Fault-tolerant control method for discrete time Markov jump power system

Abstract

The invention discloses a fault-tolerant control method for a discrete-time Markov jump power system, which belongs to the technical field of power system control and comprises the following steps of: introducing a hidden Markov process with unknown partial information to solve the problems of transient faults in a power line, subsequent switching of related circuit breakers and limited mode information of the power system; the influence of the fault-tolerant control of the power system on the stability is considered; establishing a controller model to obtain a closed-loop system model of the system; on the basis of the Lyapunov stability theory, sufficient conditions for ensuring the random stability of the closed-loop system and meeting expected performance are obtained; proving that the inequality condition is effective by utilizing a Lyapunov function and a performance index function; calculating a gain matrix of the controller by using simulation software; and realizing fault-tolerant control of the system according to the gain matrix of the controller and given system parameters. According to the invention, fault-tolerant control of the system can be realized based on a mode of combining performance index control and controller control.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system control, and particularly relates to a fault-tolerant control method for a discrete-time Markov jump power system. BACKGROUND

[0002] With the progress of modern society, the power system, as a comprehensive network integrating power generation, transmission and power consumption, is of great importance to economic development and social operation. In the process of operation, low-frequency oscillation inevitably occurs due to poor damping effect of automatic voltage regulators, which may lead to system splitting. Therefore, it is crucial to suppress oscillation and ensure system stability. At present, scholars have proposed many methods for the research of power system stabilizers. For example, scholars have proposed a new proportional-resonant power system stabilizer, which can effectively suppress ultra-low frequency oscillation. In addition, some scholars have designed an adaptive power system stabilizer, which has better comprehensive performance than ordinary power system stabilizers.

[0003] In actual engineering applications, the parameters and structure of the power system may change suddenly due to time delay, environmental interference, equipment failure and other reasons. In the above cases, the changes have randomness, and the Markov jump theory can be used to simulate this process, which is represented as a Markov jump power system. This model is suitable for describing the random changes of parameters, and therefore has been widely studied. For example, experts have proposed a novel solution to address the challenges of fault-tolerant control in power systems characterized by random mutations, especially in the case of hybrid actuator failures. In addition, some experts have studied the stability of Markov jump power systems under hybrid network attacks.

[0004] However, most of the existing research on Markov jump systems assumes that the system modes are completely understood, which is rarely the case in practical engineering scenarios, as the mode information is usually unobservable or partially observable. Therefore, the problem of mode information acquisition difficulty is effectively solved by introducing a hidden Markov model to design an observer to observe the system mode. Subsequently, this research has received extensive attention. For example, some scholars use a hidden Markov model mode detector to estimate the unknown mode information of the controller and disturbance observer. In addition, some scholars propose an integral sliding mode function from the hidden Markov model observer. However, the above research ignores the premise that the transition probability matrix and the observation probability matrix are completely known, which leads to the limitation of the results. Therefore, researchers use a partially unknown transition probability matrix to describe the different synchronization phenomena between the fuzzy fault detection filter and the system. Some researchers introduce a hidden Markov model with a partially unknown observation probability matrix to describe the phenomenon that the state estimator cannot capture the system mode in synchronization. Although the hidden Markov model has been widely studied, there is little research on the case where the transition probability matrix and the observation probability matrix information are incomplete in the hidden Markov jump power system, which motivates the research of the present invention.

[0005] In addition, due to the complexity of the device structure and the demand for high-load continuous operation, the device will inevitably fail during operation. These failures can cause the device performance to decline, and even cause major safety accidents. For example, some experts have studied the problem of mechanical failure leading to the decline of the flight performance of unmanned aerial vehicles, including rotor-stator bearing failure, propeller blade damage, etc. Therefore, in this context, by studying active or passive fault-tolerant technology, the system can still operate reliably when the controller fails, which has become a front topic and has developed rapidly. Among them, active fault-tolerant control needs to configure a corresponding controller according to the different types of faults encountered by the system to ensure the stability of the system. Passive fault-tolerant control well avoids this shortcoming. It does not need to change the existing control structure and parameters, and more importantly, it does not need online diagnosis. It uses robust control technology to make the closed-loop system insensitive to certain deterministic faults, thereby ensuring that the system can still operate according to the original performance indicators after the fault occurs. This method is simple to design and easy to implement. For example, some experts have proposed a unified passive fault-tolerant control method, which enables a hovering quadrotor to guarantee the closed-loop stability of the system without switching controllers in the case of up to three rotor failures. In addition, some experts have proposed a robust passive fault-tolerant control method that ensures the performance of the aircraft without explicit fault information of the actuator. Obviously, passive fault-tolerant control cannot be ignored in engineering applications for the positive regulation of the system. Considering that the transition probability matrix and the observation probability matrix may not be directly obtained in this case, how to handle the fault-tolerant control of the system under incomplete probability information has inspired the current research work.

[0006] The above problems are urgent to be solved, and therefore a fault-tolerant control method for a discrete-time Markov jump power system is provided. SUMMARY

[0007] The technical problem to be solved by the present application is how to obtain accurate modal data of a power system and describe the switching phenomenon of a circuit breaker and cope with possible controller failures and incomplete modal information acquisition, and introduce a fault-tolerant control strategy and a partially unknown probability matrix, so as to provide a fault-tolerant control method for a discrete-time Markov jump power system, based on Lyapunov stability theory, a sufficient condition for the random stability of a closed-loop system and the satisfaction of expected performance indicators is obtained, and fault-tolerant control of the system can be realized when a fault occurs.

[0008] As shown in Figure 7 the above technical problems are solved by the following technical solutions, the present application comprises the following steps:

[0009] Step S1: a partially information unknown hidden Markov process is introduced to establish a hidden Markov jump power system;

[0010] Step S2: according to the influence of fault-tolerant control of the power system on stability, a fault model of the actuator in the power system is determined;

[0011] Step S3: a fault-tolerant controller model is constructed to further obtain a closed-loop system model of the discrete-time Markov jump power system;

[0012] Step S4: based on Lyapunov stability theory, a sufficient condition for the random stability of the closed-loop system in step S3 and the satisfaction of expected performance is obtained;

[0013] Step S5: the sufficient condition of step S4 is proved to be effective by using Lyapunov function and performance index function;

[0014] Step S6: the gain matrix of the controller is calculated by using simulation software;

[0015] Step S7: fault-tolerant control of the system is realized according to the gain matrix of the controller in step S6 and the given system parameters.

[0016] Further, in the step S1, the specific processing process is as follows:

[0017] S11: a dynamic model of the power system is established as follows:

[0018]

[0019] wherein, δ is the rotor angle, ω is the angular velocity, T m ​​is the mechanical torque, T e is the electrical torque, M is the inertia coefficient, E q is the q-axis voltage after transient reactance, T do is the d-axis open circuit transient time constant, E fd is the generator field voltage, x d is the synchronous reactance along the d-axis, x e is the external line reactance, x 1d is the transient reactance along the d-axis, V is the infinite bus voltage, u is the stabilizing signal, V t is the terminal voltage, k E ,T E is the exciter gain and time constant;

[0020] S12: express the fourth-order state space model of the power system in step S11 as:

[0021]

[0022] wherein:

[0023]

[0024] wherein x(λ) represents the state variable of the λth node, u(λ) represents the control input of the λth node, y(λ) represents the measurement output, is the internal coupling matrix between nodes, is the output matrix of the system, is the measurement matrix of the sensor, w(λ) is the additional disturbance belonging to the interval , k1, k2, …, k6 are linearization model constants of the synchronous motor, Δω is the angular velocity deviation, Δδ is the rotor angle deviation, k E ,T E is the exciter gain and time constant, T do is the d-axis open circuit transient time constant;

[0025] S13: adopt Markov chain to simulate the random topological changes occurring inside the power system, further apply the discretization shift operator, and establish the hidden Markov jump power system as follows:

[0026]

[0027] wherein, is the discrete-time Markov chain, i.e., the mode information of the power system, x(λ+1) represents the state variable of the λ+1th node, y(λ) is the measurement output, D r(λ) ,A r(λ) is the given system parameter matrix, ω(λ) is the additional disturbance belonging to the interval ​r(λ) is the measurement matrix of the sensor, B r(λ) is the output matrix of the system.

[0028] Further, in the step S13, the transition probability matrix of the hidden Markov jump power system is wherein, is the state space of the Markov chain.

[0029] Further, in the step S2, the actuator fault model is specifically as follows:

[0030] u f (λ)=Fu(λ)

[0031] wherein, u f (λ) represents the signal sent by the controller, which is a fault-tolerant controller, u(λ) represents the signal output by the controller when no fault occurs, F = diag{f 1 ,f 2 ,...,f n} is an actuator fault matrix function, F satisfies the relationship l = 1, 2,..., n, and are known constants, and the detailed forms are as follows:

[0032]

[0033] Further, the following formula is obtained:

[0034] F = F0(I + M), |M| ≤ J < I

[0035] wherein, M = diag{m 1 ,m 2 ,...,m n}, J = diag{j 1 ,j 2 ,...,j n}, F0 represents the average fault level, M represents the fault fluctuation range, J represents the maximum allowable fluctuation, and I is the unit matrix.

[0036] Further, in the step S3, the specific processing process is as follows:

[0037] S31: design the following controller:

[0038] u(λ) = K p(λ) x(λ)

[0039] wherein, represents the controller gain matrix; when a fault occurs, u f(λ) will be replaced by u(λ), u(λ) represents the signal output by the controller when no fault occurs;

[0040] S32: The controller is brought into the hidden Markov jump power system in step S13 to obtain a fault-tolerant control closed-loop system model of the discrete-time Markov jump power system with mode detection information:

[0041]

[0042] where x(λ+1) represents a state variable of the λ+1th node, is a given system parameter matrix, is an output matrix of the system, w(λ) is an additional disturbance belonging to the interval y(λ) is a measurement output, is a measurement matrix of the sensor.

[0043] Further, in the step S4, given scalars ξ>0, φ>0; if there exists a symmetric matrix P α >0, and a matrix M, when the system in step S32 satisfies the following conditions, random stability can be achieved under the given performance index ξ:

[0044]

[0045] The conditions are as follows:

[0046] When case 1: and case 2: occur, the conditions are:

[0047]

[0048] When case 3 occurs: the conditions are:

[0049]

[0050] where:

[0051]

[0052] where φ is an adjustable parameter.

[0053] Further, in the step S5, the specific processing process is as follows:

[0054] S51: When the condition At the beginning, for w(λ)≡0 and any initial value, the system in step S32 is stochastically stable;

[0055] If at zero initial condition and for any nonzero The following conditions are met, then the system in step S32 can meet Performance index ξ:

[0056]

[0057] S52: Consider the following Lyapunov functional:

[0058] V(λ) = φ 2 x T (λ)P α x(λ);

[0059] Let We get:

[0060]

[0061] Where,

[0062] Add the inequality in step S51 to the above formula to get:

[0063]

[0064] Where:

[0065]

[0066]

[0067] S53: Through the inequality condition in step S4, we get:

[0068]

[0069] S54: Further get:

[0070]

[0071] According to the Schur complement theorem and the inequality condition in step S4, we know Then from the above formula we know

[0072] If w(λ)≡0, then The system in step S32 is stochastically stable;

[0073] At zero initial condition, w(λ)≠0, we can get The system in step S32 is stochastically stable and meets the specified Performance index ξ.

[0074] Further, in the step S6, the specific processing process is as follows:

[0075] S61: Let Wherein, is the observed mode information, r(λ) is the observed mode information;

[0076] S62: The partial inequality condition of step S4 is equivalent to the following transformation:

[0077] In case 1: And case 2: The equivalent transformation is as follows:

[0078]

[0079] In case 3: The equivalent transformation is as follows:

[0080]

[0081] Wherein:

[0082]

[0083] S63: The value of the controller gain matrix is calculated by using the simulation software combined with the given system parameters.

[0084] Compared with the prior art, the fault-tolerant control method of the discrete-time Markov jump power system has the following advantages: the fault-tolerant control method of the discrete-time Markov jump power system proposes a hidden Markov model using partial information of the power system, and compared with the hidden Markov model with complete known probability, the hidden Markov model with partial unknown probability is more practical in engineering application; in addition, the passive fault-tolerant control strategy is proposed, which can reduce the faults that the actuator may encounter without relying on real-time fault detection, thereby ensuring the stability of the system. BRIEF DESCRIPTION OF DRAWINGS

[0085] Figure 1 is a structural schematic block diagram of the fault-tolerant control method of the discrete-time Markov jump power system with mode detection information in the embodiment of the application;

[0086] Figure 2 is a modal diagram of the system and its controller in the embodiment of the application, wherein (a) is a system modal diagram, and (b) is a controller modal diagram;

[0087] Figure 3 is a comparison diagram of fault tolerance in the embodiment of the application;

[0088] Figure 4is a trajectory graph of a controller in an embodiment of the present application;

[0089] Figure 5 is a trajectory graph of a system containing a controller system in an embodiment of the present application;

[0090] Figure 6 is a state trajectory graph of a system without a controller in an embodiment of the present application;

[0091] Figure 7 is a flowchart of a fault-tolerant control method for a discrete-time Markov jump power system with mode detection information. DETAILED DESCRIPTION

[0092] The embodiments of the present application are described in detail below, and the embodiments are implemented on the premise of the technical solutions of the present application, and detailed implementation manners and specific operation processes are given, but the protection scope of the present application is not limited to the following embodiments.

[0093] As shown in the figure, the fault-tolerant control method for a discrete-time Markov jump power system with mode detection information provided by the embodiment includes the following steps: Figure 1 Step S1: Introducing a hidden Markov process with partial information unknown to effectively solve the switching problem of a circuit breaker in a power system and the case that mode information of the power system is limited;

[0094]

[0095]

[0096] Wherein, δ is a rotor angle, ω is an angular velocity, x d is a synchronous reactance along a d-axis, x 1d is a transient reactance along a d-axis, T e is an electric torque, V is an infinite bus voltage, E fd is a generator field voltage, u is a stabilizing signal, T do ' is a d-axis open-circuit transient time constant, V t is a terminal voltage, E q ' is a q-axis voltage after a transient reactance, x e is an external line reactance, M is an inertia coefficient, k E ,T E is an exciter gain and time constant, T m is a mechanical torque;

[0097] A fourth-order state space model of the SMIB system (1) is represented as:

[0098]

[0099] Wherein:

[0100] ​

[0101] where x(λ), u(λ) denote the state variable and control input of the λth node respectively, y(λ) is the measurement output, is the internal coupling matrix between nodes, w(λ) is the additional disturbance belonging to the interval is the measurement matrix of sensors, is the output matrix of the system, k1, k2,..., k6 are the linearized model constants of the synchronous motor, Δω is the angular velocity deviation, Δδ is the rotor angle deviation, k E ,T E is the exciter gain and time constant, T do ' is the d-axis open-circuit transient time constant.

[0102] Consider the following hidden Markov jump power system:

[0103]

[0104] where, is a discrete-time Markov chain, i.e., the mode information of the power system. The transition probability matrix

[0105]

[0106] where, is the state space of the Markov chain.

[0107] Since the mode information r(λ) of the power system in practical applications cannot be directly measured, a hidden Markov model is used for observation. Specifically, the information of r(λ) is detected through p(λ), where, The observation probability matrix

[0108]

[0109] Step S2: Consider what impact the fault-tolerant control of the power system has on stability

[0110] In practical engineering applications, due to equipment aging or external disturbances, etc., the actuators in the power system may fail, so it is necessary to design a fault-tolerant controller to ensure the stability of the system. Based on the above, we can derive the actuator fault model, u f (λ) represents the signal sent by the controller, F = diag{f 1 ,f 2 ,...,f n} is the actuator fault matrix function, u f ​(λ) satisfies the following formula:

[0111] u f (λ)=Fu(λ)

[0112] where F satisfies the relationship l=1,2,...,n, and are known constants. The detailed expression is as follows:

[0113]

[0114] From the above, the following formula can be obtained:

[0115] F=F0(I+M),|M|≤J<I

[0116] where:

[0117] M=diag{m 1 ,m 2 ,...,m n},J=diag{j 1 ,j 2 ,...,j n}

[0118] F0 represents the average failure level, M represents the failure fluctuation range, J represents the maximum allowed fluctuation, and I is the unit matrix.

[0119] Step S3: Constructing a controller model to obtain a fault-tolerant control closed-loop system model of the mode detection information discrete-time Markov jump power system.

[0120] The following controller is designed:

[0121] u(λ)=K p(λ) x(λ)

[0122] where, represents the controller gain matrix, and the two subscripts of K represent the system mode and the observed mode respectively; when a fault occurs, u f (λ) will replace the original u(λ), and u(λ) represents the signal output by the controller when no fault occurs, and the specific form is as follows:

[0123] u f (λ)=F0(I+M)K p(λ) x(λ) (6)

[0124] Substituting equation (6) into equation (3), the following hidden Markov jump power system with partial information unknown (i.e. the fault-tolerant control closed-loop system model of the mode detection information discrete-time Markov jump power system) can be obtained:

[0125]

[0126] where x(λ+1) denotes the state variable of the (λ+1)th node, is a given system parameter matrix, is an output matrix of the system, w(λ) is an additional disturbance belonging to the interval , y(λ) is a measured output, c α is a measurement matrix of the sensor.

[0127] Step S4: A linear matrix inequality condition is given, which is that the system is stochastically stable under disturbance and satisfies the performance index. Step S5: The condition of step S4 is proved to be effective by using Lyapunov function and performance index function.

[0128] Given a scalar ξ>0, φ>0; if there exists a symmetric matrix and a matrix M, then the system (7) can be stochastically stable under the given performance index ξ when the following conditions are satisfied:

[0129]

[0130] Case 1: and Case 2:

[0131]

[0132] Case 3:

[0133]

[0134] wherein:

[0135]

[0136] In this embodiment, φ is an adjustable parameter, which can reduce the conservatism of the result. Only when the matrix contains the parameter φ, can the corresponding feasible solution be obtained.

[0137] Step S5: The condition of step S4 is proved to be effective by using Lyapunov function and performance index function.

[0138] When the system (7) is true under the given conditions, it not only behaves as stochastically stable, but also satisfies the performance index ξ. When the condition

[0139] is true, the system (7) is stochastically stable for w(λ)≡0 and any initial value. When the condition

[0139] is true, the system (7) is stochastically stable for w(λ)≡0 and any initial value.

[0140] If the initial condition is zero and any nonzero The following conditions are met, then the system (7) can achieve the specified Performance index ξ.

[0141]

[0142] Consider selecting the following Lyapunov functional:

[0143] V(λ)=φ 2 x T (λ)P α x(λ)

[0144] Let It can be obtained:

[0145]

[0146] Where,

[0147] Through equation (11) and the above equation, we can get:

[0148]

[0149] Where:

[0150]

[0151] Through equation (8), we get:

[0152]

[0153] Further, we get:

[0154]

[0155] From the Schur complement and from equations (9), (10), we have Further, according to equation (13), we can get

[0156] If w(λ)≡0, we know The system is stochastically stable.

[0157] Under the zero initial condition, w(λ)≠0, we can get

[0158] When the above two conditions are met, it means that the system is stochastically stable and meets the specified Performance index ξ.

[0159] Step S6: Solve the gain matrix of the controller:

[0160] Let It should be noted that, is the observed mode information, and r(λ) is the observed mode information;

[0161] The partial conditions of step S4 are equivalent to the following

[0162] Case 1: and case 2:

[0163]

[0164] Case 3:

[0165]

[0166] Where:

[0167]

[0168] At this time, the Matlab simulation software can be used to calculate the gain matrix value by giving the matrix parameters.

[0169] Step S7: The feasibility of safe and stable operation of the system is verified by numerical example simulation.

[0170] When the line fails, the hidden Markov jump power system (7) controls the on-off state of the circuit breaker, which has two states, and the specific parameters are as follows:

[0171] Mode 1:

[0172]

[0173] Mode 2:

[0174]

[0175] The remaining parameters in this embodiment are assumed as follows:

[0176] λ=33, φ=2.4, w(λ)=0.3cos(0.2λ)e -0.48λ , S1=[0.59 0.69 0.88 0.29] T , S2=[0.29 0.39 0.49 0.19] T ,

[0177] G0=0.6, J=0.5.

[0178] Then the controller gain matrix is as follows:

[0179] K1 = [-0.4135 0.2486 -0.0332 -0.0169],

[0180] K2 = [-0.2027 0.0701 0.0240 -0.0004].

[0181] According to the formula (8)-(10) can be obtained Figure 4 the controller response diagram shown. Under the action of the controller, the simulation results in the system is still stable, as shown in Figure 6 . Conversely, if there is no intervention of the controller, the system is unstable, as shown in Figure 5 . On the other hand, the system and the modal diagram of the controller as shown in Figure 2 . From Figure 3 can be seen, the system state trajectory fluctuation amplitude will be greater than the fault tolerant controller, this reflects the fault tolerant controller can effectively deal with system failure to a certain extent, ensure the stable operation of the system.

[0182] Although the above has shown and described the embodiments of the present application, it can be understood that the above-mentioned embodiments are exemplary, can not be understood as limiting the present application, those skilled in the art can be changed, modified, replaced and modified within the scope of the present application.

Claims

1. A fault-tolerant control method for a discrete-time Markov jump power system, characterized in that, Includes the following steps: Step S1: Introduce a hidden Markov process with partially unknown information to establish a hidden Markov transition power system; Step S2: Determine the actuator fault model in the power system based on the impact of fault-tolerant control on stability; Step S3: Construct a fault-tolerant controller model to further obtain the closed-loop system model of the discrete-time Markov jump power system; Step S4: Based on Lyapunov stability theory, the method in step S3 that makes the closed-loop system stochastically stable and satisfies the desired outcome is obtained. Sufficient conditions for performance; Step S5: Use the Lyapunov function and the performance index function to prove that the sufficient condition in step S4 is valid; Step S6: Calculate the gain matrix of the controller using simulation software; Step S7: Implement fault-tolerant control of the system based on the controller gain matrix and the given system parameters from step S6.

2. The fault-tolerant control method for a discrete-time 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, ω is the angular velocity, and T is the rotor angle. m It is mechanical torque, T e It is the electric torque, M is the coefficient of inertia, and E is the electric torque. q ' is the q-axis voltage after transient reactance, T do ' is the d-axis open-circuit transient time constant, E fd It is the generator field voltage, x d It is the synchronous reactance along the d-axis, x e It is the external line reactance, x 1d V is the transient reactance along the d-axis, V is the infinite bus voltage, and u is the steady-state signal. t It is the terminal voltage, k E ,T E These are the exciter gain and time constant; S12: The fourth-order state-space model of the power system in step S11 is represented as: in: Where x(λ) represents the state variable of the λ-th node, u(λ) represents the control input of the λ-th node, and y(λ) represents the measurement output. It is the internal coupling matrix between nodes. It is the system's output matrix. It is the sensor's measurement matrix, w(λ) is the value belonging to the interval Additional disturbances, k1,k2,...,k6 are the linearization model constants of the synchronous motor, Δω is the angular velocity deviation, Δδ is the rotor angle deviation, k E ,T E It is the exciter gain and time constant, T do ' is the d-axis open-circuit transient time constant; S13: Markov chains are used to simulate stochastic topological changes occurring within the power system. Further discretized shift operators are applied to establish the Hidden Markov Transition Power System as follows: in, It is a discrete-time Markov chain, i.e., the mode information of the power system, where x(λ+1) represents the state variable of the (λ+1)th node, y(λ) is the measurement output, and D r(λ) A r(λ) Given the system parameter matrix, ω(λ) is a parameter belonging to the interval [0, 1]. Additional interference on C r(λ) It is the sensor's measurement matrix, B r(λ) It is the system's output matrix.

3. The fault-tolerant control method for a discrete-time Markov jump power system according to claim 2, characterized in that, In step S13, the transition probability matrix of the hidden Markov switching power system is: in, It is the state space of the Markov chain.

4. The fault-tolerant control method for a discrete-time Markov jump power system according to claim 3, characterized in that, In step S2, the actuator fault model is as follows: you f (λ)=Fu(λ) Among them, u f (λ) represents the signal emitted by the controller, which is a fault-tolerant controller, and u(λ) represents the signal output by the controller when no fault occurs. F = diag{f 1 ,f 2 ,...,f n } is the actuator fault matrix function, and F satisfies the following relation and It is a known constant, and its detailed representation is shown below: This leads to the following formula: F = F0(I+M), |M|≤J<I in, M = diag{m 1 ,m 2 ,...,m n },J=diag{j 1 ,j 2 ,...,j n }, where F0 represents the average fault level, M represents the fault fluctuation range, J represents the maximum permissible fluctuation, and I is the identity matrix.

5. The fault-tolerant control method for a discrete-time Markov jump power system according to claim 4, characterized in that, In step S3, the specific processing procedure is as follows: S31: Design the following controller: u(λ)=K p(λ) x(λ) in, Represents the controller gain matrix; when a fault occurs, u f (λ) will replace u(λ), where u(λ) represents the signal output by the controller when no fault occurs; S32: Substitute the controller into the hidden Markov jump power system in step S13 to obtain a fault-tolerant control closed-loop system model of the discrete-time Markov jump power system with mode detection information: Where x(λ+1) represents the state variable of the (λ+1)th node. Given a system parameter matrix, It is the system's output matrix, and w(λ) is the matrix belonging to the interval [0, 1]. Additional interference on the surface, y(λ) is the measurement output, It is the measurement matrix of the sensor.

6. The fault-tolerant control method for a discrete-time Markov jump power system according to claim 5, characterized in that, In step S4, given scalars ξ > 0 and φ > 0; if a symmetric matrix exists... P α >0, and matrix M, then when the system in step S32 satisfies the following conditions, it can be given... Achieving stochastic stability under performance metric ξ: The specific conditions are as follows: When situation 1 occurs: And situation 2: At that time, the conditions are: When situation 3 occurs: At that time, the conditions are: in: a＝1,2, Where φ is an adjustable parameter.

7. The fault-tolerant control method for a discrete-time Markov jump power system according to claim 6, characterized in that, In step S5, the specific processing procedure is as follows: S51: When the condition When it is established, for w(λ)≡0 and any initial value, the system in step S32 is stochastically stable; If the initial condition is zero and any non-zero condition is met... If the following conditions are met, then the system in step S32 can satisfy... Performance indicator ξ: S52: Consider the following Lyapunov functional: V(λ)=φ 2 x T (λ)P α x(λ); make get: in, Adding the inequality from step S51 to the above equation yields: in: S53: By applying the inequality conditions in step S4, we obtain: S54: Therefore, we obtain: According to Schur's complement theorem and the inequality conditions in step S4, we know... Then, from the above equation, we can know... If w(λ)≡0, then The system in step S32 is stochastically stable; Under zero initial conditions, w(λ)≠0, we can derive... The system in step S32 is stochastically stable and satisfies the specified conditions. Performance metric ξ.

8. The fault-tolerant control method for a discrete-time Markov jump power system according to claim 7, characterized in that, In step S6, the specific processing procedure is as follows: S61: Order in, r(λ) is the observed model information, and r(λ) is the observed model information. S62: The equivalent transformation of some of the inequality conditions in step S4 is as follows: In case 1: And situation 2: When the equivalent transformation is as follows: In scenario 3: When the equivalent transformation is as follows: in: f＝1,2； S63: Calculate the value of the controller gain matrix using simulation software and given system parameters.

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