of the system.
The augmentation treatment is carried out on the formula (6), and a closed-loop system model can be obtained as follows:
Wherein, the
And step S4, giving a linear matrix inequality condition that the system in the step S3 is randomly stable under disturbance and meets the performance index sigma of H ∞.
Given a scalar σ >0, if a matrix K i is present,Ρ=a, b and symmetric matrixThen the system (7) can achieve random stabilization at a given H ∞ performance index σ when the following inequality condition holds:
Wherein:
and S5, proving that the inequality condition of the step S4 is effective by using a Lyapunov function and a performance index function.
When the system (7) is established under given conditions, it not only appears to be randomly stable, but also meets the H ∞ performance index σ.
For w (t) ≡0 and any initial value, the system (7) is randomly stable, when the condition isWhen the method is established, the following steps are carried out:
when all are non-zero And the zero initial state satisfies the inequality below, the system (7) can reach the specified H ∞ performance index sigma.
Consider the following Lyapunov functional to be selected:
Wherein, the
Order theThe method can obtain:
Wherein, the
Obtainable by formula (10) and above:
Wherein: obtained by the formula (8):
Wherein, the Substituting the above inequality into equation (9), it is possible to obtain:
then, based on the inequality And Schur complement, can obtain formula (9);
from equation (12), it follows:
If w (t) ≡0, it can be seen that The system is randomly stable.
Under zero initial conditions, w (t) +.0, can be obtainedThe system is randomly stable and meets the specified H ∞ performance index σ.
And step S6, solving a gain matrix of the controller.
Let K i＝Ti -1Ui.
The partial inequality condition of step S4 is equivalently transformed as follows:
Wherein:
At this point, the values of the controller gain matrix K i may be calculated by given matrix parameters using simulation software.
And S7, realizing the safety control of the double-layer hidden Markov power system according to the gain matrix of the controller and the given system parameters in the step S6.
When a line fails, the hidden Markov jump power system shown in the formula (3) has two modes according to the on-off state of the circuit breaker, and specific parameters are as follows:
Mode 1:
Mode 2:
the remaining parameters in this embodiment are assumed as follows:
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;
Then the controller gain matrix is as follows:
K1=[-0.0076 -0.048 0.0393 0.0043];
K2=[-0.0239 -0.2067 0.0107 -0.0021]。
From the above parameters, the following simulation graphs can be obtained. Fig. 4 shows the output response u (t) over 10 sampling paths. Fig. 2 shows the evolution of the system and controller modes over time. Also, fig. 3 depicts three transmission modes under HMM. Fig. 5 shows that the system state trace is unstable over 10 sampling paths if there is no controller. In fig. 7, the state trace x 1 (t) clearly shows that the system eventually stabilized after the controller is applied. Fig. 6 illustrates that all state traces have reached stability. In addition, fig. 8-11 show three-dimensional diagrams of x 4 (t) of a single sampling path. The system state in fig. 8 and 9 is divergent from a three-dimensional perspective (without controller) and then stabilizes under the intervention of the controller, as shown in fig. 10 and 11.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.

Claims (7)

1.一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，其特征在于，包括以下步骤：1. A safety control method for a two-layer hidden Markov jump power system, characterized by comprising the following steps: S1：考虑到电力系统中线路故障引起的断路器开关动作以及电力系统与控制器之间的异步行为，引入了隐马尔可夫跳跃电力系统模型；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：为了处理数据在不可靠网络信道中传输时可能遇到的数据包丢失和DoS攻击，采用另一个独立的隐马尔可夫模型来描述这种情况，该隐马尔可夫模型中的转移概率矩阵和观测概率矩阵均可能是未知的；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：构建控制器模型，得到DoS攻击下系统的闭环系统模型；S3: Construct the controller model to obtain the closed-loop system model of the system under a DoS attack; 在所述步骤S3中，具体处理过程如下：In step S3, the specific processing procedure is as follows: S31：构建以下基于隐马尔科夫模型的异步状态反馈控制器：S31: Construct the following asynchronous state feedback controller based on a hidden Markov model: 其中，表示控制器增益矩阵，变量θζ属于表示传输状态，当ζ＝1时，表示数据传输成功；当ζ≠1时，表示无法获取当前状态信息，使用上次成功传输的数据 in, Represents the controller gain matrix. Variable θ ζ belongs to 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：进而得到以下双层隐马尔可夫跳跃电力系统：S32: This leads to the following two-layer hidden Markov jump power system: 其中，x(t+1)表示第t+1个节点的状态变量，y(t)是测量输出，是给定的系统参数矩阵，w(t)是属于区间上的额外干扰，是传感器的测量矩阵，是系统的输出矩阵；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：对步骤S32中的双层隐马尔可夫跳跃电力系统进行增广处理，得到闭环系统模型如下：S33: Augment the two-layer hidden Markov skip power system in step S32 to obtain the closed-loop system model as follows: 其中， in, S4：给出步骤S3中得到的系统在扰动下随机稳定且满足H∞性能指标σ的线性矩阵不等式条件；S4: Give the linear matrix inequality condition that the system obtained in step S3 is stochastically stable under disturbance and satisfies the performance index σ of H ∞ ; S5：利用Lyapunov函数和性能指标函数证明步骤S4的不等式条件有效；S5: Use the Lyapunov function and the performance index function to prove that the inequality conditions in step S4 are valid; S6：求解出控制器的增益矩阵；S6: Solve for the gain matrix of the controller; S7：根据步骤S6中的控制器的增益矩阵和给定的系统参数实现对双层隐马尔可夫电力系统的安全控制。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.根据权利要求1所述的一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，其特征在于，在所述步骤S1中，具体处理过程如下：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：建立电力系统动态模型如下：S11: The dynamic model of the power system is established as follows: 其中，δ是转子角度，xd是沿d轴的同步电抗，x'd是沿d轴的瞬态电抗，Te是电转矩，V是无穷大母线电压，Efd是发电机场电压，u是稳定信号，Tdo'是d轴开路瞬态时间常数，Vt是终端电压，Eq'是瞬态电抗后的q轴电压，xe是外部线路电抗，M是惯性系数，kE,TE是激励器增益和时间常数，Tm是机械扭矩；Where δ is the rotor angle, xd is the synchronous reactance along the d-axis, x'd is the transient reactance along the d-axis, Te is the electrical torque, V is the infinite bus voltage, Efd is the generator field voltage, u is the stable signal, Tdo ' is the d-axis open-circuit transient time constant, Vt is the terminal voltage, Eq ' is the q-axis voltage after the transient reactance, xe is the external line reactance, M is the inertia coefficient, kE and Te are the exciter gain and time constant, and Tm is the mechanical torque; S12：将步骤S11中电力系统的四阶状态空间模型表示为：S12: The fourth-order state-space model of the power system in step S11 is represented as: 其中：in: xT(υ)＝[Δδ Δω ΔE′q ΔEfd]；x T (υ)=[Δδ Δω ΔE′ q ΔE fd ]; x(υ)、u(υ)分别表示第υ个节点的状态变量和控制输入，y(υ)是测量输出，是节点之间的内部耦合矩阵，w(υ)是属于区间上的额外干扰，是传感器的测量矩阵，是系统的输出矩阵，k1,k2...k6是同步电机的线性化模型常数，Δω是速度偏差；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 output matrix of the system, k1 , k2 ... k6 are the linearization model constants of the synchronous motor, and Δω is the speed deviation; S13：引入部分信息未知的隐马尔可夫过程，建立如下的隐马尔可夫跳跃电力系统：S13: Introducing a partially unknown Hidden Markov Process (HMM) to establish the following Hidden Markov Jumping Electric System: 其中，是离散时间马尔可夫链；in, It is a discrete-time Markov chain; 该隐马尔可夫跳跃电力系统中的转移概率矩阵R＝{ηψj}如下：The transition probability matrix R = {η ψj } in the hidden Markov jump power system is as follows: 其中，ηψj∈[0,1]， Where η ψj ∈[0,1], 该隐马尔可夫跳跃电力系统中的观测概率矩阵如下：The observation probability matrix of this hidden Markov jump power system as follows: 其中，ξψi∈[0,1]， in, ξ ψi ∈[0,1]， 3.根据权利要求2所述的一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，其特征在于，在所述步骤S2中，DoS攻击的能量有限，可能会持续到第N个时间点，DoS攻击的模式如下：3. A security control method for a two-layer hidden Markov jump power system according to claim 2, characterized in that, in step S2, the energy of the DoS attack is limited and may continue until the Nth time point; the DoS attack pattern is as follows: 模式1：表示数据传输成功(λ(μ)＝1)；在此模式下，系统在下一个时间步骤继续成功的概率为τ11，发生传输通道故障的概率为τ12，遭受DoS攻击的概率为τ13；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 transmission channel failure is τ 12 , and the probability of suffering a DoS attack is τ 13 . 模式2：表示通信传输失败(λ(μ)＝2)；在此模式下，系统在下一时间步传输成功的概率为τ21，发生传输通道故障的概率为τ22，遭受DoS攻击的概率为τ23；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 transmission channel failure is τ 22 , and the probability of suffering a DoS attack is τ 23 . 模式3：表示在DoS攻击(λ(μ)＝3)下的传输；系统在下一时间步骤中正常传输的概率为τ31，发生传输通道故障的概率为τ32，可能继续受到DoS攻击的概率为τ34；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 transmission channel failure is τ 32 , and the probability of continuing to be attacked by DoS is τ 34 . 按照同样的原则，扩展到模式λ(μ)＝N+1；由于攻击达到λ(μ)＝N+2时攻击能量有限，因此系统在下一时间步骤中，系统可能分别以概率τ(N+2)1和τ(N+2)2返回到模式1或模式2。Following the same principle, this is extended to mode λ(μ)＝N+1; since the attack energy is limited when the attack reaches λ(μ)＝N+2, the system may return to mode 1 or mode 2 with probabilities τ (N+2)1 and τ (N+2)2 respectively in the next time step. 4.根据权利要求3所述的一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，其特征在于，在所述步骤S2中，具体处理过程如下：4. The 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：考虑使用马尔可夫变量q(μ)来模拟DoS攻击的切换，确定转移概率矩阵如下：S21: Consider using Markov variables q(μ) to simulate the switching of a DoS attack and determine the transition probability matrix. as follows: 其中， in, S22：变量λ(μ)通过q(μ)进行观察，并在中取值，且确定观测概率矩阵如下：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: 其中， in, S23：分析转移概率矩阵和观测概率矩阵部分未知的情况： 其中：S23: Analyze the case where the transition probability matrix and observation probability matrix are partially unknown: in: 具体情况分为以下三种：The specific situations can be divided into the following three categories: Case1： Case 1: Case2： Case 2: Case3： Case 3: 5.根据权利要求4所述的一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，其特征在于，在所述步骤S4中，给定标量σ＞0，如果存在矩阵Ki、ρ＝a,b；以及对称矩阵则当下列不等式条件成立时，步骤S32中的系统能够在给定的H∞性能指标σ下实现随机稳定：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 Ki , ρ = a, b; and symmetric matrix Then, the system in step S32 can achieve stochastic stability under the given performance index σ H∞ when the following inequality conditions are true: 其中：in: 6.根据权利要求5所述的一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，其特征在于，在所述步骤S5中，具体处理过程如下：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：对于w(t)≡0和任意初值，当条件成立时，步骤S32中的系统为随机稳定；当所有非零且零初始状态满足如下不等式时，步骤S32中的系统能达到规定的H∞性能指标σ：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, the system in step S32 can achieve the specified performance index σ when the zero initial state satisfies the following inequality: S52：考虑选取下列Lyapunov泛函：S52: Consider selecting the following Lyapunov functionals: 其中， in, 令得到：make get: 其中， in, 通过步骤S51中下方的不等式和上式得到：We obtain the following from the inequality below and the above equation in step S51: 其中： in: S53：通过步骤S4中不等式条件中上方的不等式，得到：S53: Using the inequality above the inequality condition in step S4, we obtain: 其中， in, S54：将步骤S53中的不等式带入步骤S4中不等式条件中下方的不等式，得到：S54: Substitute the inequality from step S53 into the inequality below the inequality condition in step S4, and we get: S55：然后，基于不等式和Schur补，能够得到步骤S4中的不等式条件中下方的不等式；S55: Then, based on the inequality By combining Schur's complement, we can obtain the inequality below the inequality condition in step S4; S56：根据步骤S54中的不等式，得到：S56: Based on the inequality in step S54, we get: 如果w(t)≡0，则系统是随机稳定的；If w(t)≡0, then The system is stochastically stable; 在零初始条件下，w(t)≠0，得知 Given zero initial conditions, w(t) ≠ 0, we know that 系统是随机稳定并且满足指定的H∞性能指标σ。The system is stochastically stable and satisfies the specified performance index σ at H∞ . 7.根据权利要求6所述的一种具有双层隐马尔科夫跳跃电力系统的安全控制方法，其特征在于，在所述步骤S6中，具体处理过程如下：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：令Ki＝Ti -1Ui；S61: Let K i =T i -1 U i ; S62：对步骤S4的不等式条件中下方的不等式做等价变换如下：S62: The inequality at the bottom of the inequality conditions in step S4 is equivalently transformed as follows: 其中：in: S63：然后使用仿真软件，通过给定矩阵参数计算出控制器增益矩阵的值。S63: Then, using simulation software, the value of the controller gain matrix is calculated using the given matrix parameters.
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