Networked system active fault-tolerant control method under random deception attack

Abstract

The application discloses a networked system active fault-tolerant control method under random deception attack, and belongs to the field of networked systems. The application studies the fault estimation and fault-tolerant control collaborative design problem of a discrete networked system with Brown parameter perturbation, partial decoupling unknown input and unexpected fault signals. While considering the phenomenon of randomly occurring deception attack, a generally considered random Brown parameter perturbation is introduced. By combining the augmented system method, the unknown input observer, the optimization algorithm and the observer-based control and signal compensation, simultaneous estimation of the state and the fault is realized. Then, an integrated fault-tolerant controller based on the observer is constructed by using the known fault reconstruction information, so as to reduce the influence of the fault signal and the random disturbance factor and also to enhance the stability and robustness of the closed-loop dynamic system. Finally, the effectiveness of the fault-tolerant control technology is verified through simulation research and examples of an electromechanical servo system.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of networked system active fault-tolerant control method under random spoofing attack, belong to networked system field. BACKGROUND

[0002] In recent years, the rapid development of computer network technology and the wide application of Internet of Things injects impetus for the digitization and intelligentization of industrial control system, unlike the point-to-point communication mode in traditional control system, networked system is a kind of closed-loop feedback control system formed by the deep integration of communication network and controlled object in network space. Compared with traditional control system, it has the advantages of low cost, flexible structure, convenient maintenance, etc., which is conducive to realizing resource sharing, easy to install and maintain, and easy to operate remotely. Therefore, networked system is widely used in smart grid, telemedicine, aerospace and other key fields.

[0003] However, the main unit components such as sensors, controllers, actuators and controlled objects in networked system generally adopt discrete distribution mode, and realize remote information interaction through digital network. The introduction of communication network increases the flexibility and expansion convenience of the system, but also brings new challenges to the analysis and design of the system, for example, due to the limitation of communication resources and network capacity, the transmission reliability of data in the network is affected, leading to time delay, data disorder, channel constraint and other problems, which adds obstacles to the analysis and synthesis of control system. These network-induced adverse factors can cause the performance of the system to deteriorate, and even affect the stability of the system, so when studying networked system, various non-ideal network factors need to be considered comprehensively. SUMMARY

[0004] In order to solve the problems existing in the prior art, the present application provides a kind of networked system active fault-tolerant control method under random spoofing attack, for Brown parameter perturbation, unknown input and accidental fault of random networked control system, an integrated robust fault estimation and fault-tolerant control technology is proposed. Malicious spoofing network attack is modeled as an unknown but bounded signal form, which no longer requires obtaining the specific prior knowledge of attack signal. Based on this modeling method, the performance index for ensuring the safety of fault estimator and fault-tolerant controller is proposed by using the extension method and linear matrix inequality, and strict mathematical proof is provided for the mean square exponential boundedness of dynamic estimation error. At the same time, the integrated fault-tolerant control strategy proposed can also ensure that the system has reliable output even in the case of fault.

[0005] The technical scheme of the present application is as follows:

[0006] The first purpose of the present application is to provide a kind of networked system active fault-tolerant control method under random spoofing attack, comprising the following steps:

[0007] Step one: Constructing a linear discrete networked system model with random Brownian motion, the state vector of the system the input vector of the system the measurable output vector of the system and possible fault signals performing preliminary modeling;

[0008] Step two: Constructing an augmented state vector and obtaining the estimated values of the system state and fault signals, the networked system constructed in step one is converted into an augmented system model;

[0009] Step three: Constructing an unknown input observer for the augmented system model to weaken the interference of unknown input items on the augmented state estimation, and obtaining the estimated value of the augmented state vector based on the unknown input observer

[0010] Step four: Constructing a state feedback-based fault-tolerant control law based on the estimated value of the augmented state vector and solving the dynamic estimation error

[0011] Step five: Substituting the new fault-tolerant control law into the original system, constructing a new closed-loop system in combination with the dynamic estimation error, and giving the design parameters;

[0012] Step six: If the design parameters make the new system mean-square exponentially bounded and meet the robustness, ending the system design; otherwise, repeating the step five and step six.

[0013] Optionally, in characteristics, the linear discrete networked system mathematical model with random Brownian motion constructed in step one is as follows:

[0014]

[0015] wherein, represents the state vector of the system, is the input vector, represents the measurable output vector of the system; represents possible actuator or sensor fault signals; is an unknown input vector satisfying norm bounded, caused by external disturbance or modeling error; represents the unknown input uncertainty part of the random Brownian noise signal; represents the unknown input uncertainty part of the random Brownian noise signal defined in the probability space Brownian motion on ω, where E{·} represents the expected value of the random variable ω(k), satisfies the following conditions: E[ω(k)]=0, E[ω 2 (k)]=0,E[ω i (k)ω j [(k)]=0(i≠j); and All are constant matrices of known dimension; furthermore, Here, it is assumed that d1(k) is a decoupled perturbation component, d2(k) is a non-decoupled perturbation component, and B and All are full-rank columns. d1 and d2 represent the dimensions of the two parts of the disturbance variable, n is the dimension of the system state vector, m is the dimension of the input vector, p is the dimension of the measurable output, q is the dimension of the Brownian noise signal, l is the dimension of the unknown input uncertainty in the Brownian noise, d is the dimension of the unknown input vector, f is the dimension of the fault signal, d1 is the dimension of the unknown input decoupled part vector, and d2 is the dimension of the unknown input non-decoupled part vector. It is represented as the real number field in Euclidean space.

[0016] Optionally, when f(k) is an actuator fault, i.e., f(k) = f a (k), E = B, D = 0 p×f When f(k) is a sensor fault, i.e., f(k) = f s (k), E = 0 n×f D = I p When f(k) represents an actuator and sensor failure, i.e. E = [E a E s ], D = [D a D s ];

[0017] Among them, E a and D a E represents the distribution coefficient matrix of actuator failures. s and D s The distribution coefficient matrix represents the sensor faults.

[0018] Optionally, the method assumes that:

[0019]

[0020] Signal transmission between the controlled object and the fault estimator is achieved through a network channel. Network attacks inevitably lead to the loss of a certain amount of observer input data during network information exchange. Therefore, the signal received by the remote fault observer unit is defined as follows:

[0021]

[0022] where v(k) represents the attack signal sent by the malicious attacker, and β(k) is a variable satisfying Bernoulli binary random sequence distribution, which is used to represent the random network attack phenomenon that the output signal may encounter in the network channel, aiming at the unknown and discontinuity of network attacks;

[0023] When β(k) = 0, it indicates that no network attack occurs in the system, and when β(k) = 1, it indicates that the network attack phenomenon is encountered in the communication channel;

[0024]

[0025] where, is a scalar parameter of the random network attack.

[0026] Optionally, the step two comprises:

[0027] A new augmented state vector is constructed, and let Thus, formula (1) is transformed into the following form:

[0028]

[0029] where:

[0030]

[0031]

[0032] I is a unit matrix;

[0033] By constructing a suitable observer and adopting the fault reconstruction strategy for the augmented state, the synchronous estimation of the system state and the actuator fault signal is realized:

[0034]

[0035] where J1 = [I n 0 n×f ], J2 = [0I f ], is the estimated value of the system state x(k), represents the estimated value of the fault signal f(k).

[0036] Optionally, the step three comprises:

[0037] An augmented state vector is established by constructing a model as shown in equation (6) to synchronize the estimated values of the fault signal and the system state, and the following observer is constructed for equation (6):

[0038]

[0039] wherein, represents the state vector of the designed observer, represents the estimated value of the augmented state vector , and and are gain matrices to be designed;

[0040] The estimated error vector is defined as The dynamic estimated error is further calculated as follows:

[0041]

[0042] The expectation of both sides of equation (9) is calculated, and equation (9) is calculated as follows by using equation (8):

[0043]

[0044] Optionally, the step four comprises:

[0045] Based on the estimated value of the augmented state vector , a signal compensation-based fault-tolerant controller is constructed as follows:

[0046]

[0047] wherein, and are controller parameter matrices to be designed, and the above fault-tolerant controller (11) is substituted into equation (1) and replaced by y c (k), as described above, the fault-tolerant controller will affect the estimated error, and therefore the fault-tolerant controller (11) is replaced by equation (8) to reconstruct the dynamic error signal after feedback control;

[0048] According to the assumption , the fault-tolerant control gain K f is designed as:

[0049]

[0050] Therefore, the following is obtained:

[0051]

[0052] wherein, B e = -BKJ1-EJ2, M e= -M2KJ1 - M3J2,

[0053] Then, the closed-loop system is established as follows using the new fault-tolerant control law:

[0054]

[0055] Equation (14) is composed of the original system and the estimation error system after signal compensation and feedback control based on state estimation, and the measurement compensator is realized on the output.

[0056] Optionally, the robustness satisfied in the step six is:

[0057]

[0058] The sufficient condition for the mean square exponential boundedness and the robust performance as equation (15) is satisfied is:

[0059]

[0060] wherein, L1 = P -1 Y, L2 = RH; * represents the transpose of the symmetric position matrix, and 0 is a zero matrix; are unknown matrices to be determined; α is a positive scalar and satisfies 0 < α ≤ 1, γ d , γ dp , γ dv and are to-be-determined robust performance parameters, l d , and respectively represent the unit matrices corresponding to the 3rd row and 3rd column, the 4th row and 4th column, the 7th row and 7th column, and the 8th row and 8th column in equation (16);

[0061]

[0062] a given constant and γ d , γ dp , γ dv and The related system performance index is used to solve formula (16) by using the LMI toolbox in MATLAB, when a positive definite matrix P and a matrix Y exist, and formula (16) is established, the system is mean-square exponential bounded, the augmented state estimation value of formula (6) can be obtained more accurately, the fault tolerance control law of the fault tolerance controller (11) is used to eliminate the influence of the fault on the system and meet the corresponding robust performance, when the unknown variable P and the unknown variable Y have no feasible solution, the system is not mean-square exponential bounded, and the augmented state estimation value of formula (3) cannot be obtained more accurately.

[0063] A second object of the present application is to provide a networked system active fault-tolerant control device under random spoofing attack, comprising a processor and a memory, the memory storing instructions executed by the processor, when the instructions are executed by the processor, the device implements the networked system active fault-tolerant control method under random spoofing attack according to any of the above.

[0064] A third object of the present application is to provide a computer readable storage medium, the computer readable storage medium storing computer executable instructions, the computer executable instructions being executed by the processor to implement the networked system active fault-tolerant control method under random spoofing attack according to any of the above.

[0065] The present application has the following advantages:

[0066] The present application proposes an integrated fault-tolerant control strategy based on fault reconstruction for a random discrete-time networked control system subject to spoofing cyber attacks. The system studied is affected by partially decoupled unknown inputs, fault signals, and Brownian disturbances. The considered unknown inputs cannot be completely decoupled, and Brownian motion exists in the state, control, fault, and uncertainty. The study of such systems is challenging but ubiquitous in practical industrial fields. Several advanced techniques are integrated, including the augmentation method, unknown input observer, optimization algorithm, observer-based control, and signal compensation. By using the proposed reconstruction and fault-tolerant control technology, the state and fault of the system can be well estimated, and the impact of the fault can be successfully mitigated. Therefore, the reliability and safety of the random discrete system can be effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0067] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0068] Figure 1is the flow chart of the active fault-tolerant control method of the networked system under random spoofing attack of the present application.

[0069] Figure 2 is the comparison chart of the state x1 of the networked system of the present application and its estimated value.

[0070] Figure 3 is the comparison chart of the state x2 of the networked system of the present application and its estimated value.

[0071] Figure 4 is the comparison chart of the actuator fault f(k) in the networked system of the present application and its estimated value.

[0072] Figure 5 is the timing chart of the random spoofing attack v(k) of the networked system of the present application.

[0073] Figure 6 is the comparison chart of the system state x1 under three different conditions of the present application.

[0074] Figure 7 is the comparison chart of the system state x2 under three different conditions of the present application. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical scheme and advantages of the present application more clear, the embodiments of the present application will be further described in detail below with the accompanying drawings.

[0076] Embodiment one:

[0077] The present embodiment provides an active fault-tolerant control method of a networked system under random spoofing attack, referring to Figure 1 , comprising:

[0078] Step one: constructing a linear discrete networked system model with random Brownian motion, preliminarily modeling the state vector of the system, the input vector of the system, the measurable output vector of the system, and the possible fault signal;

[0079] Step two: constructing an augmented state vector and obtaining the estimated value of the system state and the fault signal, converting the networked system constructed in step one into an augmented system model;

[0080] Step three: constructing an unknown input observer for the augmented system model to weaken the interference of the unknown input term on the augmented state estimation, obtaining the estimated value of the augmented state vector

[0081] Step four: estimate the augmented state vector based on the estimate value Construct the fault-tolerant control law based on state feedback, and solve the dynamic estimation error

[0082] Step five: substitute the new fault-tolerant control law into the original system, combine the dynamic estimation error to construct a new closed-loop system, and give the design parameters

[0083] Step six: if the design parameters make the new system mean-square exponential and meet the robustness, end the system design; otherwise, repeat step five and step six.

[0084] Embodiment two

[0085] The embodiment provides a networked system active fault-tolerant control method under random spoofing attack, referring to Figure 1 , the method comprises the following steps:

[0086] Step 1: establish a model of a kind of discrete-time networked system as shown below:

[0087] Consider a kind of linear discrete networked system mathematical model with random Brownian motion as formula (17):

[0088]

[0089] Disturbance decomposition can better reduce the adverse effects of interference. Therefore, it is desirable to achieve complete decoupling of the disturbance as much as possible.

[0090] For the system affected by the disturbance that cannot be completely decoupled, optimization techniques are usually used to decouple part of the disturbance component, while attenuating the disturbance component that cannot be decoupled. For the bounded unknown input vector that may be caused by interference or modeling error, wherein it is assumed that d1(k) is unknown but can be decoupled, and d2(k) is not decoupled;

[0091] Assumption 2

[0092]

[0093] Assumption 3: for complex number z, Re(z)≥0, the following formula is true:

[0094]

[0095] For concealment considerations, network attackers usually do not adopt long-term persistence attacks, i.e. the probability of attack occurrence is not equal to 1, in addition, due to the energy consumption problem to be considered in the attack, the attack signal is often bounded, the embodiment considers that the signal transmission between the controlled object and the fault estimator is realized through a network channel, and the influence of the network attack phenomenon in the network information interaction process inevitably leads to the loss of a certain amount of observer input data. Thus, the signal received by the fault observer unit at the remote end is set as:

[0096]

[0097] In the formula, v(k) represents the attack signal sent by a malicious attacker, in view of the unknownness and discontinuity of the network attack, the general processing method is to use the variable β(k) satisfying the Bernoulli binary random sequence distribution to represent the random network attack phenomenon that the output signal may encounter in the network channel. When β(k) = 0, it indicates that no network attack occurs in the system, and when β(k) = 1, it indicates that the network attack phenomenon is encountered in the communication channel; the probability of occurrence of the deception attack is represented as is a scalar parameter of the random network attack;

[0098] Step 2: Construct the model of the augmented system;

[0099] Let From formula (17), the following form can be obtained:

[0100]

[0101] Wherein:

[0102]

[0103] I is a unit matrix.

[0104] Step 3: Design an unknown input observer;

[0105] In order to weaken its interference on the final estimation result, the following observer is constructed for formula (22):

[0106]

[0107] Wherein, represents the state vector of the designed observer, represents the estimated value of the augmented state vector . And and are gain matrices to be designed.

[0108] The estimation error vector is defined as:

[0109]

[0110] With assumption 2-3, equation (25) can be obtained:

[0111]

[0112] Then, with equations (23)-(25), and due to the existence of random number, to ensure that the estimation error value is as small as possible, the expectation of both sides of the estimation error value to be solved is calculated simultaneously, and the calculation result obtained by using equation (25) is as follows:

[0113]

[0114] Assumption 2 and assumption 3 are reasonable in fault reconstruction and fault-tolerant control, and are also general conditions for fault estimation based on an unknown input observer. Specifically, assumption 2 ensures that the equation is solvable, in other words, the unknown input can be decoupled, and thus, the particular solution of the equation is:

[0115]

[0116] Assumption 3 indicates that the augmented system model is observable. Assumption 1 is a condition for the existence of the signal compensator based on the estimator. To be precise, it is a signal compensation condition without random disturbance on the fault, and assumption 1 is a modified condition, so that fault signals of different types can also be compensated.

[0117] It is worth noting that equation (25) is established by selecting a suitable observer gain H, and d1(k) can be completely decoupled by introducing H to meet the relevant conditions. However, the dynamic error is still affected by d2(k) and the Brown disturbance signal, and the next task is to design a reasonable observer gain, so that the estimation error vector e(k) remains stable and is as robust as possible to the disturbance vector d2(k).

[0118] The Brown perturbation makes the estimation error dependent on the trajectory of the system under study. In other words, it is relatively difficult to separate the design of the fault estimation observer and the fault-tolerant controller. Therefore, the specific value of the estimation parameter gain cannot be directly determined at this stage, and a fault-tolerant control scheme is first constructed.

[0119] Description 2: The present invention considers fault and Brownian disturbance signals in addition to system states and control inputs. Therefore, the system under study is more general, but it brings non-trivial challenges to achieve convergent estimation error. Specifically, the goal of the fault-tolerant control strategy includes reducing the system stability fluctuation caused by faults, while existing work only reduces the fluctuation caused by faults. In addition, disturbances also cause the increase of estimation error, so in addition to completing the decoupling work of d1(k), it is also necessary to robustness is achieved.

[0120] By reconstructing the extended state, simultaneous estimation of system state and fault is achieved:

[0121]

[0122] where J1 = [I n 0 n×f ], J2 = [0I f ], is the estimated value of the system state x(k), is the estimated value of the fault signal f(k).

[0123] Step 4: Fault estimation and fault-tolerant control integrated design of networked systems;

[0124] Based on the estimated value of the augmented state vector The fault-tolerant controller based on signal compensation can be constructed as follows:

[0125]

[0126] Substituting the above fault-tolerant controller (29) into equation (17) and replacing y c (k) with y(k) can obtain:

[0127] x(k+1)

[0128] = (A + BK)x(k) + B d d(k) + (BK f + E)f(k) - BKJ1e(k)

[0129] - BK f J2e(k) + [(M1 + M2K)x(k) - M2KJ1e(k)

[0130] + (M2K f + M3)f(k) - M2K f J2e(k) + M4d p (k)]ω(k) (31)

[0131] y c(k) = [1 - β(k)]Cx(k) + [1 - β(k)]DJ2e(k) + β(k)v(k) (32)

[0132] As mentioned above, the fault-tolerant controller will affect the estimation error, so here the fault-tolerant controller (29) is replaced by equation (23), and the dynamic error signal after feedback control can be reconstructed as:

[0133]

[0134] According to assumption 1, The fault-tolerant control gain K f can be designed as:

[0135]

[0136] Therefore, here we can get:

[0137]

[0138] Then equation (31) and equation (33) can be simplified as:

[0139] x(k + 1) = (A + BK)x(k) + B d d(k) + B e e(k)

[0140] + [(M1+ M2K)x(k) + M e e(k) + M4d p (k)]ω(k) (34)

[0141]

[0142] Where B e = -BKJ1- EJ2, M e = -M2KJ1- M3J2,

[0143] Then combined with equation (32), equation (34) and equation (35), the closed-loop system can be established as follows:

[0144]

[0145] It can be noted that the new constructed closed-loop system (36) is composed of the original system and the estimation error system after the signal compensation and the state estimation based feedback control, and the measurement compensator is implemented on the output. Due to the existence of Brownian motion, it is difficult to distinguish the system dynamics and the error dynamics. That is, the observer gain and the controller gain are interactive, which brings challenges to the integrated fault-tolerant control scheme. A typical method to reduce complexity is to choose a controller gain K such that the modulus of all eigenvalues of A+BK and M1+M2K are less than 1, and the next problem is to find a suitable observer gain to ensure the boundedness and robustness of the entire closed-loop system. Before designing the observer gain, the following lemma is introduced.

[0146] Lemma 1 (Schur complement lemma) For a symmetric matrix The following three conditions are equivalent:

[0147] (1) S < 0;

[0148] (2) S 11 <0,

[0149] (3) S 22 <0,

[0150] Lemma 2. Suppose there exists a stochastic process term V n (σ n ), and any real number μ>0 and 0<α≤1 such that each solution of the new constructed closed-loop system (36) satisfies the following two conditions, then this stochastic process term can be called mean square exponentially bounded.

[0151] ψ1||σ n || 2 ≤V n (σ n )≤ψ2||σ n || 2 (37)

[0152] E{V n+1 (σ n+1 )|σ n}-V n (σ n )≤μ-αV n (σ n ) (38)

[0153] The next step is to give the related theorem and its specific proof to ensure that the new constructed closed-loop system (36) is mean square exponentially bounded and satisfies the following robust performance.

[0154]

[0155] Step 5: The newly constructed closed-loop system (36) is mean-square exponentially bounded and satisfies the sufficient condition of robust performance as in equation (39);

[0156] Step 5.1: The sufficient condition that the newly constructed closed-loop system (36) is mean-square exponentially bounded is:

[0157] A Lyapunov function of the following form is constructed for the newly constructed closed-loop system (36):

[0158]

[0159] wherein, and P are positive definite matrices, let It is obviously known that, satisfies equation (37). Wherein, λ min represents the minimum eigenvalue of a real symmetric matrix, λ max represents the maximum eigenvalue of a real symmetric matrix;

[0160] Using Lyapunov stability theory and linear matrix inequality analysis method, the sufficient condition that the newly constructed closed-loop system (36) is mean-square exponentially bounded and satisfies the robust performance as in equation (39) is obtained. The steps are as follows:

[0161] Assume that equation (41) is established:

[0162]

[0163] wherein: L1=P -1 Y, L2=RH; * represents the transpose of the symmetric position matrix, 0 is the zero matrix; are unknown matrices to be determined; α is a positive scalar and satisfies 0 < α ≤ 1, γ d , γ dp , γ dv and are to-be-determined robust performance parameters, l d , and respectively represent the unit matrix corresponding to the 3rd row and 3rd column, the 4th row and 4th column, the 7th row and 7th column, and the 8th row and 8th column in equation (16);

[0164]

[0165] Further calculation is made on equation (40), and the polynomials of equation (42) are added and subtracted on the right side of equation (40):

[0166]

[0167] Equation (40) can be rewritten as:

[0168]

[0169] where,

[0170] From equation (25), we have where Y = PL1.

[0171] LMI (41) implies that

[0172]

[0173] where,

[0174]

[0175] Multiplying equation (44) by matrices diag{I, I, I, I, I, P -1 I, I} on the left and right respectively, we have

[0176]

[0177] Using the Schur complement lemma of Lemma 1, equation (45) is equivalent to Ω < 0.

[0178] Since d(k), and d p (k) are all bounded vectors, there exists a positive scalar μ such that the following equation holds for equation (43):

[0179]

[0180] Then we have

[0181]

[0182] This shows that the newly constructed closed-loop system (36) is mean-square exponentially bounded.

[0183] If there exists a positive definite matrix P > 0 and a matrix Y such that equation (41) holds, then the closed-loop system is mean-square exponentially bounded. If the closed-loop system obtained in step 5.1 is mean-square exponentially bounded, then step 5.2 is executed; if the closed-loop system obtained in step 5.1 is not mean-square exponentially bounded, then step 5.2 cannot be executed.

[0184] Step 5.2: The newly constructed closed-loop system (36) satisfies the sufficient condition for robust performance as shown in equation (39)

[0185] Let:

[0186]

[0187]

[0188] For Γ, use the equation transformation to add and subtract polynomials It follows that

[0189]

[0190] where

[0191]

[0192] Θ 12 = Φ 12 + C T DJ2, Θ 15 = Φ 15 ,

[0193] Θ 25 = Φ 25 , Θ 55 = Φ 55 , Θ 66 = Φ 66 , Θ 67 = Φ 67 , Θ 77 = Φ 77 .

[0194] Note that under zero state condition, we have

[0195]

[0196] By multiplying the left and right of equation (41) by matrices diag{I, I, I, I, P -1 I, I} respectively, and using the Schur complement lemma, we can further obtain

[0197] Θ < 0 (51)

[0198] This shows that

[0199]

[0200] The proof is complete. Therefore, the newly constructed closed loop system (36) is mean square exponentially stable and satisfies the robust performance as in equation (39).

[0201] According to Lyapunov stability theory, given constants and γ d , γ dp , γdv and The related system performance index is utilized, and the LMI toolbox in MATLAB is utilized to solve formula (41), when there is a positive definite matrix P and a matrix Y, so that formula (41) is established, the system is mean square exponential bounded, accurate augmented state estimation of the system (22) can be obtained, and the fault tolerance control law of the fault tolerance controller (29) is utilized to eliminate the influence of the fault on the system and satisfy the corresponding robust performance; when the above unknown variable has no feasible solution, the system is not mean square exponential bounded, and accurate augmented state estimation of the system (22) cannot be obtained.

[0202] The networked system active fault tolerance control method under random deception attack is adopted, under the condition of considering external disturbance and faults, the newly constructed closed loop system (36) is mean square exponential bounded and satisfies certain robust performance, and the specific implementation method is as follows:

[0203] Electromechanical servo technology has been widely applied in the servo control field of launch vehicles and flight devices due to its simple composition and structure, convenient operation and maintenance, compact structure and high power density, and typical applications include realizing thrust vector control of a swing rocket engine nozzle or realizing air dynamic force control of an aircraft aerodynamic rudder, thereby completing attitude stability control of a launch vehicle. Many countries in the world have funded a large number of electromechanical control technology research projects, and some aircraft auxiliary flight control systems are partially equipped with electromechanical servo systems. In this embodiment, several typical indexes in the electromechanical servo system case are used to construct a discrete time model to verify the effectiveness of the designed fault tolerance control technology, and the specific form is as follows:

[0204]

[0205] Among them, x1(k) represents a load angle position, x2(k) represents an axis rotation speed, and u(k) is an input voltage. The sampling time is 0.1 s, and the system description matrix is as follows:

[0206]

[0207] Considering the influence of faults, unknown uncertainties and Brown motion, the system can be described by a random discrete time model (53). The unknown input sample is represented by a random signal with a value ranging from -0.1 to 0.1, and the parameter matrix is as follows: Among them The uncertainty d p (k) is represented by a random noise signal with a value ranging from -0.01 to 0.01, and the random distribution coefficient of Brown motion can be set as M1=0.05A, M2=0.1B, M3=0.1E,

[0208] The original controller gain of the embodiment can be set as K = [0.0046 0.0173], and the parameter gain of the fault compensator is The randomly generated network attack signal is set as a point signal with an amplitude of 1 or -1 at a certain time in the running time, and the Bernoulli parameter of the random attack is The actuator fault f(k) in the system is:

[0209]

[0210] According to formula (27), the corresponding observer gain matrix can be given here as The eigenvalues of the system matrices A and M2 are all within the unit circle, so by solving the linear matrix inequality (41), the system parameters are α = 0.1, γ d = 10, and γ dp = 10, and the global optimal solution t min < 0 of the inequality is obtained, indicating that the system is strictly feasible, and the values of the parameter matrices P and Y are given.

[0211] In addition, the initial state value of the system and the initial value of the fault are set as x(0) = [10; 10], f(0) = 1, and the initial state value of the observer is z(0) = [0; 0]. At the same time, using formula (25) and L1 = P -1 Y, the observer (23) gain matrix can be calculated as:

[0212] Through MATLAB software simulation, the data required by the embodiment can be obtained, and the specific simulation graphs are shown in the accompanying Figures 2-7 drawings.

[0213] The fault reconstruction and fault-tolerant control technology is applied to the electromechanical servo system. By setting the standard Brownian motion and unknown input signal, the estimated values of the state and fault are compared with the original signal, and the results are shown in Figures 2 to 7 . Figure 5 The timing diagram is shown as a random deception attack, Figure 6 and Figure 7 The state comparison of the system under three conditions of no fault, fault with fault-tolerant control, and fault without fault-tolerant control is shown.

[0214] In the presence of multiple factors such as Brown disturbance, measurement noise signal and randomly occurring spoofing attack, the estimation trajectory of system state and fault can still be clearly obtained from the simulation results, which further confirms the feasibility and applicability of the observer constructed in the embodiment. This is because after the observer is designed, a new fault-tolerant strategy is proposed to compensate the influence of fault signal, multiple disturbances and randomly occurring spoofing attack on the normal performance of the system. Randomly occurring spoofing attack and actuator fault will cause large fluctuations in the system state, and under the action of the fault-tolerant controller based on signal compensation, all state vectors can tend to normal values. The research of the embodiment also fully illustrates the effectiveness of the fault estimation and active fault-tolerant control strategy proposed in the application.

[0215] In summary, according to the simulation results, in the presence of random spoofing attack and Brown disturbance signal, the unknown input observer designed in the application can effectively obtain the estimation values of the system state and fault. In the networked system, the fault-tolerant control method based on signal compensation effectively reduces the influence of fault on the stability of the system. It can be seen that the unknown input strategy can well cope with the problem of multiple faults and disturbance forms, and it also shows that the active fault-tolerant control method of the networked system under random spoofing attack proposed in the application is effective.

[0216] Part of the steps in the embodiment of the application can be implemented by software, and the corresponding software program can be stored in a readable storage medium such as an optical disc or a hard disk.

[0217] The above description is only the preferred embodiment of the application and is not intended to limit the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A proactive fault-tolerant control method for a networked system under random deception attacks, characterized in that, Includes the following steps: Step 1: Construct a linear discrete network system model with stochastic Brownian motion, and define the system's state vector. System input vector The system's measurable output vector and possible fault signals Perform preliminary modeling; Step 2: Construct augmented state vectors In order to obtain timely estimates of system status and fault signals, the networked system constructed in step one is transformed into an augmented system model; Step 3: Construct an unknown input observer for the augmented system model to reduce the interference of unknown input terms on the augmented state estimation, and obtain the augmented state vector based on the unknown input observer. The estimated value Step 4: Estimated value based on the augmented state vector A fault-tolerant control law based on state feedback is constructed, and the dynamic estimation error is obtained by solving the problem. Step 5: Substitute the new fault-tolerant control law into the original system, construct a new closed-loop system by combining it with the dynamic estimation error, and provide the design parameters; Step Six: If the design parameters make the mean square exponent of the new system bounded and satisfy robustness, then end the system design; otherwise, repeat Steps Five and Six. The mathematical model of the linear discrete network system with random Brownian motion constructed in step one is shown below: in, Represented as the system's state vector. For the input vector, Represented as the system's measurable output vector; This indicates a possible actuator or sensor malfunction signal; For unknown input vectors that satisfy the boundedness of the l2[0,+∞) norm, the problem is caused by external perturbation or modeling error; The unknown input uncertainty is represented as a random Brownian noise signal; Represented as defined in probability space Brownian motion on ω, where E{·} represents the expected value of the random variable ω(k), satisfies the following conditions: E[ω(k)]=0, E[ω 2 (k)]=0,E[ω i (k)ω j [(k)]=0(i≠j); and All are constant matrices of known dimension; furthermore, d1(k) is the decoupled perturbation part, d2(k) is the non-decoupled perturbation part, and B and All are full-rank columns. d1 and d2 represent the dimensions of the two parts of the disturbance variable, n is the dimension of the system state vector, m is the dimension of the input vector, p is the dimension of the measurable output, q is the dimension of the Brownian noise signal, l is the dimension of the unknown input uncertainty in the Brownian noise, d is the dimension of the unknown input vector, f is the dimension of the fault signal, d1 is the dimension of the unknown input decoupled part vector, and d2 is the dimension of the unknown input non-decoupled part vector. It is represented as the real number field in Euclidean space.

2. The active fault-tolerant control method for networked systems under random deception attacks according to claim 1, characterized in that, When f(k) is an actuator fault, i.e., f(k) = f a (k), E = B, D = 0 p×f When f(k) is a sensor fault, i.e., f(k) = f s (k), E = 0 n×f D = I p When f(k) represents an actuator and sensor failure, i.e. E = [E a E s ], D = [D a D s ]; Among them, E a and D a E represents the distribution coefficient matrix of actuator failures. s and D s The distribution coefficient matrix represents the sensor faults.

3. The active fault-tolerant control method for networked systems under random deception attacks according to claim 1, characterized in that, The method assumes that: Signal transmission between the controlled object and the fault estimator is achieved through a network channel. Network attacks inevitably lead to the loss of a certain amount of observer input data during network information exchange. Therefore, the signal received by the remote fault observer unit is defined as follows: In the formula, v(k) represents the attack signal sent by the malicious attacker. In view of the unknown and discontinuous nature of network attacks, the variable β(k) that satisfies the Bernoulli binary random sequence distribution is used to represent the random network attack phenomenon that the output signal may encounter in the network channel. When β(k) = 0, it indicates that no network attack has occurred in the system, while when β(k) = 1, it indicates that a network attack has occurred in the communication channel. in, Scalar parameters for random network attacks.

4. The active fault-tolerant control method for networked systems under random deception attacks according to claim 1, characterized in that, Step two includes: Construct a new augmented state vector, let Equation (1) is thus transformed into the following form: in: I is the identity matrix; By constructing a suitable observer and employing a fault reconstruction strategy for the augmented state, synchronous estimation of the system state and actuator fault signals can be achieved. Where J1=[I n 0 n×f J2 = [0 I] f ], It is an estimate of the system state x(k). It is represented as an estimate of the fault signal f(k).

5. The active fault-tolerant control method for networked systems under random deception attacks according to claim 4, characterized in that, Step three includes: An augmented state vector is constructed using a model as shown in equation (6) to simultaneously obtain estimates of fault signals and system states. The following observer is constructed for equation (6): in, This represents the state vector of the designed observer. Represented as an augmented state vector The estimated value, and and The gain matrix to be designed; Define the estimation error vector as The dynamic estimation error was further calculated as follows: Find the expected value of both sides of equation (9): Simultaneously, the calculation results using equations (8) and (9) are shown in equation (10).

6. The active fault-tolerant control method for a networked system under random deception attacks according to claim 5, characterized in that, Step four includes: Estimated value based on augmented state vector Construct the following fault-tolerant controller based on signal compensation: in, and For the controller parameter matrix to be designed, substitute the above fault-tolerant controller (11) into the original equation (1) and use y c (k) replace y(k). As mentioned above, the fault-tolerant controller will affect the estimation error. Therefore, here we replace the fault-tolerant controller (11) with Equation (8) to reconstruct the dynamic error signal after feedback control. According to the assumption Then the fault-tolerant control gain K f Designed as follows: Therefore, we get: Among them, B e =-BKJ1-EJ2,M e =-M2KJ1-M3J2, Then, using the new fault-tolerant control law, a closed-loop system of the following form can be established: Equation (14) consists of the original system and the estimation error system after signal compensation and feedback control based on state estimation, and a measurement compensator is implemented on the output.

7. The active fault-tolerant control method for networked systems under random deception attacks according to claim 6, characterized in that, The robustness satisfied in step six is ​​as follows: The sufficient condition for the mean square exponent to be bounded and to satisfy the robust performance as in equation (15) is: in, L1 = P -1 Y, L2 = RH; * represents the transpose of the symmetric position matrix, 0 is the zero matrix; All are unknown matrices to be determined; α is a positive scalar and satisfies 0 < α ≤ 1. γ d γ dp γ dv and These are robust performance parameters to be determined. l d , and Let them represent the identity matrices corresponding to the 3rd row and 3rd column, the 4th row and 4th column, the 7th row and 7th column, and the 8th row and 8th column in equation (16), respectively. Given constant α, as well as γ d γ dp γ dv and The relevant system performance indicators are used to solve equation (16) using the LMI toolbox in MATLAB. When there exists a positive definite matrix P and matrix Y such that equation (16) holds, the system is mean square exponentially bounded. It can obtain a more accurate estimate of the augmented state of equation (6). At the same time, the fault-tolerant control law of the fault-tolerant controller (11) is used to eliminate the impact of faults on the system and satisfy the corresponding robust performance. When there is no feasible solution for unknown variables P and Y, the system is not mean square exponentially bounded and a more accurate estimate of the augmented state of equation (3) cannot be obtained.

8. A networked system active fault-tolerant control device under random spoofing attacks, comprising a processor and a memory, characterized in that, The memory stores instructions that are executed by the processor. When the instructions are executed by the processor, the device implements the active fault-tolerant control method for networked systems under random spoofing attacks according to any one of claims 1 to 7.

9. A computer-readable storage medium storing computer-executable instructions, characterized in that, When the computer-executable instructions are executed by the processor, they implement the active fault-tolerant control method for networked systems under random spoofing attacks according to any one of claims 1 to 7.

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