Intermittent control method, device and storage medium for complex cyber-physical systems under multi-source attacks

Abstract

The present invention discloses an intermittent control method, device and storage medium for a complex information-physical system under multi-source attacks, which relates to the technical field of network system control. The system is considered to be subjected to physical attacks and mixed network attacks at the same time, and a random variable obeying Bernoulli distribution is used to characterize the probability of occurrence of malicious network attacks; the mixed time delay is composed of distributed state delay and time-varying delay; the actuator saturation situation is taken into account, and a discrete time system model containing multiple constraints is established on this basis; secondly, sufficient conditions for exponential stability of closed-loop errors are given with the help of Lyapunov stability theory and linear matrix inequality technology, and an intermittent controller that ensures the stability of the closed-loop system is designed. The present invention uses the designed intermittent controller to improve the reliability and safety of the system.

Description

Technical Field

[0001] The present invention relates to the field of network system control technology, and more specifically to a method, device and storage medium for intermittent control of a complex information-physical system under multi-source attacks. Background Art

[0002] With the deep integration of complex networks and cyber-physical systems in modern industry, complex cyber-physical systems have been formed. The deep integration of cyber space and physical space has an important impact on the normal operation of the system. With the development of the information age, more and more important infrastructures can be considered as complex cyber-physical systems, such as power grid systems, transportation systems, and the Internet of Things. Due to the complexity of the system and the openness of the communication protocol, it is easily threatened by malicious network attacks. At present, there are three main types of network attacks against the system: Denial of service (DoS) attack, replay attack, and false data injection (FDI) attack. Among them, DoS attack acts on the network and blocks the data transmission between information transmission channels. DoS attack is one of the easiest attacks to implement, but it will cause more serious damage. FDI attack destroys the authenticity and integrity of data by tampering with the content of the data packet, which is highly concealed and destructive.

[0003] It is difficult for the system to remain stable in an environment with complex disturbances, and necessary feedback control methods need to be adopted to achieve the system's stabilization requirements. Recently, an intermittent control method has been proposed, which combines the advantages of continuous feedback control and pulse control. Compared with the common continuous control, it has better economy and has attracted widespread attention from scholars. At present, the study of intermittent safety control strategies for hybrid time-delay systems with actuator saturation under complex attacks is still an open topic and deserves further in-depth research.

[0004] Therefore, how to adopt intermittent control methods to further improve the stability and reliability of complex systems is an urgent problem that technicians in this field need to solve. Summary of the invention

[0005] In view of this, the present invention provides a method, device and storage medium for intermittent control of a complex information-physical system under multi-source attacks, which can enhance the system's resistance to multi-source attacks and enhance the system's robustness to external disturbances and internal changes, thereby improving the system's stability and reliability.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A method for intermittent control of a complex cyber-physical system under multi-source attacks, comprising the following steps:

[0008] Step 1: Establish a system state space model of a discrete-time complex cyber-physical system consisting of N identically coupled nodes;

[0009] Step 2: Establish a state space model of the attacked system after the physical attack based on the system state space model;

[0010] Step 3: Construct an isolated node model corresponding to the discrete-time complex information-physical system, and calculate the synchronization error based on the isolated node model;

[0011] Step 4: Build a hybrid network attack model;

[0012] Step 5: Taking the synchronization error as input, construct an intermittent controller based on the event-triggered mechanism and the actuator saturation problem;

[0013] Step 6: Construct a closed-loop synchronization error system in a complex network environment based on the system state space model, the attacked system state space model, the hybrid network attack model and the intermittent controller;

[0014] Step 7: If the closed-loop synchronization error system meets the performance index constraint, an intermittent controller is used to control the complex information-physical system; otherwise, the output feedback gain matrix of the intermittent controller is adjusted and steps 5 to 7 are repeated.

[0015] Preferably, in step 1, a system state space model of a discrete-time complex cyber-physical system consisting of N identically coupled nodes is established in the following form:

[0016]

[0017] Where k represents a discrete time series, represents the state vector at the next moment in the system state space model, represents the state vector, represents control input; is the distributed state delay, where υ l is a known weight coefficient; η: is a nonlinear vector-valued function; Γ=diag{w1,w2,…,w n} represents the inner coupling matrix and diag is represented as a diagonal matrix; represents the external coupling configuration matrix; the function sat(u i ): is the standard saturation function of the standard vector, described as sat(u i )=[sat(u i(1) )sat(u i(2) )…sat(u i(m) )]T ,in is the known saturation; ω i (k) is a one-dimensional Gaussian white noise sequence defined in the probability space (Π, F, P), satisfying E[ω i (k)] = 0, A∈R n×n , B∈R n×m , C∈R n×n , D d ∈R n×n is a known constant matrix.

[0018] Preferably, step 2 assumes that there is a scalar The following conditions are established:

[0019]

[0020] Considering that the stable operation of subsystems in complex information-physical networks may be destroyed by physical attacks, a state space model of the attacked system after physical attacks is established. The state equation of the controlled object after physical attacks is as follows:

[0021]

[0022] Among them, x i (k+1) represents the state vector of the attacked system in the state space model at the next moment, The nonlinear physical attack signal injected into the abnormal state, τ k Indicates that τ is satisfied m ≤τ k ≤τ M (τ k is a positive integer) and τ m and τ M is a known positive integer.

[0023] Preferably, in step 3, an isolated node model of a complex cyber-physical system is established, and it is considered that the isolated nodes in the system have the following form:

[0024]

[0025] in, represents the state vector, represents the distributed state delay of isolated nodes, f(z(k-τ k )) represents the physical attack of isolated nodes, ω(k) represents the one-dimensional Gaussian white noise sequence; is the nonlinear function existing in the system; A vector-valued function representing the result of a physical attack;

[0026] Assumptions: There are nonlinear functions in the system And the vector value function generated by physical attack Assume that the function is continuous and η(0) = f(0) = 0, and the following conditions are met:

[0027]

[0028] Then for the function The following inequality holds

[0029]

[0030] in, are known constant matrices respectively; e(k) represents synchronization error, e(k)=x i (k)-z(k).

[0031] Preferably, in step 4, a hybrid network attack model is established by introducing FDI attack and DoS attack, as shown in formula (7), to obtain the actual input of the system after being affected by the hybrid network attack;

[0032] The transmission signal of the sensor is sent to the controller through the network. Due to the openness of the communication network, the signal transmission process may be subject to hybrid network attacks. Assuming that the attacker has the ability to randomly launch network attacks and the probability of successful attacks is certain, it is considered that the transmission signal may be tampered by FDI attacks when it is transmitted through the network, thereby affecting the safe and stable operation of the system; the details are as follows:

[0033] Step 41: Using a random variable δ(k) that obeys Bernoulli distribution to indicate whether an FDI attack occurs, the actual input signal after the FDI attack is:

[0034]

[0035] in, is the false data signal injected by the attacker; δ(k)∈{0,1} is a random variable that obeys the Bernoulli distribution; x(k) represents the current state vector of the hybrid network attack model;

[0036] Step 42: Simultaneous transmission of signals may cause DoS attacks, using random variables that follow Bernoulli distribution To indicate whether a DoS attack occurs, the actual input of the hybrid network attack model after being attacked by the hybrid network can be expressed as:

[0037]

[0038] DoS attack parameters in the parameters of the hybrid network attack model The probability of the FDI attack parameter δ(k) satisfies:

[0039]

[0040] Among them, Pr means finding probability, and E means finding expectation; represents the probability of δ(k) = 0, and the expectation of δ(k) = 0 is the corresponding probability;

[0041] Assumptions: To ensure the concealment of the attack and avoid being discovered by the detection mechanism, the attacker usually actively limits the FDI attack energy. For the constant matrix, it is assumed that the energy of the FDI attack signal is limited to:

[0042] ||g(x(k))||2≤||G g x(k)||2 (8)

[0043] in, It is the constraint matrix related to the FDI attack energy, thus constraining the attack to not be infinite.

[0044] Preferably, step 5 establishes an intermittent controller for the complex cyber-physical system;

[0045] The following event trigger mechanism is used to determine the conditions for intermittent controller switching, indicating the switch between intermittent control and continuous event triggering:

[0046] t k+1 = inf{t>t k +h k |εe T (k)Υe(k)<[e(k)-e(t k )] T Υ[e(k)-e(t k )]} (9)

[0047] where h k ∈[h1,h2](h1,h2(h2≥h1>0)) is a given scalar; the event trigger mechanism divides the time interval between two consecutive intermittent controls into two parts; after sending the control input, the controller will wait for at least h k seconds; at t k +h k At this moment, the event trigger condition starts to monitor the intermittent controller until the next event trigger condition is met;

[0048] In order to achieve the security control of CPS under multi-source attacks, an event-based discrete-time intermittent controller u(k) is constructed as follows:

[0049]

[0050] Where K is the output feedback gain matrix to be designed; t k+1 -t k =T k is the control period; h k To control the width; it is worth noting that at t k At this moment, the intermittent controller should send the control input information and h k The size of the intermittent controller is k +h k Automatically change its gain at all times;

[0051] The generalized sector condition is used to deal with saturation nonlinearity, and the dead zone nonlinearity of the intermittent controller is defined as:

[0052]

[0053] Preferably, step 6 constructs a closed-loop synchronization error system in a complex network environment affected by a complex environment;

[0054] Considering equations (1) to (11) comprehensively, the closed-loop synchronization error system affected by the complex environment is as follows:

[0055]

[0056]

[0057] The synchronization error

[0058] Preferably, in step 7, the performance index constraint of the intermittent stability of the system is introduced, and the designed intermittent control law is substituted into the open-loop synchronization error system constructed according to the system state space model, the attacked system state space model, and the hybrid network attack model to obtain a closed-loop synchronization error system. If the closed-loop synchronization error system satisfies the performance index constraint, the system design is terminated; otherwise, the output feedback gain matrix of the intermittent controller is adjusted, and steps 6 and 7 are repeated; the performance index constraint is converted into a linear matrix inequality, and the closed-loop synchronization error system is made to meet the performance index constraint by solving the linear matrix inequality;

[0059] Step 71: Using Lyapunov stability theory and linear matrix inequality analysis method, sufficient conditions for the exponential boundedness of the closed-loop synchronization error system are obtained, so that the synchronization error closed-loop system with an intermittent controller is stable. First, a Lyapunov-Krasovskii function of the following form is constructed:

[0060] V(k)=e T(k)Pe(k)+V1(k)+V2(k)+V3(k) (13)

[0061] in,

[0062] By using Lyapunov stability theory and linear matrix inequality analysis method, sufficient conditions for the exponential boundedness of the closed-loop synchronization error system are obtained:

[0063]

[0064]

[0065] Where Ω1 represents the first time interval t under the action of the intermittent controller. k ≤k<t k +h k Sufficient conditions for the inner closed-loop synchronization error system to be bounded; Θ1 represents the second time interval t k +h≤k<t k+1 Under this condition, the closed-loop synchronization error system is bounded; Formula (16) represents the transformation of the previous actuator saturation condition into a solvable linear matrix inequality; Formula (17) represents the exponential boundedness condition of the closed-loop synchronization error system, which is less than 1 and indicates convergence; Θ1 and Ω1 represent the conditional matrices that make the system stable, represents a matrix in Ω1 whose first row and first column have the same dimensions as the following columns, represents the matrix of the first row and first column in Θ1; l = 1, 2, ..., n; i = 1, 2, ..., N; K i(l) With Φ i(l) Respectively represent K i With Φ i The lth row of ;

[0066]

[0067]

[0068] Where X i(l) and Respectively represent X i and The lth row of , then the corresponding trajectory of the closed-loop synchronous error system is converged to the origin exponentially through the intermittent controller, and the output feedback gain matrix of the intermittent controller is This means that under the control of the intermittent controller, the trajectory of the closed-loop synchronization error system converges to the origin with an exponential change;

[0069] When LMI equations (14) and (15) are feasible, according to matrix theory, the submatrices on the main diagonal must be negative definite. Therefore, it is easy to verify that This shows is reversible, assuming is reasonable;

[0070] Step 72: Based on the above-obtained sufficient conditions (14)-(17) for the exponential boundedness of the closed-loop synchronization error system, the following solution of the controller gain that can be solved by software is given by variable substitution, and sufficient conditions for the synchronization error system to be exponentially bounded and the existence of an intermittent controller are obtained:

[0071] According to Definition 1 and (14)-(17), the closed-loop synchronization error system is exponentially bounded. The sufficient conditions for the closed-loop synchronization error system to be exponentially bounded and for the existence of an intermittent controller are: Considering a given DoS probability FDI attack probability Scalar 0<α<1 and β<0, if there exists a positive definite matrix

[0072]

[0073] and positive scalars and wait;

[0074]

[0075] Among them, o1 is a scalar, representing a known parameter;

[0076]

[0077] Where o1 is a given parameter; multiply equation (14) by and its transposition to obtain equation (18); similarly, multiply equation (15) front and back And its transposition can get formula (19), and the proof is complete;

[0078] X i(l) and Respectively represent X i and The lth row of i is a diagonal matrix, then the trajectory of the closed-loop synchronization error system is converged to the origin in an exponential manner through the intermittent controller, and the output feedback gain matrix of the intermittent controller is

[0079] Through the above technical solutions, it can be known that compared with the prior art, the present invention discloses a method, device and storage medium for intermittent synchronization control of complex information-physical systems under multi-source attacks, and studies the problem of event-triggered intermittent security synchronization control for complex information-physical systems with actuator saturation and mixed time delay under multi-source attack environments. First, consider that the system is simultaneously subjected to physical attacks and mixed network attacks, and use random variables that obey Bernoulli distribution to characterize the probability of occurrence of malicious network attacks; mixed time delays are composed of distributed state delays and time-varying delays; actuator saturation is taken into account, and on this basis, a discrete-time system model containing multiple constraints is established; secondly, with the help of Lyapunov stability theory and linear matrix inequality technology, sufficient conditions for exponential stability of closed-loop errors are given, and an intermittent controller that ensures the stability of the closed-loop system is designed. The present invention utilizes intermittent controller design to enhance the system's resistance to multi-source attacks. By adopting robust control strategies and algorithms, the system can better cope with interference and attacks from multiple attack sources, thereby protecting the system from malicious behavior. In view of the problem that saturated actuators and mixed time delays may cause system instability, the intermittent controller design can adjust the system's response through effective control strategies and algorithms, thereby reducing the impact of actuator saturation and time delay on system stability, ensuring that the system can maintain stable operation under various conditions. Through the intermittent controller design, the system can more effectively utilize resources and optimize control performance. By dynamically adjusting the control strategy to adapt to different working conditions and attack scenarios, the system can find a balance between performance and safety, achieve the best working state, improve the reliability and safety of the system, ensure that the system can still operate normally in the face of attacks and abnormal situations, and protect important information and resources in the system from damage. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0081] Figure 1 A flow chart of an intermittent control method of an observer of a power grid control system based on complex cyber-physical system modeling provided by the present invention;

[0082] Figure 2 A schematic diagram of the time series of FDI attacks and DoS attacks provided by the present invention;

[0083] Figure 3 A schematic diagram of the working cycle of the intermittent controller provided by the present invention;

[0084] Figure 4 A schematic diagram of the state trajectory of the closed-loop synchronization error system provided by the present invention. DETAILED DESCRIPTION

[0085] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0086] An embodiment of the present invention discloses an intermittent synchronization control method for a complex cyber-physical system under multi-source network attacks.

[0087] Embodiment 1:

[0088] This embodiment provides an intermittent security control method for a complex cyber-physical system with actuator saturation under multi-source attacks. The complex cyber-physical system may be an intermittent control system for a power grid. Figure 1 ,include:

[0089] S1: Establish a state space model of a discrete-time complex cyber-physical system consisting of N identically coupled nodes;

[0090]

[0091] represents the state vector at the next moment in the system state space model, represents the state vector, represents control input; is the distributed state delay; η: is a nonlinear vector-valued function; Γ=diag{w1,w2,…,w n} represents the internal coupling matrix; represents the out-coupling configuration matrix;

[0092] S2: For the cyber-physical system model in S1, a state space model of the cyber-physical system after being subjected to a physical attack is established;

[0093]

[0094] Among them, x i (k+1) represents the state vector of the attacked system in the state space model at the next moment, The nonlinear physical attack signal injected into the abnormal state, τ k Indicates that τ is satisfied m ≤τ k ≤τ M (τ kis a positive integer) and τ m and τ M is a known positive integer;

[0095] S3: Establish an isolated node model of the cyber-physical system after a physical attack;

[0096]

[0097] in, represents the state vector, ω i (k) represents a one-dimensional Gaussian white noise sequence; represents the distributed state delay of isolated nodes, f(z(k-τ k )) represents a physical attack on isolated nodes; is the nonlinear function existing in the system; A vector-valued function representing the result of a physical attack;

[0098] Assumptions: There are nonlinear functions in the system And the vector value function generated by physical attack Assume that the function is continuous and η(0) = f(0) = 0, and the following conditions are met:

[0099]

[0100] Then for the function The following inequality holds

[0101]

[0102] in, are known constant matrices respectively;

[0103] Define the synchronization error as e(k)=x i (k)-z(k), and the following new symbols are given:

[0104]

[0105]

[0106] S4: A random variable δ(k) that follows a Bernoulli distribution is used to indicate whether an FDI attack occurs, and a random variable Indicates whether a DoS attack has occurred; establishes a hybrid network attack model and obtains the actual input of the system after being affected by the hybrid network attack:

[0107] The random variable δ(k) following the Bernoulli distribution is used to indicate whether the FDI attack occurs. The actual input signal after the FDI attack is:

[0108]

[0109] in, is the false data signal injected by the attacker; δ(k)∈{0,1} is a random variable that obeys the Bernoulli distribution; x(k) represents the current state vector of the hybrid network attack model; while the transmission signal may cause a DoS attack, a random variable that obeys the Bernoulli distribution is used Indicates whether a DoS attack occurs. The actual input after a hybrid network attack can be expressed as

[0110]

[0111] Parameters of the hybrid network attack model The probability of δ(k) satisfies

[0112]

[0113] Assumptions: To ensure the concealment of the attack and avoid being discovered by the detection mechanism, the attacker usually actively limits the FDI attack energy; for the constant matrix, it is assumed that the energy of the FDI attack signal is limited to

[0114] ||g(x(k))||2≤||G g x(k)||2 (8)

[0115] in, is the upper bound of the energy of FDI attack;

[0116] S5: Design of intermittent controller based on event-triggered mechanism and actuator saturation problem:

[0117] The following event trigger mechanism is used to determine the conditions for switching the intermittent controller, indicating the switching between intermittent control and continuous event triggering

[0118] t k+1 = inf{t>t k +h k εe T (k)Υe(k)<[e(k)-e(t k )] T Υ[e(k)-e(t k )]} (9)

[0119] where h k∈[h1,h2](h1,h2(h2≥h1>0)) is a given scalar. After sending the control input, the controller will wait for at least h k seconds; at t k +h k At this moment, the event trigger condition starts to monitor the intermittent controller until the next event trigger condition is met;

[0120] In order to achieve the security control of CPS under multi-source attacks, an event-based discrete-time intermittent controller of the following form is constructed:

[0121]

[0122] Where K is the output feedback gain matrix to be designed; t k+1 -t k =T k is the control period, h k To control the width; it is worth noting that at t k At this moment, the controller should send control input information and h k The size of the controller makes the k +h k Automatically change its gain at all times;

[0123] The generalized sector condition is used to deal with the saturation nonlinearity, and the dead zone nonlinearity of the intermittent controller is defined as follows:

[0124]

[0125] S6: Construct a closed-loop synchronization error system in a complex network environment based on S1-S5;

[0126] Considering equations (1) to (11) comprehensively, the closed-loop synchronization error system affected by the complex environment is as follows:

[0127]

[0128] The synchronization error

[0129] Lemma 1: Definition in Given a matrix And the polyhedron set is given as follows:

[0130]

[0131] Where l = 1, 2, ..., n, i = 1, 2, ..., N, K i(l) With Φ i(l) Respectively represent K i With Φ iWhen the first line of It can be seen that there is ψ T (u i (k))Ψ i [ψ(u i (k))-Φ i e(k)]≤0, then for any n×n diagonal matrix, Φ i >0; the following sector conditions are met:

[0132] -2ψ T (u(k))Ψ[ψ(u(k))-Φe(k)]≥0 (23)

[0133] Lemma 2: Assume there exists a positive definite matrix Z, Scalar a i ≥0 and b i ≥0(i=1,2,…), then the following matrix inequality holds:

[0134]

[0135] Lemma 3: Let P be a positive definite matrix, and define in is a non-singular matrix, the following inequality holds, then P<P0;

[0136]

[0137] Lemma 4: For a given matrix There are two positive integers satisfy and a vector function q: Then the following inequality holds

[0138]

[0139] Definition 1: When there is a constant And ζ>0 makes the following inequality hold, then the evolution of the closed-loop synchronization error system is exponentially stable;

[0140]

[0141] Definition 2: There exists a positive definite matrix And scalar The following are expressed:

[0142]

[0143] S7: Introduce the performance evaluation index of exponential stability of the closed-loop synchronization error system, substitute the designed intermittent controller into the open-loop synchronization error system constructed according to the system state space model, the attacked system state space model, and the hybrid network attack model, and obtain the closed-loop synchronization error system. If the error system meets the performance index constraint, the system design is terminated; otherwise, repeat S6 and S7;

[0144] S71: Using Lyapunov stability theory and linear matrix inequality analysis method, sufficient conditions for the exponential boundedness of the closed-loop W synchronization error system and the existence of the controller are obtained, as shown in the following formula:

[0145] First, construct the Lyapunov-Krasovskii function of the following form:

[0146] V(k)=e T (k)Pe(k)+V1(k)+V2(k)+V3(k) (13)

[0147] in,

[0148] Using Lyapunov stability theory and linear matrix inequality analysis method, sufficient conditions for the exponential boundedness of the closed-loop synchronization error system are obtained; the steps are as follows:

[0149] When equations (14)-(17) hold, it means that under the intermittent controller, the corresponding trajectory of the closed-loop synchronization error system converges to the origin exponentially;

[0150]

[0151] in,

[0152] When equations (14) and (15) hold, according to matrix theory, the submatrix on the main diagonal must be negative definite. Therefore, it is easy to verify that This shows is reversible, assuming It is reasonable. According to Definition 1 and Equations (14)-(17), the closed-loop synchronization error system is exponentially bounded;

[0153] Proof of the sufficient condition conclusion for the above exponential boundedness:

[0154] For t k ≤k<t k +h k , V(k) is calculated by taking the forward difference along any trajectory of the closed-loop synchronous error system as follows:

[0155]

[0156] From formula (7), we can know

[0157]

[0158] Using Lemma 2, we know that

[0159]

[0160] There is a scalar γ i ≥0(i=1,2), according to the assumptions:

[0161]

[0162] From formula (14), we can know

[0163] -2ψ T (u(k))Ψ[ψ(u(k))-Φe(k)]≥0;

[0164] Considering the above formulas comprehensively, we can know

[0165]

[0166] From formula (17), we can see that there is a matrix with appropriate dimension Then the following holds:

[0167] According to the properties of ω(k), we can get:

[0168]

[0169]

[0170] From Schur's complement lemma, we can see that Ω<0 for equation (14);

[0171] In summary,

[0172] in,

[0173] When t k +h k ≤k<t k+1 When V(k) is calculated along any trajectory of the closed-loop synchronization error system represented by formula (13), the forward difference is calculated as follows:

[0174]

[0175] Considering the above formulas comprehensively, we can get:

[0176]

[0177] Similar to the above formula, we can get:

[0178]

[0179]

[0180] From the event trigger mechanism formula (10), we can see that at t k +h k ≤k<t k+1 In the interval, the following inequalities hold

[0181] 0≤εe T (k)Υx(k)-θ T (k)Υθ(k)

[0182] Where θ(k) = e(k) - e(t k )

[0183] Applying Schur's complement lemma to equation (15) shows that: Θ<0

[0184] Then we can get:

[0185] According to the known conditions 0<α<1, β<0 and the forward difference calculation formula, the above formula is equivalent to:

[0186]

[0187] in,

[0188] When t k ≤k<t k +h k , for formula (14) and the above formula, we can know:

[0189]

[0190] When t k +h k ≤k<t k+1 , it can be seen

[0191]

[0192] By induction, when t k ≤k<t k +h k When , the following inequality holds:

[0193]

[0194] When t k +h k ≤k<t k+1 When

[0195]

[0196] From the above formula, we can see that when t k ≤k<t k+1 Sometimes, there are

[0197]

[0198] in, It can be inferred from the above formula that

[0199]

[0200] in,

[0201]

[0202] Therefore, according to Definition 1, the closed-loop synchronization error system is exponentially bounded; According to Definition 1 and (14)-(17), the closed-loop synchronization error system is exponentially bounded;

[0203] S72: Solve the gain of the intermittent controller to obtain sufficient conditions for the existence of the controller.

[0204] Converting (14)-(17) into the form (18)-(21) that can be solved by computer, we can obtain that the closed-loop synchronization error system is exponentially bounded and the sufficient conditions for the existence of the controller are:

[0205] Consider a given DoS probability FDI attack probability Scalar 0<α<1 and β<0, if there exists a positive definite matrix and positive scalars and The following inequalities (18)-(21) hold true. Then, the corresponding trajectory of the closed-loop synchronous error system converges to the origin exponentially through the intermittent controller, and the output feedback gain matrix of the intermittent controller is:

[0206]

[0207]

[0208] in,

[0209] Where X i(l) and Respectively represent X i and The lth row of .

[0210] Embodiment 2

[0211] On the other hand, in a specific embodiment, a complex cyber-physical system intermittent safety control method with actuator saturation under multi-source network attacks is proposed. In the case of considering external disturbances and nonlinear factors, the closed-loop synchronization error system is mean square bounded. The specific implementation method is as follows:

[0212] Consider a time-delay discrete complex cyber-physical system with three nodes and choose a synchronization error system model with the following parameters:

[0213]

[0214] υ i =2 -i , τ k =3+[1+(-1) k ] / 2

[0215] Assume that the attack probabilities of physical attack and FDI attack are and And has the following form:

[0216]

[0217] Select Parameters

[0218]

[0219] Assume that the inner coupling matrix is ​​Γ and the outer coupling matrix is

[0220] The saturation limit of the actuator is h1=1,h2=10. By solving LMI, the required controller gain is

[0221]

[0222] The specific simulation graphics are as attached Figure 2-Figure 4 As shown, Figure 2 is the time series of FDI attack and DoS attack, Figure 3 is the intermittent controller working cycle, Figure 4 The three curves in represent the three components of the closed-loop synchronization error system trajectory.

[0223] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0224] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for intermittent control of complex cyber-physical systems under multi-source attacks, characterized in that: The following steps are involved: Step 1: Establish a system state space model of a discrete-time complex cyber-physical system consisting of N identically coupled nodes; Step 2: Establish a state space model of the attacked system after the physical attack based on the system state space model; Step 3: Construct an isolated node model corresponding to the discrete-time complex information-physical system, and calculate the synchronization error based on the isolated node model; Step 4: Build a hybrid network attack model; Step 5: Taking the synchronization error as input, construct an intermittent controller based on the event-triggered mechanism and the actuator saturation problem; Step 6: Construct a closed-loop synchronization error system in a complex network environment based on the system state space model, the attacked system state space model, the hybrid network attack model and the intermittent controller; Step 7: If the closed-loop synchronization error system meets the performance index constraint, the intermittent controller is used to control the complex information physical system; otherwise, the output feedback gain matrix of the intermittent controller is adjusted, and steps 5 to 7 are repeated; In step 2, a state space model of the attacked system after physical attack is established in the following form: Among them, x i (k+1) represents the state vector of the attacked system in the state space model at the next moment, The nonlinear physical attack signal injected into the abnormal state, τ k Indicates that τ is satisfied m ≤τ k ≤τ M The time-varying delay, τ k is a positive integer, and τ m and τ M is a known positive integer; In step 3, an isolated node model of a complex cyber-physical system is established in the following form: Consider an isolated node in the system with the following form: in, represents the state vector, represents the distributed state delay of isolated nodes, f(z(k-τ k )) represents the physical attack of isolated nodes, ω(k) represents the one-dimensional Gaussian white noise sequence; is the nonlinear function existing in the system; A vector-valued function representing the result of a physical attack; The assumptions of the isolated node model are: Assume that the function is continuous and η(0) = f(0) = 0, and the following conditions are met: Then for the function The following inequality holds: in, are known constant matrices respectively; e(k) represents synchronization error, e(k)=x i (k)-z(k); Step 5: Establish the intermittent controller u(k) of the complex cyber-physical system, which is constructed as follows: t k+1 =inf{t>t k +h k |εe T (k)γe(k)<[e(k)-e(t k )] T γ[e(k)-e(t k )]} (9) Where K is the output feedback gain matrix to be designed; t k+1 -t k =T k is the control period; h k To control the width; at t k At this moment, the intermittent controller sends the control input information and h k The size of the intermittent controller is k +h k Automatically change its gain at all times; The generalized sector condition is used to deal with saturation nonlinearity, and the dead zone nonlinearity of the intermittent controller is defined as: The closed-loop synchronization error system in step 6 under the complex network environment affected by the complex environment is expressed as: The synchronization error A∈R n×n , B∈R n×m , C∈R n ×n , D d ∈R n×n is a known constant matrix; Γ=diag{w1,w2,L,w n } represents the inner coupling matrix and diag is represented as a diagonal matrix; Indicates DoS probability; represents the probability of FDI attack; represents the state vector, is a nonlinear function existing in the system; function is the standard saturation function of the standard vector; is the distributed state delay, where υ l is the weight coefficient.

2. The intermittent control method of a complex cyber-physical system under multi-source attacks according to claim 1 is characterized in that: In step 1, a system state space model of a discrete-time complex cyber-physical system consisting of N identically coupled nodes is established in the following form: Where k represents a discrete time series, represents the state vector at the next moment in the system state space model, represents the state vector, represents control input; is the distributed state delay, where υ l is the weight coefficient and satisfies is a nonlinear vector-valued function; Γ=diag{w1,w2,L,w n } represents the inner coupling matrix and diag is represented as a diagonal matrix; represents the external coupling configuration matrix; function is the standard saturation function of the standard vector, described as sat(u i )=[sat(u i(1) )sat(u i(2) )Lsat(u i(m) )] T ,in is the known saturation; ω i (k) is defined in the probability space One-dimensional Gaussian white noise sequence on, satisfying Ε[ω i (k)] = 0, A∈R n×n , B∈R n×m , C∈R n×n , D d ∈R n×n is a known constant matrix.

3. The intermittent control method of a complex cyber-physical system under multi-source attacks according to claim 2 is characterized in that: In step 4, a hybrid network attack model is established by introducing FDI attack and DoS attack to obtain the actual input after being affected by the hybrid network attack, as follows: Step 41: Using a random variable δ(k) that obeys Bernoulli distribution to indicate whether an FDI attack occurs, the actual input after the FDI attack is: in, is the false data signal injected by the attacker; δ(k)∈{0,1} is a random variable that obeys the Bernoulli distribution; x(k) represents the current state vector of the hybrid network attack model; Step 42: Use a random variable that follows a Bernoulli distribution To indicate whether a DoS attack occurs, the actual input of the hybrid network attack model after being attacked by a hybrid network is: The parameters of the hybrid network attack model are and δ(k), where the DoS attack parameter The probability of the FDI attack parameter δ(k) satisfies: Among them, Pr means finding probability, and E means finding expectation; In addition, the energy limit of FDI attack is expressed as: ||g(x(k))||2≤||G g x(k)||2 (8) in, is the constraint matrix related to FDI attack energy.

4. The intermittent control method of a complex cyber-physical system under multi-source attacks according to claim 3 is characterized in that: The specific steps of step 7 are: Step 71: Substitute the intermittent controller into the open-loop synchronization error system constructed according to the system state space model, the attacked system state space model, and the hybrid network attack model to obtain a closed-loop synchronization error system, introduce the performance index constraint of the system intermittent stability, convert the performance index constraint into a linear matrix inequality, solve the linear matrix inequality to make the closed-loop synchronization error system meet the performance index constraint, and use the Lyapunov stability theory and the linear matrix inequality analysis method to obtain the sufficient condition for the exponential boundedness of the closed-loop synchronization error system; Construct the Lyapunov-Krasovskii function, expressed as: V(k)=e T (k)Pe(k)+V1(k)+V2(k)+V3(k) (13) in, According to the Lyapunov-Krasovskii function, the sufficient condition for exponential boundedness is obtained by using Lyapunov stability theory and linear matrix inequality analysis method: When the above sufficient conditions are met, the corresponding trajectory of the closed-loop synchronization error system converges to the origin exponentially through the intermittent controller; where Θ1 and Ω1 represent the conditional matrix that makes the system stable, represents a matrix in Ω1 whose first row and first column have the same dimensions as the following columns, represents the matrix of the first row and first column in Θ1; l = 1, 2, L, n; i = 1, 2, L, N; K i(l) With Φ i(l) Respectively represent K i With Φ i The lth row of ; Where X i(l) and Respectively represent X i and The controller gain matrix is Under the intermittent controller, the trajectory of the closed-loop synchronization error system converges to the origin in an exponential manner; Step 72: According to the sufficient conditions for exponential boundedness, the solution formula of the controller gain matrix is ​​obtained by variable substitution. Solving the synchronous error system is a sufficient condition for exponential boundedness and the existence of an intermittent controller: According to Definition 1 and Formulas (14)-(17), considering the given DoS probability FDI attack probability Scalar 0<α<1 and β<0, if there exists a positive definite matrix and positive scalars and Among them, o1 is a scalar, representing a known parameter; Among them, o1 is the set parameter; multiply the equation (14) before and after and its transposition to obtain equation (18); multiply equation (15) front and back And its transposition to get formula (19).

5. An intermittent control device for a complex cyber-physical system under multi-source attacks, comprising a processor and a memory, characterized in that: The memory stores instructions executed by the processor. When the instructions are executed by the processor, the device implements the intermittent control method of a complex information-physical system under multi-source attacks according to any one of claims 1-4.

6. A computer-readable storage medium storing computer-executable instructions, characterized in that: When the computer executable instructions are executed by the processor, the intermittent control method of a complex information-physical system under multi-source attacks according to any one of claims 1-4 is implemented.

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