A method, device and storage medium for estimating distributed security status of information-physical system

Abstract

The present invention discloses a distributed safety state estimation method, device and storage medium for an information-physical system, belonging to the technical field of information-physical systems. The distributed safety state estimation method for an information-physical system includes: performing observable decomposition on a system dynamic model to obtain a local observable matrix pair; obtaining a gain matrix of a distributed observer according to the local observable matrix pair and the local unobservable matrix; communicating based on a local system state vector to obtain a local system state vector after communication; obtaining an output system state vector of a distributed observer based on the gain matrix and the local system state vector after communication; and controlling an adaptive attack compensation function in the distributed observer to compensate for a deception attack signal, so as to achieve consistency between the output system state vector and the system state vector in the system dynamic model. The present invention can solve the problem of state estimation of information-physical systems deployed on a large scale under the interference of deception attacks.

Description

Technical Field

[0001] The present invention relates to the technical field of information-physical systems, and in particular to a method, device and storage medium for estimating the distributed security status of an information-physical system. Background Art

[0002] In recent years, with the advancement of computing and communication technologies, cyber-physical systems (CPS), which closely integrate sensing, computing, communication, and physical processes, have flourished. A prominent feature of cyber-physical systems is that their operations and communications are often carried out through network media, which brings great advantages to practical applications, but also makes cyber-physical systems vulnerable to malicious network attacks. Since the system state is the key information connecting perception and decision-making, the problem of safe state estimation has become a research hotspot in the field of cyber-physical system security and has received widespread attention. In particular, the distributed safe state estimation of large-scale deployed cyber-physical systems such as driverless car fleets, power grids, and civil infrastructure determines whether the cyber-physical systems can operate safely and stably.

[0003] Based on this, in various malicious network attacks, destroying the integrity of the system to change the system state data is considered a common deception attack. However, existing research on deception attacks mainly adopts centralized processing methods, which cannot solve the state estimation problem of large-scale deployed cyber-physical systems, thus affecting the safe and stable operation and further promotion of cyber-physical systems. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and to provide a method, device and storage medium for distributed security state estimation of an information-physical system, which can solve the problem of state estimation of large-scale deployed information-physical systems under the interference of deception attacks.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0006] In a first aspect, the present invention provides a method for estimating a distributed safety state of an information-physical system, which is executed on the basis of a safety state estimation system, wherein the safety state estimation system includes a sensor model for collecting measurement data of the information-physical system, a distributed observer for receiving the measurement data, and a system dynamic model established based on the measurement data, wherein the distributed observer corresponds to the sensor model one by one, and is characterized in that it includes:

[0007] Performing observable decomposition on the system dynamic model and the sensor model to obtain a local observable matrix pair and a local unobservable matrix;

[0008] Obtaining a gain matrix of the distributed observer according to the local observable matrix pair and the local unobservable matrix;

[0009] Observing the system dynamic model through the distributed observer to obtain a local system state vector, communicating according to a preset communication network topology between the distributed observers and the local system state vector to obtain a local system state vector after communication;

[0010] Obtaining an output system state vector of the distributed observer based on the gain matrix and the communicated local system state vector;

[0011] When there is a deception attack signal input in the system dynamic model, the adaptive attack compensation function in the distributed observer is controlled to compensate the deception attack signal to achieve consistency between the output system state vector and the system state vector in the system dynamic model.

[0012] Furthermore, the expression of the system dynamic model is:

[0013] ,

[0014] in, is the system state vector constructed based on the measurement data, Express The first-order derivative of is the control input, is a nonlinear function, is the attack matrix, It is a deception attack signal. is the system matrix, is the system input matrix, t represents time;

[0015] The expression of the sensor model is:

[0016] ,

[0017] in, is the local observation matrix of the i-th cluster sensor, is the number of sensor clusters, is the output vector of the i-th cluster sensor.

[0018] Further, performing observable decomposition on the system dynamic model and the sensor model to obtain a local observable matrix pair and a local unobservable matrix includes:

[0019] Defining the transformation matrix T i =[ T io T iu ] ∈ R n×n , in is an unobservable subspace The perpendicular orthogonal basis of yes A perpendicular orthogonal basis of Represents n rows Column Transformation Matrix The dimension of express OK Perpendicular orthogonal basis The dimension of Represents n rows Perpendicular orthogonal basis Dimensions;

[0020] According to the transformation matrix The structure of the system matrix A of the system dynamic model and the local observation matrix of the sensor model Perform observable decomposition:

[0021] Based on the system matrix A and the local observation matrix , through the matrix rank judgment method, it is determined that the dimension of the system state observable by the current i-th cluster of sensors is (n- );

[0022] Then the transformed matrix Before proceeding Line and front Extract the columns to obtain the local observable system matrix , after Line and front Extract the columns to obtain the local unobservable system matrix , after Line and after Extract the columns to obtain the local unobservable system matrix , further transform the matrix Before proceeding Extraction of columns to obtain the local observable measurement matrix ;in, yes The transpose of express Line and A zero matrix of columns.

[0023] Further, obtaining the gain matrix of the distributed observer according to the local observable matrix pair and the local unobservable matrix includes:

[0024] Defining the local stability matrix , free matrix and attack matching matrix According to Lyapunov's stability theorem, combined with the local observable matrix pair and the local unobservable matrix, solve the following linear matrix inequality , , :

[0025] ,

[0026] =

[0027] in, ,

[0028] ,

[0029] ,

[0030] ,

[0031] ,

[0032] ,

[0033] in, represents the zero matrix, is the attack matrix of the i-th cluster sensor, is the Nn-dimensional identity matrix, , is the n-dimensional identity matrix, for dimensional identity matrix, , is the local observer stability matrix, is the vertical orthogonal basis of the local observer stability matrix, for The transposed matrix of , diag() is the diagonal matrix function, is an orthogonal basis of the observable space of the system, are the 1st, 2nd, ... Nth orthogonal vectors in the orthogonal basis of the observable space of the system, satisfy , is the nonlinear function The Lipschitz constant;

[0034] Based on the , , , obtain the gain matrix of the distributed observer , , and The formula is:

[0035] ,

[0036] ,

[0037] ,

[0038] ,

[0039] in,

[0040] ,

[0041] ,

[0042] ,

[0043] ,

[0044] ,

[0045] is the Lyapunov matrix of the i-th distributed observer, is the Lyapunov augmented matrix of N distributed observers including nonlinear factors, is the negative Lyapunov sum matrix of N distributed observers including nonlinear factors, is the local stability matrix of the ith distributed observer including nonlinear factors, is the Nth local stability matrix, is the minimum non-zero eigenvalue of the Laplacian matrix composed of the connection weights of the distributed observer.

[0046] Further, communicating based on the local system state vector, obtaining the local system state vector after communication includes:

[0047] Determine the connection weight according to the pre-set communication network topology between the distributed observers , when the connection weight is 1, the jth distributed observer transmits the observed local system state vector to the i-th distributed observer, and when the connection weight is 0, the jth distributed observer stops communicating with the ith distributed observer, and the communication obtains the local system state vector that is not observable by the ith distributed observer itself but observable by the jth distributed observer , i.e., the local system state vector after the communication;

[0048] The output system state vector of the distributed observer is obtained based on the gain matrix and the local system state vector after communication. The expression of the output system state vector includes:

[0049]

[0050] ,

[0051] ,

[0052] in, is the local system state vector obtained by the i-th distributed observer observing the system dynamic model, yes The derivative with respect to time t is the output system state vector of the i-th distributed observer, is the local system state vector obtained by the jth distributed observer observing the system dynamic model, is the output vector of the ith distributed observer, is the adaptive attack compensation function, is the connection weight between the i-th distributed observer and the j-th distributed observer.

[0053] Further, when there is a deception attack signal input in the system dynamic model, controlling the adaptive attack compensation function in the distributed observer to compensate the deception attack signal to achieve consistency between the output system state vector and the system state vector in the system dynamic model includes:

[0054] The expression of the adaptive attack compensation function is:

[0055] ,

[0056] ,

[0057] ,

[0058] ,

[0059] in, is the difference between the measured output value of the i-th distributed observer and the measured output value of the i-th cluster sensor, For about The symbol function of is the adaptive parameter in the jth distributed observer, is an adaptive parameter, and is an arbitrarily chosen constant greater than zero;

[0060] The output system state vector is subtracted from the system state vector to obtain the estimated error dynamics of the i-th distributed observer :

[0061] ,

[0062] The estimated error is made based on the gain matrix Convergence only keeps , through the parameters Adaptive update compensation attack signal The energy impact of The symbolic function of The direction of influence is achieved, so that the distributed observer outputs the system state vector consistent with the system state vector in the system dynamic model. The estimated error dynamic To 0, the system status is estimated.

[0063] In a second aspect, the present invention provides a distributed security state estimation device for a cyber-physical system, comprising:

[0064] A decomposition module, used for performing observable decomposition on the system dynamic model and the sensor model to obtain a local observable matrix pair and a local unobservable matrix;

[0065] A gain matrix acquisition module, used for obtaining a gain matrix of the distributed observer according to the local observable matrix pair and the local unobservable matrix;

[0066] A communication module, configured to obtain a local system state vector by observing the system dynamic model through the distributed observer, and to communicate according to a preset communication network topology between the distributed observers and the local system state vector to obtain a local system state vector after communication;

[0067] An output system state vector acquisition module, used to obtain an output system state vector of the distributed observer based on the gain matrix and the local system state vector after communication;

[0068] The compensation module is used to control the adaptive attack compensation function in the distributed observer to compensate for the deception attack signal when there is a deception attack signal input in the system dynamic model, so as to achieve consistency between the output system state vector and the system state vector in the system dynamic model.

[0069] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] The present invention designs a distributed state observer to perform observability decomposition on the system dynamic model and the sensor model. On the basis of the communication network topology set between the distributed observers, the output system state vector is finally obtained through the observed local system state vector. When there is deception attack interference, the deception signal is compensated by the adaptive attack compensation function in the distributed observer, so that the output system state vector and the system state vector are consistent, which solves the state estimation problem of large-scale deployed information-physical systems and ensures the safe and stable operation of information-physical systems.

[0072] On this basis, the adaptive mechanism adopts an independent structure to provide more degrees of freedom for non-attack and attack situations, improving the estimation performance and intrusion tolerance. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 A method flow chart of a method for estimating a distributed security state of an information-physical system provided in Embodiment 1 of the present invention;

[0074] Figure 2 A diagram of a distributed observer communication method in a distributed safety state estimation method for an information-physical system provided in Example 1 of the present invention;

[0075] Figure 3 The system state vector in the method for estimating the distributed safety state of an information-physical system provided in Example 1 of the present invention is Operation curve diagram with estimated values ​​of each observer;

[0076] Figure 4 The system state vector in the method for estimating the distributed safety state of an information-physical system provided in Example 1 of the present invention is Operation curve diagram with estimated values ​​of each observer;

[0077] Figure 5 The system state vector in the method for estimating the distributed safety state of an information-physical system provided in Example 1 of the present invention is Operation curve diagram with estimated values ​​of each observer;

[0078] Figure 6 The adaptive parameters in the distributed safety state estimation method of a cyber-physical system provided in Example 1 of the present invention are Run the curve graph. DETAILED DESCRIPTION

[0079] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations on the technical solution of the present application. In the absence of conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

[0080] The term "and / or" in this article is only a description of the association relationship of the associated objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0081] Example 1

[0082] Figure 1 1 is a flow chart of the method for estimating the distributed security state of an information-physical system in Example 1 of the present invention. This flow chart only shows the logical sequence of the method in this embodiment. In other possible embodiments of the present invention, different methods may be used without conflict. Figure 1 The steps shown or described are accomplished in the order shown.

[0083] The distributed safety state estimation method for the information-physical system provided in this embodiment is executed on the basis of a safety state estimation system. The safety state estimation system includes a sensor model for collecting measurement data of the information-physical system, a distributed observer for receiving the measurement data, and a system dynamic model established based on the measurement data. The distributed observer corresponds to the sensor model one by one, such as Figure 1 As shown, the method disclosed in this embodiment specifically includes the following steps:

[0084] Step 1: Perform observable decomposition on the system dynamic model and sensor model to obtain local observable matrix pairs and local unobservable matrices.

[0085] The expression of the system dynamic model is:

[0086] ,

[0087] in, is the system state vector constructed based on the measurement data, Express The first-order derivative of is the control input, which will affect the system state vector is a nonlinear function, is the attack matrix, It is a deception attack signal. is the system matrix, is the system input matrix, Indicates time;

[0088] The expression of the sensor model is:

[0089] ,

[0090] in, is the local observation matrix of the i-th cluster sensor, is the number of sensor clusters, is the output vector of the i-th cluster sensor;

[0091] Specifically, A, B, ,W, and These are preset values ​​determined according to actual application scenarios;

[0092] Defining the transformation matrix T i =[ T io T iu ] ∈ R n×n , in is an unobservable subspace The perpendicular orthogonal basis of yes A perpendicular orthogonal basis of Represents n rows Column Transformation Matrix The dimension of express OK Perpendicular orthogonal basis The dimension of Represents n rows Perpendicular orthogonal basis The dimension of and are all positive integers;

[0093] According to the transformation matrix The structure of the system matrix A of the system dynamic model and the local observation matrix of the sensor model Perform observable decomposition:

[0094] Based on the system matrix A and the local observation matrix , through the matrix rank judgment method, it is determined that the dimension of the system state observable by the current sensor i is (n- );

[0095] Then the transformed matrix Before proceeding Line and front Extract the columns to obtain the local observable system matrix , after Line and front Extract the columns to obtain the local unobservable system matrix , after Line and after Extract the columns to obtain the local unobservable system matrix , further transform the matrix Before proceeding Extraction of columns to obtain the local observable measurement matrix ,in, yes The transpose of express Line and zero matrix of columns;

[0096] Local Observable System Matrix and the local observable measurement matrix Form a pair of local observable matrices;

[0097] Step 2: Obtain the gain matrix of the distributed observer based on the local observable matrix pair and the local unobservable matrix. Define the local stability matrix , free matrix and attack matching matrix According to Lyapunov's stability theorem, combined with the local observable matrix pair and the local unobservable matrix, we can solve the following linear matrix inequality: , , :

[0098] ,

[0099] =

[0100] in, ,

[0101] ,

[0102] ,

[0103] ,

[0104] ,

[0105] ,

[0106] in, represents the zero matrix, is the attack matrix of the i-th cluster sensor, is the Nn-dimensional identity matrix, , is the n-dimensional identity matrix, for dimensional identity matrix, , is the local observer stability matrix, is the vertical orthogonal basis of the local observer stability matrix, for The transposed matrix of , diag() is the diagonal matrix function, is an orthogonal basis of the observable space of the system, are the 1st, 2nd, ... Nth orthogonal vectors in the orthogonal basis of the observable space of the system, satisfy , It is a nonlinear function Lipschitz constant, Y is an intermediate quantity in the calculation process and has no practical significance;

[0107] based on , , , and obtain the gain matrix of the distributed observer , , and The formula is:

[0108] ,

[0109] ,

[0110] ,

[0111] ,

[0112] in,

[0113] ,

[0114] ,

[0115] ,

[0116] ,

[0117] ,

[0118] is the Lyapunov matrix of the i-th distributed observer, is the Lyapunov augmented matrix of N distributed observers including nonlinear factors, is the negative Lyapunov sum matrix of N distributed observers including nonlinear factors, is the local stability matrix of the ith distributed observer including nonlinear factors, is the Nth local stability matrix, It is the minimum non-zero eigenvalue of the Laplace matrix composed of the connection weights of the distributed observers. The minimum non-zero eigenvalue is a preset value designed according to the actual application needs.

[0119] Step 3: Communicate based on the local system state vector. The local system state vector obtained after communication includes:

[0120] Determine the connection weights based on the pre-set communication network topology between distributed observers , when the connection weight is 1, the jth distributed observer transmits the observed local system state vector to the i-th distributed observer, and when the connection weight When the jth distributed observer stops communicating with the ith distributed observer, the communication obtains the local system state vector that is not observable by the ith distributed observer but observable by the jth distributed observer. , which is the local system state vector after communication.

[0121] Step 4: Obtain the output system state vector of the distributed observer based on the gain matrix and the local system state vector after communication. The expression of the output system state vector includes:

[0122]

[0123] ,

[0124] ,

[0125] in, is the local system state vector obtained by the i-th distributed observer observing the system dynamic model, yes The derivative with respect to time t is the output system state vector of the i-th distributed observer, is the local system state vector obtained by the jth distributed observer observing the system dynamic model, is the output vector of the ith distributed observer, is the adaptive attack compensation function, is the connection weight between the i-th distributed observer and the j-th distributed observer.

[0126] Step 5: When there is a deception attack signal input in the system dynamic model, the adaptive attack compensation function in the distributed observer is controlled to compensate for the deception attack signal to achieve consistency between the output system state vector and the system state vector in the system dynamic model, including:

[0127] The expression of the adaptive attack compensation function is:

[0128] ,

[0129] ,

[0130] ,

[0131] ,

[0132] in, is the difference between the measured output value of the i-th distributed observer and the measured output value of the i-th cluster sensor, For about The symbol function of is the adaptive parameter in the jth distributed observer, is an adaptive parameter, and is an arbitrarily chosen constant greater than zero, specifically, , and All are preset values ​​designed according to actual application needs;

[0133] The output system state vector is subtracted from the system state vector to obtain the estimated error dynamics of the i-th distributed observer :

[0134] ,

[0135] Based on the gain matrix, the estimation error Convergence only keeps , through the parameters Adaptive update compensation attack signal The energy impact of The symbolic function of The direction of influence is achieved, so that the distributed observer outputs the system state vector consistent with the system state vector in the system dynamic model, and the error dynamics is estimated. To 0, the system status is estimated.

[0136] In this embodiment, the number of distributed observers is four, and the communication method between the distributed observers is as follows: Figure 2 As shown, the system state vector is , , and , the adaptive parameters are , the parameters of the system dynamic model are as follows:

[0137] , , , ,

[0138] , , , ,

[0139] ,

[0140] The parameters of the adaptive attack compensation function are as follows:

[0141] , 5. Initial value = = = =0.5,

[0142] Substituting into the above formula we get:

[0143] ,

[0144] ,

[0145] ,

[0146] ,

[0147]

[0148] .

[0149] The specific calculation process will not be repeated in this embodiment. The operation curve between the system state vector and the estimated values ​​of each observer is as follows: Figure 3 , Figure 4 , Figure 5 As shown;

[0150] Adaptive parameters The running curve is as follows Figure 6 shown.

[0151] Example 2

[0152] The present invention provides a distributed security state estimation device for a cyber-physical system, comprising:

[0153] A decomposition module is used to perform observable decomposition on the system dynamic model and the sensor model to obtain local observable matrix pairs and local unobservable matrices;

[0154] A gain matrix acquisition module, used for obtaining a gain matrix of a distributed observer according to a local observable matrix pair and a local unobservable matrix;

[0155] A communication module is used to observe the system dynamic model through a distributed observer to obtain a local system state vector, communicate according to a preset communication network topology between distributed observers and the local system state vector, and obtain the local system state vector after communication;

[0156] An output system state vector acquisition module is used to obtain an output system state vector of a distributed observer based on a gain matrix and a local system state vector after communication;

[0157] The compensation module is used to control the adaptive attack compensation function in the distributed observer to compensate for the deception attack signal when there is a deception attack signal input in the system dynamic model, so as to achieve consistency between the output system state vector and the system state vector in the system dynamic model.

[0158] An information-physical system distributed safety status estimation device provided in an embodiment of the present invention can execute an information-physical system distributed safety status estimation method provided in an embodiment of the present invention, and has functional modules and beneficial effects corresponding to the execution method.

[0159] Example 3

[0160] The embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps of the method of embodiment 1 are implemented, and the program has functional modules and beneficial effects corresponding to the execution method.

[0161] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, devices, or computer program products. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0162] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (apparatus), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0163] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0164] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0165] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for estimating the distributed safety state of an information-physical system, which is performed on the basis of a safety state estimation system, wherein the safety state estimation system comprises a sensor model for collecting measurement data of the information-physical system, a distributed observer for receiving the measurement data, and a system dynamic model established based on the measurement data, wherein the distributed observer corresponds to the sensor model one by one, and is characterized in that: include: Performing observable decomposition on the system dynamic model and the sensor model to obtain a local observable matrix pair and a local unobservable matrix; Obtaining a gain matrix of the distributed observer according to the local observable matrix pair and the local unobservable matrix; Observing the system dynamic model through the distributed observer to obtain a local system state vector, communicating according to a preset communication network topology between the distributed observers and the local system state vector to obtain a local system state vector after communication; Obtaining an output system state vector of the distributed observer based on the gain matrix and the communicated local system state vector; When there is a deception attack signal input in the system dynamic model, controlling the adaptive attack compensation function in the distributed observer to compensate for the deception attack signal, so as to achieve consistency between the output system state vector and the system state vector in the system dynamic model; The expression of the system dynamic model is: ， in, is the system state vector constructed based on the measurement data, Express The first-order derivative of is the control input, is a nonlinear function, is the attack matrix, It is a deception attack signal. is the system matrix, is the system input matrix, t represents time; The expression of the sensor model is: ， in, is the local observation matrix of the i-th cluster sensor, is the number of sensor clusters, is the output vector of the i-th cluster sensor; Performing observable decomposition on the system dynamic model and the sensor model to obtain a local observable matrix pair and a local unobservable matrix includes: Defining the transformation matrix , in is an unobservable subspace The perpendicular orthogonal basis of yes A perpendicular orthogonal basis of Represents n rows Column Transformation Matrix The dimension of express OK Perpendicular orthogonal basis The dimension of Represents n rows Perpendicular orthogonal basis Dimensions; According to the transformation matrix The structure of the system matrix A of the system dynamic model and the local observation matrix of the sensor model Perform observable decomposition: Based on the system matrix A and the local observation matrix , through the matrix rank judgment method, it is determined that the dimension of the system state observable by the current i-th cluster of sensors is (n- ); Then the transformed matrix Before proceeding Line and front Extract the columns to obtain the local observable system matrix , after Line and front Extract the columns to obtain the local unobservable system matrix , after Line and after Extract the columns to obtain the local unobservable system matrix , further transform the matrix Before proceeding Extraction of columns to obtain the local observable measurement matrix ;in, is the transformation matrix The transpose of express Line and zero matrix of columns; Obtaining the gain matrix of the distributed observer according to the local observable matrix pair and the local unobservable matrix comprises: Defining the local stability matrix , free matrix and attack matching matrix According to Lyapunov's stability theorem, combined with the local observable matrix pair and the local unobservable matrix, solve the following linear matrix inequality , , : ， = ， in, , ， ， ， ， ， in, represents the zero matrix, is the attack matrix of the i-th cluster sensor, is the Nn-dimensional identity matrix, , is the n-dimensional identity matrix, for dimensional identity matrix, , is the local observer stability matrix, is the vertical orthogonal basis of the local observer stability matrix, for The transposed matrix of , diag() is the diagonal matrix function, is an orthogonal basis of the observable space of the system, are the 1st, 2nd, ... Nth orthogonal vectors in the orthogonal basis of the observable space of the system, satisfy , is the nonlinear function The Lipschitz constant; Based on the , , , obtain the gain matrix of the distributed observer , , and The formula is: ， ， ， ， in, ， ， ， ， ， is the Lyapunov matrix of the i-th distributed observer, is the Lyapunov augmented matrix of N distributed observers including nonlinear factors, is the negative Lyapunov sum matrix of N distributed observers including nonlinear factors, is the local stability matrix of the ith distributed observer including nonlinear factors, is the Nth local stability matrix, is the minimum non-zero eigenvalue of the Laplacian matrix consisting of the connection weights of the distributed observer; When there is a deception attack signal input in the system dynamic model, controlling the adaptive attack compensation function in the distributed observer to compensate the deception attack signal to achieve consistency between the output system state vector and the system state vector in the system dynamic model includes: The expression of the adaptive attack compensation function is: ， ， ， ， in, is the difference between the measured output value of the i-th distributed observer and the measured output value of the i-th cluster sensor, For about The symbol function of is the adaptive parameter in the jth distributed observer, is an adaptive parameter, and is an arbitrarily chosen constant greater than zero; The output system state vector is subtracted from the system state vector to obtain the estimated error dynamics of the i-th distributed observer : ， The estimated error is made based on the gain matrix Convergence only keeps , through the parameters Adaptive update compensation attack signal The energy impact of The symbolic function of The direction of influence is achieved, so that the distributed observer outputs the system state vector consistent with the system state vector in the system dynamic model. The estimated error dynamic To 0, the system status is estimated.

2. According to the method of claim 1, the method is characterized in that: Communicating based on the local system state vector, obtaining the local system state vector after communication includes: Determine the connection weight according to the pre-set communication network topology between the distributed observers , when the connection weight is 1, the jth distributed observer transmits the observed local system state vector to the i-th distributed observer, and when the connection weight is 0, the jth distributed observer stops communicating with the ith distributed observer, and the communication obtains the local system state vector that is not observable by the ith distributed observer itself but observable by the jth distributed observer , i.e., the local system state vector after the communication; The output system state vector of the distributed observer is obtained based on the gain matrix and the local system state vector after communication. The expression of the output system state vector includes: ， ， in, is the local system state vector obtained by the i-th distributed observer observing the system dynamic model, yes The derivative with respect to time t is the output system state vector of the i-th distributed observer, is the local system state vector obtained by the jth distributed observer observing the system dynamic model, is the output vector of the ith distributed observer, is the adaptive attack compensation function, is the connection weight between the i-th distributed observer and the j-th distributed observer.

3. A distributed safety state estimation device for a cyber-physical system, characterized in that: include: A decomposition module is used to perform observable decomposition on the system dynamic model and the sensor model to obtain local observable matrix pairs and local unobservable matrices; A gain matrix acquisition module, used for obtaining the gain matrix of the distributed observer according to the local observable matrix pair and the local unobservable matrix; A communication module, configured to obtain a local system state vector by observing the system dynamic model through the distributed observer, and to communicate according to a preset communication network topology between the distributed observers and the local system state vector to obtain a local system state vector after communication; An output system state vector acquisition module, used to obtain an output system state vector of the distributed observer based on the gain matrix and the local system state vector after communication; A compensation module, used for controlling the adaptive attack compensation function in the distributed observer to compensate for the deception attack signal when there is a deception attack signal input in the system dynamic model, so as to achieve consistency between the output system state vector and the system state vector in the system dynamic model; The expression of the system dynamic model is: ， in, is the system state vector constructed based on the measurement data, Express The first-order derivative of is the control input, is a nonlinear function, is the attack matrix, It is a deception attack signal. is the system matrix, is the system input matrix, t represents time; The expression of the sensor model is: ， in, is the local observation matrix of the i-th cluster sensor, is the number of sensor clusters, is the output vector of the i-th cluster sensor; Performing observable decomposition on the system dynamic model and the sensor model to obtain a local observable matrix pair and a local unobservable matrix includes: Defining the transformation matrix , in is an unobservable subspace The perpendicular orthogonal basis of yes A perpendicular orthogonal basis of Represents n rows Column Transformation Matrix The dimension of express OK Perpendicular orthogonal basis The dimension of Represents n rows Perpendicular orthogonal basis Dimensions; According to the transformation matrix The structure of the system matrix A of the system dynamic model and the local observation matrix of the sensor model Perform observable decomposition: Based on the system matrix A and the local observation matrix , through the matrix rank judgment method, it is determined that the dimension of the system state observable by the current i-th cluster of sensors is (n- ); Then the transformed matrix Before proceeding Line and front Extract the columns to obtain the local observable system matrix , after Line and front Extract the columns to obtain the local unobservable system matrix , after Line and after Extract the columns to obtain the local unobservable system matrix , further transform the matrix Before proceeding Extraction of columns to obtain the local observable measurement matrix ;in, is the transformation matrix The transpose of express Line and zero matrix of columns; Obtaining the gain matrix of the distributed observer according to the local observable matrix pair and the local unobservable matrix comprises: Defining the local stability matrix , free matrix and attack matching matrix According to Lyapunov's stability theorem, combined with the local observable matrix pair and the local unobservable matrix, solve the following linear matrix inequality , , : ， = ， in, , ， ， ， ， ， in, represents the zero matrix, is the attack matrix of the i-th cluster sensor, is the Nn-dimensional identity matrix, , is the n-dimensional identity matrix, for dimensional identity matrix, , is the local observer stability matrix, is the vertical orthogonal basis of the local observer stability matrix, for The transposed matrix of , diag() is the diagonal matrix function, is an orthogonal basis of the observable space of the system, are the 1st, 2nd, ... Nth orthogonal vectors in the orthogonal basis of the observable space of the system, satisfy , is the nonlinear function The Lipschitz constant; Based on the , , , obtain the gain matrix of the distributed observer , , and The formula is: ， ， ， ， in, ， ， ， ， ， is the Lyapunov matrix of the i-th distributed observer, is the Lyapunov augmented matrix of N distributed observers including nonlinear factors, is the negative Lyapunov sum matrix of N distributed observers including nonlinear factors, is the local stability matrix of the ith distributed observer including nonlinear factors, is the Nth local stability matrix, is the minimum non-zero eigenvalue of the Laplacian matrix consisting of the connection weights of the distributed observer; When there is a deception attack signal input in the system dynamic model, controlling the adaptive attack compensation function in the distributed observer to compensate the deception attack signal to achieve consistency between the output system state vector and the system state vector in the system dynamic model includes: The expression of the adaptive attack compensation function is: ， ， ， ， in, is the difference between the measured output value of the i-th distributed observer and the measured output value of the i-th cluster sensor, For about The symbol function of is the adaptive parameter in the jth distributed observer, is an adaptive parameter, and is an arbitrarily chosen constant greater than zero; The output system state vector is subtracted from the system state vector to obtain the estimated error dynamics of the i-th distributed observer : ， The estimated error is made based on the gain matrix Convergence only keeps , through the parameters Adaptive update compensation attack signal The energy impact of The symbolic function of The direction of influence is achieved, so that the distributed observer outputs the system state vector consistent with the system state vector in the system dynamic model. The estimated error dynamic To 0, the system status is estimated.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 2 are implemented.

Images