Method and system for detecting reference signal attack of tracking control system

Abstract

The invention provides a method and a system for detecting reference signal attack of a tracking control system, and relates to the technical field of information physical system security. The method comprises the following steps: firstly, designing a remote reference signal tracking controller to ensure that a reference signal sent by a remote control center can be tracked in real time when a measured value of a tracking control system is not attacked; then, tracking errors before and after the tracking control system is attacked by the set point are quantitatively analyzed, a batch data detector is designed based on the change of probability statistical characteristics of the tracking errors before and after the attack, and reference signal attack detection is achieved. According to the method, in the aspect of tracking control, a novel tracking scene is considered, that is, a system reference signal is not generated locally but generated by a remote control center, in the aspect of system detection, a set point attack detection method is provided, and a batch data detector is provided; the method is superior to a detector which performs detection at each time step in the aspects of detection efficiency and resource saving.

Description

Technical Field

[0001] The present invention relates to the technical field of cyber - physical system security, and particularly to a method and system for detecting reference signal attacks in a tracking control system. Background Art

[0002] A cyber - physical system (CPS) is an integrated system that combines computing, communication, and physical components to interact with the physical world. CPS has advantages such as system autonomy, easy installation, and strong reliability, and is widely used in fields such as smart grids, unmanned aerial vehicles, and mobile robots. When a reference signal is sent to a remote controlled system in a tracking control system through a wireless communication network, the tracking control system can be regarded as a special CPS. However, with the introduction of the network, the reference signal faces the risk of being tampered with by an attacker, that is, the tracking control system may be subject to a reference signal attack. Therefore, it is crucial to study how to enable the tracking control system to detect whether it has suffered a set - point attack when the reference signal value is transmitted through a wireless communication network.

[0003] Existing network attacks on CPS are divided into two categories: one is a denial - of - service attack, and the research focus is on how to make the target network no longer provide normal services; the other is a spoofing attack, and the research focus is on how to inject false data or replay historical data to manipulate normal data. However, the current network attack research scenarios target attacks on control inputs or measured values. When the tracking control system is subject to a set - point attack, traditional detectors such as χ 2 detectors will not be able to effectively detect it. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for detecting reference signal attacks in a tracking control system in view of the above - mentioned deficiencies of the prior art, so as to be able to detect whether the system has suffered a set - point attack when the reference signal of the tracking control system is tampered with.

[0005] To solve the above - mentioned technical problem, the technical solution adopted by the present invention is: on the one hand, the present invention provides a method for detecting reference signal attacks in a tracking control system, designing a remote reference signal tracking controller to ensure that the measured value of the tracking control system can track the reference signal sent by the remote control center in real time when not under attack;

[0006] Quantitatively analyze the tracking error of the tracking control system before and after being subject to a set - point attack, and design a batch data detector based on the change in the probability - statistical characteristics of the tracking error before and after the attack to achieve the detection of reference signal attacks.

[0007] It includes the following steps:

[0008] S1: Construct a dynamic model of the remotely controlled system to describe the physical process changes of the system itself and the process from the data collected by the sensors to the output to the estimator.

[0009] S2: Estimate the system process state based on the sensor measurement values and control input signals in the remotely controlled system, and calculate the error covariance corresponding to the system state and the system state estimate using the Kalman filtering algorithm.

[0010] S3: Design a remote reference signal tracking controller so that the output of the remotely controlled system can track the remote reference signal, where the reference signal is generated by the remote control center and transmitted to the remote reference signal tracking controller through a wireless communication channel. The specific process is as follows:

[0011] S3.1: Construct a cost function J for the reference signal generated by the remote control center and the control input signal k :

[0012]

[0013] where r k+1 represents the reference signal generated by the remote control center, Q 1 and Q 2 represent weight matrices, satisfying: Q 1 ≥0, Q 2 >0; y k+1 is the output of the remotely controlled system, i.e., the sensor measurement vector, and u k is the control input vector.

[0014] S3.2: Obtain the optimal control input signal by minimizing the cost function which is expressed as follows:

[0015]

[0016] where A, B, and C represent the control system state matrix, control input matrix, and sensor measurement output matrix respectively, satisfying (A, C) is observable, controllable; represents the posterior estimate of the system state x k ;

[0017] S4: Determine the tracking error of the tracking control system under the remote tracking controller and determine the tracking performance:

[0018]

[0019] where P k represents the corresponding posterior error covariance; S represents the process noise covariance; R represents the measurement noise covariance; and I is the identity matrix. Denote \(e\) k as the expectation, \(e\) k represents the tracking error, which is the difference between the current measurement value and the reference signal value at that moment. \(e\) k follows a Gaussian distribution with the expectation given by Equation (3) and the covariance given by Equation (4); \(L\) 1 , \(L\) 2 and \(M\) k-1 are all intermediate variables, which are respectively expressed as follows:

[0020] \(L\) 1 = [Q 2 + B T C T Q 1 CB] -1 B T C T Q 1 (5)

[0021] \(L\) 2 = -[Q 2 + B T C T Q 1 CB] -1 B T C T Q 1 (6)

[0022]

[0023] S5: Conduct a quantitative analysis of the tracking error before and after the set-point attack on the tracking control system to determine the quantitative relationship between the probability and statistical characteristics of the tracking error of the tracking control system after being attacked and the attack vector; where the attack scenario is that the attacker launches an attack when the reference signal is transmitted over the network and has no access permission to the remote control center. The specific process is as follows:

[0024] S5.1: Determine the form of the set-point attack on the tracking control system;

[0025] The form of the set-point attack on the tracking control system is expressed as follows:

[0026]

[0027] where represents the reference signal value after the tracking control system is subjected to a set-point attack, and \(a\) k represents the attack vector injected by the attacker during network transmission;

[0028] S5.2: Determine the probability and statistical characteristics of the tracking error after the tracking control system is attacked;

[0029] Among them, the tracking error after the tracking control system is attacked represents the measured value after the system is attacked; The probability statistical characteristics of are expressed as follows:

[0030]

[0031] S5.3: Quantitatively analyze the tracking performance of the tracking control system and the attack vector a k to obtain the explicit expression result of the influence of the attack vector a k on the tracking performance of the tracking control system, which is expressed as follows:

[0032]

[0033] Among them, equation (11) represents the difference between the expected value of the tracking error after the system is attacked by the set-point attack and the expected value of the tracking error during the normal operation of the system; equation (12) represents the difference between the trace of the covariance of the tracking error after the system is attacked by the set-point attack and the trace of the covariance of the tracking error during the normal operation of the system; Tr represents the operation of taking the trace of a matrix;

[0034] S6: Design a batch data detector based on whether the probability statistical characteristics of the tracking error change as the basis for whether the system is attacked by the set-point attack, and use the batch data detector to detect whether the tracking control system is attacked by the set-point attack;

[0035] First, introduce a wireless communication channel between the sensor of the remote controlled system and the remote control center; second, transmit the measured value of the system at each moment to the remote control center through the wireless communication network; finally, the remote control center compares the real-time measured value of the system with the real reference signal value through the batch data detector to determine whether the tracking control system is attacked, and the specific form is expressed as follows:

[0036]

[0037] Among them, τ represents the window size, which represents the time step of the detection data; g k represents the cumulative deviation degree between the measured value of the system and the real reference signal within τ moments; η represents the detection threshold of the data detector set according to the probability statistical characteristics of the tracking error. If g k < η, it is considered that the tracking control system is operating normally; if g k ≥ η, it is considered that the tracking control system is attacked by the set-point attack.

[0038] On the other hand, the present invention provides a detection system for an attack on the reference signal of a tracking control system, including:

[0039] A model construction module, configured to construct a dynamic model of a remotely controlled system, and describe the physical process change of the system itself and the process of outputting the data collected by the sensor to the estimator;

[0040] A system state error calculation module, which estimates the system process state based on the sensor measurement value and the control input signal in the remotely controlled system, and calculates the error covariance corresponding to the system state and the system state estimation value using the Kalman filter estimation algorithm;

[0041] A tracking controller construction module, which constructs a remote reference signal tracking controller so that the output of the remotely controlled system can track the remote reference signal;

[0042] A tracking error calculation module, which determines the tracking error of the tracking control system under the remote tracking controller and determines the tracking performance;

[0043] A tracking error analysis module, which quantitatively analyzes the tracking error before and after the set-point attack on the tracking control system, and determines the quantitative relationship between the probability statistical characteristics of the tracking error of the tracking control system after being attacked and the attack vector;

[0044] An attack detection module, which designs a batch data detector based on whether the probability statistical characteristics of the tracking error change as the basis for whether the system is under a set-point attack, and uses the batch data detector to detect whether the tracking control system is under a set-point attack.

[0045] In a third aspect, the present application proposes an electronic device, including: one or more processors, and a memory, where the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the detection method for the reference signal attack of the tracking control system.

[0046] In a fourth aspect, the present application proposes a computer-readable storage medium, which stores executable instructions, and when the instructions are executed, the processor executes the detection method for the reference signal attack of the tracking control system.

[0047] In a fifth aspect, the present application proposes a computer program product, including a computer program or instructions, and when the computer program or instructions are executed by a processor, the detection method for the reference signal attack of the tracking control system is implemented.

[0048] The beneficial effects of adopting the above technical solution are as follows: A detection method and system for attacks on the reference signal of a tracking control system provided by the present invention consider a new tracking scenario in terms of tracking control, that is, the system reference signal is not generated locally but by a remote control center. The remote tracking controller only needs to receive the reference signal value at the next moment to update the control signal, rather than the reference signal values at all moments. In terms of system attacks, a new attack scenario is considered, where the attacker initiates a set-point attack to tamper with the reference signal value, while the scenarios considered in traditional network attacks are attacks on control inputs and measured values. In addition, a quantitative analysis of the relationship between the system tracking error and the attack vector is carried out, and an explicit expression is given. In terms of system detection, a detection method for set-point attacks is given, and a batch data detector is proposed, which will be superior to detectors that perform detection at each time step in terms of detection efficiency and resource savings. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 FIG. is a schematic diagram of a detection method for attacks on the reference signal of a tracking control system provided in Embodiment 1 of the present invention;

[0050] Figure 2 FIG. is a flowchart of a detection method for attacks on the reference signal of a tracking control system provided in Embodiment 1 of the present invention;

[0051] Figure 3 FIG. is a simulation effect diagram of the tracking of the controller and the detection of attacks by the detector provided in Embodiment 1 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] The following further describes in detail the specific embodiments of the present invention in conjunction with the drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0053] Embodiment 1:

[0054] Based on a discrete linear time-invariant system, this embodiment uses the detection method for attacks on the reference signal of the tracking control system of the present invention. The batch data detector can detect whether the reference signal generated by the remote control center is subject to a set-point attack. The principle is as Figure 1 shown. This method includes two parts: The first part is to design a remote reference signal tracking controller to ensure that the measured value of the tracking control system can track the reference signal sent by the remote control center in real time when not under attack. The second part is to quantitatively analyze the tracking error of the tracking control system before and after being subject to a set-point attack, and design a batch data detector based on the change in the probability statistical characteristics of the tracking error before and after the attack to achieve the detection of reference signal attacks. The specific detailed implementation steps are as Figure 2 shown, including the following steps:

[0055] S1: Construct a dynamic model of the remotely controlled system to describe the physical process changes of the system itself and the process from the data collected by the sensor to the output to the estimator. Represent the process state, control input, measurement value, and noise influence in the form of the system state space as follows:

[0056] x k+1 = Ax k + Bu k + ω k (1)

[0057] y k = Cx k + v k (2)

[0058] Wherein, x k+1 is the state vector of the remotely controlled system, y k is the output of the remotely controlled system, i.e., the sensor measurement vector, u k is the control input vector; ω k and v k represent process noise and measurement noise respectively. Both are zero-mean Gaussian white noises and satisfy: j and k are both time, represents expectation, S represents the process noise covariance, R represents the measurement noise covariance; A, B, and C represent the control system state matrix, control input matrix, and sensor measurement output matrix respectively, and satisfy (A, C) observable, controllable;

[0059] S2: Estimate the system process state based on the sensor measurement value and control input signal in the remotely controlled system, and calculate the error covariance corresponding to the system state and the system state estimate value using the Kalman filter estimation algorithm;

[0060] The Kalman filter estimation includes two calculation steps: time update and state update. Among them, the time update is shown in the following formula:

[0061]

[0062] The state update is shown in the following formula:

[0063]

[0064] Wherein, respectively represent the prior and posterior estimates of the system state x k , P k respectively represent the corresponding prior and posterior error covariances; represents the vector {y 1 ,…, yk The spanned space; Called the innovation, also known as the residual, which represents the difference between the current measurement value and the estimated value of the current measurement value by the prior estimate at the previous moment. K k Is the Kalman filter gain. A T , B T and C T Respectively represent the transposes of matrices A, B, and C; I is the identity matrix.

[0065] S3: Design a remote reference signal tracking controller such that the output y k of the remotely controlled system can track the remote reference signal r k , where the reference signal is generated by the remote control center and transmitted to the remote reference signal tracking controller through the wireless communication channel. The specific process is as follows:

[0066] S3.1: Construct a cost function J k :

[0067]

[0068] where r k+1 represents the reference signal generated by the remote control center, and Q 1 and Q 2 represent weight matrices, satisfying: Q 1 ≥0, Q 2 >0;

[0069] S3.2: Obtain the optimal control input signal by minimizing the cost function which is expressed as follows:

[0070]

[0071] S4: Determine the tracking error of the tracking control system under the remote tracking controller and determine the tracking performance:

[0072]

[0073] where e k represents the tracking error, which is the difference between the current measurement value and the reference signal value at this moment. e k follows a Gaussian distribution with an expectation of equation (10) and a covariance of equation (11); L 1 , L 2 and M k-1 are all intermediate variables and are respectively expressed as follows:

[0074] L 1 =[Q2 +B T C T Q 1 CB] -1 B T C T Q 1 (12)

[0075] L 2 = -[Q 2 +B T C T Q 1 CB] -1 B T C T Q 1 (13)

[0076]

[0077] S5: Quantitatively analyze the tracking error of the tracking control system before and after a setpoint attack, and determine the quantitative relationship between the probability and statistical characteristics of the tracking error of the tracking control system after being attacked and the attack vector; among them, the attack scenario is that the attacker launches an attack when the reference signal is transmitted over the network and has no access permission to the remote control center. The specific process is as follows:

[0078] S5.1: Determine the form of the setpoint attack on the tracking control system;

[0079] The form of the setpoint attack on the tracking control system is expressed as follows:

[0080]

[0081] Among them, represents the reference signal value after the tracking control system is subjected to a setpoint attack, and a k represents the attack vector injected by the attacker during network transmission;

[0082] S5.2: Determine the tracking error of the tracking control system after being attacked

[0083] The probability and statistical characteristics of the tracking error after the tracking control system is attacked are expressed as follows:

[0084]

[0085] S5.3: Quantitatively analyze the tracking performance of the tracking control system and the attack vector a k to obtain the attack vector a kThe explicit expression results of the influence on the tracking performance of the tracking control system are shown as follows:

[0086]

[0087] Among them, equation (18) represents the difference between the expected tracking error of the system after being attacked by the setpoint and the expected tracking error during normal system operation; equation (19) represents the difference between the trace of the tracking error covariance of the system after being attacked by the setpoint and the trace of the tracking error covariance during normal system operation; Tr represents the trace operation on the matrix;

[0088] S6: Use whether the probabilistic and statistical characteristics of the tracking error change as the basis for whether the system is attacked by the setpoint to design a batch data detector, and use the batch data detector to detect whether the tracking control system is attacked by the setpoint;

[0089] First, introduce a wireless communication channel between the sensor of the remotely controlled system and the remote control center; second, transmit the system measurement value at each moment to the remote control center through the wireless communication network; finally, the remote control center compares the real-time measurement value of the system with the real reference signal value through the batch data detector to determine whether the tracking control system is attacked. The specific form is shown as follows:

[0090]

[0091] Among them, τ represents the window size, which represents the time step of the detection data; g k represents the cumulative deviation degree between the system measurement value and the real reference signal within τ moments; η represents the detection threshold of the data detector set according to the probabilistic and statistical characteristics of the tracking error. If g k < η, it is considered that the tracking control system is operating normally; if g k ≥ η, it is considered that the tracking control system is attacked by the setpoint.

[0092] This embodiment also verifies the tracking effect of the remote reference signal tracking controller and the effectiveness of the batch data detector in detecting setpoint attacks.

[0093] In this embodiment, the system state matrix:

[0094]

[0095] The control input matrix:

[0096]

[0097] The sensor measurement output matrix:

[0098]

[0099] System noise covariance:

[0100]

[0101] Measurement noise covariance:

[0102]

[0103] Secondly, verify the tracking performance of the remote reference signal tracking controller. The reference signal is set as r k =[50 40 30] T , under the normal operation of the system, that is, within the first 30 time steps of the system operation, the system output measurement value can track the reference signal in real time. The tracking simulation effect of the controller is shown in Figure 3 .

[0104] Finally, initiate a set-point attack from the 30th time step to the 120th time step of the system operation. The attack vector is set as a k =[100 100 100] T , that is At this time, the tracking error is greater than the set detection threshold, and the batch data detector triggers an alarm. The detection attack simulation effect of the detector is shown in Figure 3 .

[0105] Example 2:

[0106] A model construction module for constructing a dynamic model of the remotely controlled system to describe the change of the system's own physical process and the process of the data collected by the sensor and output to the estimator;

[0107] A system state error calculation module for estimating the system process state based on the sensor measurement value and the control input signal in the remotely controlled system, and calculating the error covariance corresponding to the system state and the system state estimated value using the Kalman filter estimation algorithm;

[0108] A tracking controller construction module for constructing a remote reference signal tracking controller so that the output of the remotely controlled system can track the remote reference signal;

[0109] A tracking error calculation module for determining the tracking error of the tracking control system under the remote tracking controller and determining the tracking performance;

[0110] A tracking error analysis module for quantitatively analyzing the tracking error of the tracking control system before and after being attacked by the set-point attack, and determining the quantitative relationship between the probability statistical characteristics of the tracking error of the tracking control system after being attacked and the attack vector;

[0111] The attack detection module designs a batch data detector based on whether the probability statistical characteristics of the tracking error change, which is used as the basis for whether the system is under a set-point attack, and uses the batch data detector to detect whether the tracking control system is under a set-point attack.

[0112] Embodiment 3:

[0113] This embodiment proposes an electronic device, including: one or more processors, and a memory, where the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors are caused to execute the detection method for an attack on the reference signal of the tracking control system as described above.

[0114] The electronic device can be a mobile phone, a computer, a tablet computer, etc., including a memory and a processor. A computer program is stored on the memory, and when the computer program is executed by the processor, it implements the detection method for an attack on the reference signal of the tracking control system as described in the embodiment. It can be understood that the electronic device can also include an input / output (I / O) interface and a communication component.

[0115] Among them, the processor is used to execute all or part of the steps in the detection method for an attack on the reference signal of the tracking control system as described in the above embodiment. The memory is used to store various types of data, which can include, for example, instructions for any application program or method in the electronic device, and data related to the application program.

[0116] The processor can be implemented by an application specific integrated circuit (ASIC), a digital signal processor (DSP), a programmable logic device (PLD), a field programmable gate array (FPGA), a controller, a microcontroller, a microprocessor, or other electronic components, and is used to execute the detection method for an attack on the reference signal of the tracking control system as described in the above embodiment.

[0117] Embodiment 4:

[0118] This embodiment proposes a computer-readable storage medium that stores executable instructions. When the instructions are executed and implemented in the form of a software functional unit and sold or used as an independent product, they can be stored in a computer-readable storage medium.

[0119] The computer software product is stored in a storage medium, including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method for detecting a reference signal attack of the tracking control system described in various embodiments of the present application.

[0120] The aforementioned storage medium includes: flash memory, hard disk, multimedia card, card-type memory (such as SD (Secure Digital Memory Card, secure digital memory card) or DX (abbreviation for Memory Data Register, MDR, memory data register) memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, server, APP (abbreviation for Application, application software) application store, and other various media that can store program check codes. A computer program is stored thereon, and when the computer program is executed by a processor, it can implement each step of the method for detecting a reference signal attack of the tracking control system described above.

[0121] Embodiment 5:

[0122] This embodiment provides a computer program product, including a computer program or instructions, and when the computer program or instructions are executed by a processor, they implement the method for detecting a reference signal attack of the tracking control system described above.

[0123] Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a computer program product.

[0124] Each embodiment in the present application is described in a progressive manner. For the same or similar parts among the various embodiments, reference can be made to each other, and the key point of each embodiment is to illustrate the differences from other embodiments.

[0125] The protection scope of the present application is not limited to the above embodiments. Obviously, those skilled in the art can make various changes and modifications to the present disclosure without departing from the scope and spirit of the present disclosure. If these changes and modifications fall within the scope of the claims of the present disclosure and their equivalent technologies, the intention of the present disclosure also includes these changes and modifications.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope defined by the claims of the present invention.

Claims

1. A method for detecting a reference signal attack in a tracking control system, characterized in that: Design a remote reference signal tracking controller to ensure that the tracking control system measurement value can track the reference signal sent by the remote control center in real time when it is not attacked; The tracking error of the tracking control system before and after the set point attack is quantitatively analyzed. A batch data detector is designed based on the change in the probability statistical characteristics of the tracking error before and after the attack to detect the reference signal attack.

2. A method for detecting a reference signal attack in a tracking control system according to claim 1, characterized in that: The following steps are involved: S1: Construct a dynamic model of the remote controlled system to describe the changes in the system's own physical processes and the process of outputting data to the estimator after the sensor collects data; S2: Estimate the system process state based on the sensor measurement value and control input signal in the remote controlled system, and use the Kalman filter estimation algorithm to calculate the error covariance between the system state and the system state estimate; S3: Design a remote reference signal tracking controller so that the output of the remote controlled system can track the remote reference signal, wherein the reference signal is generated by the remote control center and transmitted to the remote reference signal tracking controller through a wireless communication channel; S4: determining the tracking error of the tracking control system under the remote tracking controller and determining the tracking performance; S5: quantitatively analyzing the tracking error before and after the tracking control system is attacked by the set point, and determining the quantitative relationship between the probability statistical characteristics of the tracking error after the tracking control system is attacked and the attack vector; S6: A batch data detector is designed based on whether the probability statistical characteristics of the tracking error have changed as a basis for determining whether the system has been attacked by the set point. The batch data detector is used to detect whether the tracking control system has been attacked by the set point.

3. A method for detecting a reference signal attack of a tracking control system according to claim 2, characterized in that: The step S3 comprises: S3.1: Construct the cost function J for the reference signal and control input signal generated by the remote control center k : Among them, r k+1 represents the reference signal generated by the remote control center, Q1 and Q2 represent weight matrices, satisfying: Q1 ≥ 0, Q2 > 0; y k+1 is the output of the remote controlled system, i.e. the sensor measurement vector, u k is the control input vector; S3.2: Obtaining the optimal control input signal by minimizing the cost function It is expressed as follows: Among them, A, B and C represent the control system state matrix, control input matrix and sensor measurement output matrix respectively, satisfying (A, C) observable, Controllable; Represents the system state x k The posterior estimate of .

4. A method for detecting a reference signal attack in a tracking control system according to claim 3, characterized in that: The tracking error of the tracking control system determined in step S4 under the remote tracking controller obeys a Gaussian distribution with expectation (3) and covariance (4): Among them, P k express The corresponding a posteriori error covariance; S represents the process noise covariance; R represents the measurement noise covariance; I is the unit matrix; Represents e k expectations, e k Represents the tracking error, which indicates the difference between the current measurement value and the reference signal value at that moment. e k The Gaussian distribution is subject to the expectation (3) and the covariance (4); L1, L2 and M k-1 They are all intermediate variables, which are expressed as follows: L1=[Q2+B T C T Q1CB] -1 B T C T Q1 (5) L2=-[Q2+B T C T Q1CB] -1 B T C T Q1 (6) 5. A method for detecting a reference signal attack in a tracking control system according to claim 4, characterized in that: The attack scenario set in step S5 is that the attacker launches an attack when the reference signal is transmitted over the network, and has no access to the remote control center. The specific process is as follows: S5.1: Determine the form of set point attack on the tracking control system; The tracking control system is attacked by the set point in the form of: in, represents the reference signal value of the tracking control system after the set point is attacked, a k Represents the attack vector injected by the attacker during network transmission; S5.2: Determine the tracking error after the tracking control system is attacked The probability and statistical characteristics of Among them, the tracking error after the tracking control system is attacked Represents the measured value after the system is attacked; The probability and statistical characteristics of are expressed as follows: S5.3: Compare the tracking performance of the tracking control system with the attack vector a k Perform quantitative analysis and obtain attack vector a k The explicit expression of the impact on the tracking performance of the tracking control system is expressed as follows: Wherein, equation (11) represents the difference between the expected tracking error after the system is attacked by the set point and the expected tracking error when the system is operating normally; equation (12) represents the difference between the trace of the tracking error covariance after the system is attacked by the set point and the trace of the tracking error covariance when the system is operating normally; Tr represents the matrix trace operation.

6. A method for detecting a reference signal attack in a tracking control system according to claim 5, characterized in that: The step S6 comprises: Introducing a wireless communication channel between the sensors of the remote controlled system and the remote control center; Transmit the system measurement values ​​at each moment to the remote control center via the wireless communication network; The remote control center compares the real-time measurement value of the system with the real reference signal value through the batch data detector to determine whether the tracking control system is attacked. The specific form is as follows: Among them, τ represents the window size, which represents the time step of the detection data; g k represents the cumulative deviation between the system measurement value and the true reference signal within τ moments; η represents the detection threshold of the data detector set according to the probability and statistical characteristics of the tracking error. If g k <η, the tracking control system is considered to be operating normally; if g k ≥η, the tracking control system is considered to be attacked by the set point.

7. A detection system for tracking control system reference signal attack, characterized in that: include: The model building module is used to build a dynamic model of the remote controlled system, describing the changes in the system's own physical process and the process of outputting data to the estimator after the sensor collects data; The system state error calculation module estimates the system process state based on the sensor measurement value and the control input signal in the remote controlled system, and uses the Kalman filter estimation algorithm to calculate the error covariance between the system state and the system state estimation value; A tracking controller building module is used to build a remote reference signal tracking controller so that the output of the remote controlled system can track the remote reference signal; A tracking error calculation module determines the tracking error of the tracking control system under the remote tracking controller and determines the tracking performance; The tracking error analysis module quantitatively analyzes the tracking error before and after the tracking control system is attacked by the set point, and determines the quantitative relationship between the probability statistical characteristics of the tracking error after the tracking control system is attacked and the attack vector; The attack detection module uses the change of the probability statistical characteristics of the tracking error as the basis for determining whether the system is attacked by the set point to design a batch data detector, and uses the batch data detector to detect whether the tracking control system is attacked by the set point.

8. An electronic device, comprising: One or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the method for detecting a reference signal attack of a tracking control system as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing executable instructions, which instructions, when executed, if implemented in the form of software functional units and sold or used as independent products, can be stored in a computer-readable storage medium; The computer software product is stored in a storage medium and includes a plurality of instructions for enabling a computer device to execute the method for detecting a reference signal attack of a tracking control system as claimed in any one of claims 1 to 6.

10. A computer program product, comprising a computer program or an instruction, which, when executed by a processor, implements the method for detecting a reference signal attack of a tracking control system according to any one of claims 1 to 6.

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