Cps-based random event-triggered security state estimation method and related apparatus
By introducing a random event triggering mechanism and Kalman filtering into the cyber-physical system, the problem of state estimation for resource-constrained systems under DoS attacks is solved, achieving efficient and robust state estimation results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2022-11-25
- Publication Date
- 2026-06-02
AI Technical Summary
Existing technologies cannot effectively estimate the state of resource-constrained cyber-physical systems under DoS attacks, and traditional time-triggered mechanisms cannot adapt to the increasing power consumption and communication burden of cyber-physical systems.
A CPS-based random event-triggered security state estimation method is adopted. By establishing an event-triggered local estimator for the sensor subsystem and a random event-triggered scheduler under denial-of-service attacks, the random event triggering mechanism is used to control sensor data transmission, and Kalman filtering is combined for state estimation.
In resource-constrained environments, efficient state estimation is achieved, communication burden is reduced, and estimation accuracy and system robustness are improved.
Smart Images
Figure CN116150759B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of cyber-physical system security technology, and particularly to a method and related apparatus for estimating security status based on random events triggered by cyber-physical systems (CPS). Background Technology
[0002] Cyber-physical systems (CPS) are a new type of intelligent system characterized by the highly integrated interaction of a network environment (communication, computing, and control) and physical processes within that network environment. They are characterized by diversity, robustness, efficiency, and high performance. Based on the deep integration of cyberspace and physical reality, CPS involve multiple disciplines such as control theory and computer science, and are applied in various sectors of society, including smart grids, public transportation, smart healthcare, implantable medical devices, and industrial control systems. Compared to traditional physical control systems, CPS incorporates many information system elements, but this also presents them with more complex security challenges. Due to the openness and flexibility brought about by their integration with the internet, CPS are highly vulnerable to multi-layered and diverse cyberattacks from hackers, potentially causing significant personal injury and property damage.
[0003] Existing technologies are used for state estimation of cyber-physical systems under DoS attack environments.
[0004] Limitations: As cyber-physical systems (CPS) expand in scale, their power consumption and communication burden increase exponentially, rendering traditional time-triggered mechanisms inadequate. In other words, there is currently a lack of state estimation for resource-constrained CPS systems under DoS attacks. Summary of the Invention
[0005] The purpose of this invention is to provide a method and related apparatus for security state estimation based on CPS-triggered random events, in order to solve the problem of lack of state estimation for resource-constrained cyber-physical systems under DoS attacks.
[0006] To achieve the above objectives, the present invention adopts the following technical solution:
[0007] A CPS-based method for estimating security states triggered by random events, including
[0008] Based on the sensor information obtained from the event triggering mechanism and the irregular information obtained from denial-of-service attacks, an event-triggered local estimator for the sensor subsystem is established.
[0009] Establish a random event-triggered scheduler for a single-sensor cyber-physical system under denial-of-service attacks;
[0010] The random event-triggered scheduler determines whether the sensor should send the measurement observation data to the event-triggered local estimator;
[0011] If the result indicates that the request has been sent, the event triggers the local estimator to process the local estimate using the estimation algorithm to obtain the local estimate and covariance matrix; the local estimate and covariance matrix are then sent to the fusion center to obtain the global estimate and covariance matrix.
[0012] Furthermore, the establishment of a random event-triggered scheduler:
[0013] Establish the following linear time-varying system
[0014]
[0015]
[0016] Where k is time, i∈[1,2…N] is the number of sensors, and x k Let y be the system state vector. k A is the system observation vector obtained from sensor observations. k and W is a known system matrix with appropriate dimensions. k It is zero-mean Gaussian white noise with covariance Q. k , It is measurement noise, with a covariance of This indicates whether the system has experienced a denial-of-service attack. This indicates that the attacker did not launch an attack. This indicates that the attacker has launched an attack; Follows a binary Bernoulli distribution
[0017]
[0018] Where, β i ∈[0,1] is a constant scalar, representing the failure rate of a denial-of-service attack at the i-th sensor;
[0019] First, calculate the measurement innovation that reflects the dynamic changes of the system. for:
[0020]
[0021] State x k Given a Gaussian probability density function, design a random event triggering mechanism. This mechanism involves using the random variable... With evaluation function A comparison is made to determine whether the sensor sends the measurement observation data to the event-triggered local estimator;
[0022]
[0023]
[0024] in, Let [the variable] be randomly distributed between [0, 1]. Z is the evaluation function for the event triggering condition, and Z is a positive definite coefficient matrix to be predefined. These are decision variables.
[0025] Furthermore, the specific judgment in the random event trigger scheduler is as follows:
[0026] This indicates that the raw measurement information is directly transmitted to the remote estimator. This indicates that no information is being transmitted on the communication network.
[0027] Furthermore, when the fusion center is estimated within the sequential fusion estimation framework:
[0028] Step 1: Initialize the estimator parameters x0 and P0, set the system time k to 1, and start running the system state estimation algorithm;
[0029] Step 2: Sensor 1 obtains the measurement value at the current time.
[0030] Step 3: Put β 1 and returned from local estimator 1 Pass-in event trigger;
[0031] Step 4: Determine whether to update the measured value based on the event trigger result. Input to the local estimator, This indicates that the raw measurement information is directly transmitted to the remote estimator. This indicates that no information is being transmitted on the communication channel;
[0032] Step 5: Local estimator 1 processes the local estimates according to the estimation algorithm to obtain the local estimates. Covariance Matrix
[0033] Step 6: Local estimation of local estimator 1 Treated as a one-step prediction estimate of local estimator 2 Local estimator 2, covariance matrix The covariance matrix of the local estimator 2 Send to local estimator 2;
[0034] Step 7: Repeat steps 2 through 6 until the number of local estimators is N. The local estimators N are then used to calculate the local estimates. Covariance Matrix That is, global estimation Covariance Matrix
[0035] Furthermore, when fusion center estimation is performed within a parallel fusion estimation framework:
[0036] Step 1: Initialize the estimator parameters x0 and P0, set the system time to 1, and start running the system state estimation algorithm;
[0037] Step 2: Each sensor obtains the measurement value at the current time.
[0038] Step 3: Put β i and returned from the local estimator Pass-in event trigger;
[0039] Step 4: Determine whether to update the measured value based on the event trigger result. Input to the local estimator, This indicates that the raw measurement information is directly transmitted to the remote estimator. This indicates that no information is being transmitted on the communication channel;
[0040] Step 5: The local estimator processes the local estimates in parallel according to the estimation algorithm to obtain the local estimate. Covariance Matrix
[0041] Step 6: Local estimation of the local estimator Covariance Matrix The data is sent to the fusion center to obtain a global estimate. Covariance Matrix
[0042] Furthermore, the estimation algorithm is as follows:
[0043] Time update equation:
[0044]
[0045]
[0046] Metric update equation:
[0047]
[0048]
[0049] The gain matrix is:
[0050]
[0051] Where Z is a predefined positive definite coefficient matrix. for:
[0052]
[0053] Furthermore, a CPS-based random event-triggered security state estimation system includes:
[0054] The estimator building module is used to build an event-triggered local estimator for the sensor subsystem based on sensor information from the event-triggered mechanism and irregular information from denial-of-service attacks.
[0055] The scheduler establishment module is used to establish a random event-triggered scheduler for a single-sensor cyber-physical system under denial-of-service attacks.
[0056] The judgment module is used by the random event-triggered scheduler to determine whether the sensor sends the measurement observation data to the event-triggered local estimator;
[0057] The fusion center calculation module is used to determine if the result has been sent. The event triggers the local estimator to process the local estimate according to the estimation algorithm to obtain the local estimate and covariance matrix; the local estimate and covariance matrix are sent to the fusion center to obtain the global estimate and covariance matrix.
[0058] Furthermore, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of a CPS-based random event-triggered security state estimation method.
[0059] Furthermore, a computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of a CPS-based random event-triggered security state estimation method.
[0060] Compared with the prior art, the present invention has the following technical effects:
[0061] This invention discloses a method and related apparatus for security state estimation based on CPS (Cyber-Physical Systems), comprising: establishing an event-triggered local estimator for a sensor subsystem; establishing a random event-triggered scheduler for a single-sensor cyber-physical system under a denial-of-service attack; the random event-triggered scheduler determining whether the sensor has sent measurement observation data to the event-triggered local estimator; if the determination result is that the data has been sent, the event-triggered local estimator processes the local estimate according to an estimation algorithm to obtain a local estimate and a covariance matrix; and sending the local estimate and covariance matrix to a fusion center to obtain a global estimate and a covariance matrix. This invention uses an event-triggered mechanism, where communication information is only sent to the estimator when specific conditions are met. Therefore, this novel mechanism can solve the state estimation problem of resource-constrained cyber-physical systems. Attached Figure Description
[0062] Figure 1 Schematic diagram of sequential fusion estimation;
[0063] Figure 2 Schematic diagram of parallel fusion estimation;
[0064] Figure 3 RMSE curve of the algorithm under single sensor;
[0065] Figure 4 RMSE curve of multi-sensor fusion estimation algorithm;
[0066] Figure 5 Flowchart of the parallel fusion estimation algorithm;
[0067] Figure 6 Flowchart of the sequential fusion estimation algorithm. Detailed Implementation
[0068] The present invention will be further described below with reference to the accompanying drawings:
[0069] Please see Figures 1 to 6 A method and related apparatus for estimating the safety state triggered by random events based on CPS, considering the following linear time-varying system.
[0070]
[0071] Where k is time, i∈[1,2…N] is the number of sensors, and x k Let y be the system state vector. k A is the system observation vector obtained from sensor observations. k and W is a known system matrix with appropriate dimensions. k It is zero-mean Gaussian white noise with covariance Q. k , It is measurement noise, with a covariance of This indicates whether the system has experienced a denial-of-service attack. This indicates that the attacker did not launch an attack. This indicates that the attacker has launched an attack. Follows a binary Bernoulli distribution
[0072]
[0073] Where, β i ∈[0,1] is a constant scalar, representing the failure rate of a denial-of-service attack at the i-th sensor.
[0074] Every resource-constrained sensor is equipped with an event-triggered mechanism; however, current event-triggered mechanisms cannot always guarantee the Gaussian property of the system. Therefore, we propose a novel random event-triggered mechanism to address this problem.
[0075] First, based on (1), the measurement innovation reflecting the dynamic changes of the system is calculated. for
[0076]
[0077] To make the design of the optimal estimator for a random event-triggered scheduler easier to handle, this paper assumes that state x k The probability density function follows a Gaussian distribution. An effective random event triggering mechanism was designed, which involves using random variables... With evaluation function The comparison is used to determine whether the sensor sends the measured observation data to the remote estimator.
[0078]
[0079]
[0080] in Let [the variable] be randomly distributed between [0,1]. Z is the evaluation function for the event triggering condition, and Z is a positive definite coefficient matrix to be predefined. As the decision variable, we can derive from (3) This indicates that the raw measurement information is directly transmitted to the remote estimator. This indicates that no information is being transmitted on the communication network.
[0081] Before performing fusion estimation in an event-triggered multi-sensor cyber-physical system (CPS) in response to denial-of-service (DoS) attacks, an event-triggered local estimator for the sensor subsystem needs to be designed based on the sensor information brought by the event-triggered mechanism and the irregular information brought by the DoS attack. Since the resource-constrained CPS uses the random event-triggered scheduler in (3) to control data transmission from the sensor to the estimator, the Gaussian property of the system state condition distribution still holds. During system operation, when the sensor acquires new observations, the scheduler calculates the evaluation function. Then, run the event-triggered scheduler based on the decision variables. Or 0, to decide whether to innovate the current measurement. The signal is sent to the i-th local estimator. However, the communication channel may be affected by denial-of-service attacks. Therefore, in the case of simultaneous event-triggered scheduling and network attacks, we introduce Kalman filtering and (1)-(3) to design random event-triggered security state estimation of a single-sensor cyber-physical system under denial-of-service attacks.
[0082] Time update equation:
[0083]
[0084]
[0085] Metric update equation:
[0086]
[0087] The gain matrix is:
[0088]
[0089] Where Z is a predefined positive definite coefficient matrix. for:
[0090]
[0091] In the sequential fusion estimation framework, sensor information is sequentially fused, and a global estimate is obtained through a recursive iterative process. The number of iterations is equal to the number of sensors N.
[0092] Sequential fusion estimation uses the posterior estimate of the (i-1)th recursion as the prediction estimate of the ith recursion at the fusion center. For a multi-sensor network with N nodes, the overall estimate of the system state is represented by the Nth recursive local estimate within the sequential framework.
[0093]
[0094] Recursive calculation of one-step prediction estimation and its error covariance
[0095]
[0096] Then, it can be calculated directly. Evaluation function The scheduler will be triggered by the event in (3). A random variable uniformly distributed on [0,1] Compare the measurements. Decide whether to use the current sensor measurements. The data is sent to the fusion center. In the i-th iteration step, the local estimate is updated using the event-triggered security state estimation algorithm proposed in (4)-(6). and its covariance matrix The estimation steps described above are repeated sequentially for i = 1, 2, ..., N. Simultaneously, sensor measurements affected by event-triggered mechanisms and network attacks are sequentially fused at the fusion center. Finally, after N recursions, the following is obtained: and
[0097] Parallel fusion estimation transmits overall sensor information in parallel to the fusion center through an N-node sensor network. Parallel fusion estimation feeds back the one-step prediction of the global estimate to the local sensors, improving the accuracy of the local estimates and increasing communication efficiency. The one-step prediction of the i-th local estimator is...
[0098]
[0099] in It is the global estimate and corresponding covariance matrix of the previous time step.
[0100] Then, similar to the sequential fusion algorithm, the global prior estimate in the parallel fusion framework is returned to all sensor nodes. At each sensor node, It is calculated together with the global prior estimate in (2). Furthermore, the evaluation function is calculated. The evaluation function will be evaluated through the event-triggered scheduler in (3). and random decision variables Comparison. All local estimators process the local estimates in parallel according to the estimation algorithms proposed in (4)-(6). At the parallel fusion center, all local estimates are combined based on a weighted sum of matrices with local covariance to obtain the global estimate. and the corresponding covariance matrix
[0101]
[0102] To demonstrate the effectiveness and efficiency of our proposed random event-triggered security state estimation algorithm, this section presents a linear time-invariant system with a coefficient matrix. Furthermore, all subsequent experiments employ the Monte Carlo method with a corresponding parameter of 500. The system model consists of (1), where the relevant parameters are...
[0103]
[0104] Where A k This is the state transition matrix. System parameters T = 1, α = 0.01, σ 2 =5.
[0105] Assuming the target system has three sensors with limited sensing capabilities, a DoS attack aims to disrupt the sensors' sensing capabilities, with a failure rate of β. i =0.8, i=1,2,3. The sensor periodically measures the system state and transmits the measurement information to the remote estimator. The measurement matrix corresponding to sensor i is: The noise covariance matrix is R i =I 3×3Furthermore, within the framework of classical Kalman filtering, the steady-state error covariance was obtained.
[0106]
[0107] To ensure a Gaussian distribution in the innovation process, the random event-triggered scheduling mechanism in (3) is adopted to improve resource efficiency, and the coefficient matrix Z is set to be large. Then, a coefficient matrix is selected within the coefficient matrix {0.5Z, Z, 2Z} to evaluate the impact of the random event triggering mechanism on system performance. Taking the first component of the system state X(1) as an example, the security estimation performance of the proposed algorithm is analyzed. The root mean square error (RMSE) is introduced as an analytical metric to evaluate the estimation performance in the simulation. The communication efficiency of the proposed algorithm is analyzed by calculating the average communication rate R.
[0108]
[0109] Where M represents the number of Monte Carlo runs.
[0110] The single-sensor results of the security estimation algorithm of this invention are as follows: Figure 3 As shown, this paper sets up event-triggered scheduling in three different scenarios, corresponding to the scarcity of communication bandwidth. In the figure, the red line represents the RMSE curve of the intermittent Kalman filter algorithm, and the black line represents the RMSE curve of the classic Kalman filter algorithm. Intermittent Kalman filtering means that if the original sensor measurements are not transmitted, only time updates are performed. Figure 3 It can be seen that the communication rates of the single-sensor curves corresponding to the coefficient matrices {0.5Z, Z, 2Z} are 0.4572, 0.6238, and 0.7688, respectively. The larger the coefficient matrix Z, the higher the data scheduling frequency and the better the estimation quality. For example, when the coefficient matrix is 2Z, the algorithm can achieve accuracy comparable to the classic Kalman filter algorithm, but with a 23% reduction in communication burden. Specifically, a reasonable Z can strike a good trade-off between resource scarcity and system performance.
[0111] Performance comparison of fusion estimation algorithms, such as Figure 4 As shown, local estimation is performed by the proposed event-triggered estimation algorithm, the classical Kalman filter algorithm, and the intermittent Kalman filter algorithm, respectively. Simulation results show that, compared with the intermittent Kalman-based fusion estimation algorithm, the proposed sequential and parallel algorithms improve performance by 32% and 34%, respectively, under the condition of essentially equal communication burden. Figure 4It can be seen that the RMSE curves of the fusion algorithms presented in this paper are lower than those of the corresponding intermittent Kalman filter algorithms, but higher than those of the classic Kalman filter algorithm. This indicates that the estimation performance of both fusion estimation algorithms is worse than that of the intermittent Kalman filter algorithm, but not as good as that of the classic Kalman filter algorithm. This is because the implicit information is filtered by the event-triggered mechanism to update the security estimate.
[0112] In another embodiment of the present invention, a CPS-based random event-triggered security state estimation system is provided, which can be used to implement the above-mentioned CPS-based random event-triggered security state estimation method. Specifically, the system includes:
[0113] The estimator building module is used to build an event-triggered local estimator for the sensor subsystem based on sensor information from the event-triggered mechanism and irregular information from denial-of-service attacks.
[0114] The scheduler establishment module is used to establish a random event-triggered scheduler for a single-sensor cyber-physical system under denial-of-service attacks.
[0115] The judgment module is used by the random event-triggered scheduler to determine whether the sensor sends the measurement observation data to the event-triggered local estimator;
[0116] The fusion center calculation module is used to determine if the result has been sent. The event triggers the local estimator to process the local estimate according to the estimation algorithm to obtain the local estimate and covariance matrix; the local estimate and covariance matrix are sent to the fusion center to obtain the global estimate and covariance matrix.
[0117] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.
[0118] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions from the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of a CPS-based random event-triggered security state estimation method.
[0119] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the CPS-based random event-triggered security state estimation method in the above embodiments.
[0120] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0121] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0122] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0123] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.
Claims
1. A method for estimating security status based on CPS-triggered random events, characterized in that, include Based on the sensor information obtained from the event triggering mechanism and the irregular information obtained from denial-of-service attacks, an event-triggered local estimator for the sensor subsystem is established. Establish a random event-triggered scheduler for a single-sensor cyber-physical system under denial-of-service attacks; A random event triggers the scheduler to determine whether the sensor should send the raw measurement observation data to the local estimator; The local estimator processes the local estimates according to the estimation algorithm to obtain local estimates and covariance matrices; the local estimates and covariance matrices are then sent to the fusion center to obtain global estimates and covariance matrices. Establishment of a random event-triggered scheduler: Establish the following linear time-varying system in, For time, For the number of sensors, Let be the system state vector. It is the system observation vector obtained from sensor observations. and It is a known system matrix with appropriate dimensions. It is zero-mean Gaussian white noise with a covariance of , It is measurement noise, with a covariance of ; This indicates whether the system has experienced a denial-of-service attack. This indicates that the attacker did not launch an attack. This indicates that the attacker has launched an attack; Follows a binary Bernoulli distribution in, Let be a constant scalar, representing the denial-of-service attack at the _th ... Failure rate at each sensor; First, calculate the measurement innovation that reflects the dynamic changes of the system. for: state Given a Gaussian probability density function, design a random event triggering mechanism. This mechanism involves using the random variable... With evaluation function A comparison is made to determine whether the sensor sends the measurement observation data to the event-triggered local estimator; in, Let [the variable] be randomly distributed between [0, 1]. This is the evaluation function for the event triggering conditions. It is a positive definite coefficient matrix to be predefined; For decision variables; The estimation algorithm is as follows: Time update equation: Metric update equation: The gain matrix is: in, For a predefined positive definite coefficient matrix, for: 。 2. The method for estimating security status based on CPS-triggered random events according to claim 1, characterized in that, The specific judgment in the random event trigger scheduler is as follows: This indicates that the raw measurement information is directly transmitted to the remote estimator. This indicates that no information is being transmitted on the communication network.
3. The CPS-based random event-triggered security state estimation method according to claim 1, characterized in that, When fusion center estimation is within the sequential fusion estimation framework: Step 1: Initialize the estimator parameters , Set the system time k to 1 and start running the system state estimation algorithm; Step 2: Sensor 1 obtains the measurement value at the current time. ; Step 3: Put , and returned from local estimator 1 Pass-in event trigger; Step 4: Determine whether to update the measured value based on the event trigger result. Input to the local estimator, This indicates that the raw measurement information is directly transmitted to the remote estimator. This indicates that no information is being transmitted on the communication channel; Step 5: Local estimator 1 processes the local estimates according to the estimation algorithm to obtain the local estimates. Covariance Matrix ; Step 6: Local estimation of local estimator 1 Treated as a one-step prediction estimate of local estimator 2 Local estimator 2, covariance matrix The covariance matrix of the local estimator 2 Send to local estimator 2; Step 7: Repeat steps 2 through 6 until the number of local estimators is [value missing]. Local estimator Local estimation Covariance Matrix That is, global estimation Covariance Matrix .
4. The CPS-based random event-triggered security state estimation method according to claim 1, characterized in that, When fusion center estimation is performed within a parallel fusion estimation framework: Step 1: Initialize the estimator parameters , Set the system time to 1 and start running the system state estimation algorithm; Step 2: Each sensor obtains the measurement value at the current time. ; Step 3: Put , and returned from the local estimator Pass-in event trigger; Step 4: Determine whether to update the measured value based on the event trigger result. Input to the local estimator, This indicates that the raw measurement information is directly transmitted to the remote estimator. This indicates that no information is being transmitted on the communication channel; Step 5: The local estimator processes the local estimates in parallel according to the estimation algorithm to obtain the local estimate. Covariance Matrix ; Step 6: Local estimation of the local estimator Covariance Matrix The data is sent to the fusion center to obtain a global estimate. Covariance Matrix .
5. A CPS-based random event-triggered security state estimation system, characterized in that, include: The estimator building module is used to build an event-triggered local estimator for the sensor subsystem based on sensor information from the event-triggered mechanism and irregular information from denial-of-service attacks. The scheduler establishment module is used to establish a random event-triggered scheduler for a single-sensor cyber-physical system under denial-of-service attacks. The judgment module is used by the random event-triggered scheduler to determine whether the sensor sends the measurement observation data to the event-triggered local estimator; The fusion center calculation module is used to determine if the result has been sent. The event triggers the local estimator to process the local estimate according to the estimation algorithm to obtain the local estimate and covariance matrix; the local estimate and covariance matrix are then sent to the fusion center to obtain the global estimate and covariance matrix. Establishment of a random event-triggered scheduler: Establish the following linear time-varying system in, For time, For the number of sensors, Let be the system state vector. It is the system observation vector obtained from sensor observations. and It is a known system matrix with appropriate dimensions. It is zero-mean Gaussian white noise with a covariance of , It is measurement noise, with a covariance of ; This indicates whether the system has experienced a denial-of-service attack. This indicates that the attacker did not launch an attack. This indicates that the attacker has launched an attack; Follows a binary Bernoulli distribution in, Let be a constant scalar, representing the denial-of-service attack at the _th ... Failure rate at each sensor; First, calculate the measurement innovation that reflects the dynamic changes of the system. for: state Given a Gaussian probability density function, design a random event triggering mechanism. This mechanism involves using the random variable... With evaluation function A comparison is made to determine whether the sensor sends the measurement observation data to the event-triggered local estimator; in, Let [the variable] be randomly distributed between [0, 1]. This is the evaluation function for the event triggering conditions. It is a positive definite coefficient matrix to be predefined; For decision variables; The estimation algorithm is as follows: Time update equation: Metric update equation: The gain matrix is: in, For a predefined positive definite coefficient matrix, for: 。 6. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the CPS-based random event-triggered security state estimation method as described in any one of claims 1 to 4.
7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the CPS-based random event-triggered security state estimation method as described in any one of claims 1 to 4.