System control method and device and related equipment
By constructing a controller model adapted to DoS and FDI attacks, the problem of poor stability of cyber-physical systems is solved, stable control is achieved in attack environments, system disturbances are reduced, and system stability is improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-25
- Publication Date
- 2026-03-13
AI Technical Summary
In the existing technology, the control methods of cyber-physical systems, which adopt the average residence time model, cannot effectively cope with the randomness and dynamism of denial-of-service (DoS) attacks, resulting in poor system stability.
By obtaining the minimum dormancy period and state estimate of a DoS attack, a controller model is constructed. Combined with the estimate of a False Data Injection (FDI) attack, the controller gain is configured in segments to construct a controller model adapted to both DoS and FDI attacks, thereby achieving stable control of the controlled system.
It improves the stability of cyber-physical systems under DoS and FDI attacks, reduces the disturbance of network attacks to the system, and ensures the stable operation of the system during attacks.
Smart Images
Figure CN121664555A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of network security technology, and in particular to a system control method, apparatus and related equipment. Background Technology
[0002] Cyber-Physical Systems (CPS) are a class of dynamic systems tightly coupled with computing and communication networks and physical processes. Current control methods for CPS employ the average residence time (AST) model to design controllers, which then control the controlled systems within the CPS. However, the AST model's modeling of the frequency and duration of Denial-of-Service (DoS) attacks is overly idealistic and fails to accurately reflect the randomness and dynamics of DoS attacks. Therefore, using the AST model to design controllers is insufficient for effective control of CPS, resulting in poor stability. Summary of the Invention
[0003] This application provides a system control method, apparatus, and related equipment that can solve the technical problem of poor stability in cyber-physical systems.
[0004] In a first aspect, embodiments of this application provide a system control method, the method comprising:
[0005] Obtain the minimum dormancy period of a cyber-physical system under a denial-of-service (DoS) attack within a preset time range, and obtain the state estimate of the cyber-physical system and the estimate of the FDI (fictitious data injection) attack suffered by the actuators of the cyber-physical system during the dormancy period of the DoS attack.
[0006] Based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate, a controller model for the cyber-physical system is constructed.
[0007] The controlled system is controlled according to the controller model.
[0008] Optionally, the method further includes one of the following:
[0009] Within the time range from the initial moment of the DoS attack's dormancy period to the expiration of the minimum dormancy period of the DoS attack, the first gain of the controller model is obtained; based on the negative value of the product of the first gain and the state estimate, a first intermediate quantity is determined; and based on the difference between the first intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined.
[0010] Within the time range from the expiration of the minimum dormancy period of the DoS attack to the end of the dormancy period of the DoS attack, the second gain of the controller model is obtained; based on the negative value of the product of the second gain and the state estimate, the second intermediate quantity is determined; and based on the difference between the second intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined.
[0011] During the active period of the DoS attack on the cyber-physical system within the preset time range, the output of the controller model is determined based on the negative value of the FDI attack estimate.
[0012] The output of the controller model is used to control the controlled system.
[0013] Optionally, the method further includes:
[0014] Based on the DoS attacks suffered by the cyber-physical system within the preset time range, construct a network attack model;
[0015] Based on the model of the cyber-physical system and the network attack model, construct an estimator model for the cyber-physical system;
[0016] The process of obtaining the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuators of the cyber-physical system includes:
[0017] Based on the model of the cyber-physical system and the estimator model, obtain the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuator of the cyber-physical system.
[0018] Optionally, the method further includes:
[0019] Based on the estimator model, an augmented error model of the cyber-physical system is constructed. Based on the augmented error model and the model of the cyber-physical system, a closed-loop cyber-physical system model of the cyber-physical system under the DoS attack and the FDI attack is constructed.
[0020] The first gain and the second gain of the controller are obtained based on the stable operating conditions of the closed-loop cyber-physical system model.
[0021] Optionally, obtaining the first gain and the second gain of the controller based on the stable operating conditions of the closed-loop cyber-physical system model includes:
[0022] Based on the first Lyapunov function constructed by the DoS attack and the stable operating conditions of the closed-loop cyber-physical system model, the first gain and the second gain of the controller are obtained.
[0023] Optionally, constructing the estimator model of the cyber-physical system based on the model of the cyber-physical system and the network attack model includes:
[0024] Determine the estimator gain based on the stable operating conditions of the augmented error model;
[0025] Based on the estimator gain, the cyber-physical system model, and the network attack model, an estimator model for the cyber-physical system is constructed.
[0026] Secondly, embodiments of this application provide a system control device, the device comprising:
[0027] The acquisition module is used to acquire the minimum dormancy period of a cyber-physical system under a denial-of-service (DoS) attack within a preset time range, and to acquire the state estimate of the cyber-physical system and the estimate of the spoofed data injection (FDI) attack suffered by the actuators of the cyber-physical system during the dormancy period of the DoS attack.
[0028] The first processing module is used to construct a controller model of the cyber-physical system based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate.
[0029] The execution module is used to control the controlled system according to the controller model.
[0030] Thirdly, embodiments of this application provide an electronic device, including: a processor, a memory, and a program stored in the memory and executable on the processor, wherein when the program is executed by the processor, it implements the steps of the system control method as described in the first aspect.
[0031] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the system control method as described in the first aspect.
[0032] Fifthly, embodiments of this application provide a computer program product including computer instructions that, when executed by a processor, implement the steps of the system control method as described in the first aspect.
[0033] In this embodiment, the minimum dormancy period of a cyber-physical system (CPS) under a denial-of-service (DoS) attack within a preset time range is obtained. The state estimate of the CPS during the dormancy period and the estimate of a fictitious data injection (FDI) attack suffered by the CPS's actuators are also obtained. Based on the dormancy period, the minimum dormancy period, the state estimate, and the FDI attack estimate, a controller model for the CPS is constructed. The controlled system is then controlled according to the controller model. Because the controller model construction incorporates the temporal characteristics of DoS attacks and the tampering characteristics of FDI attacks, the control process of the controller model for the controlled system matches the minimum dormancy period of the DoS attack, reducing the disturbance of the CPS to the CPS by FDI and / or DoS attacks and improving the stability of the linear CPS. Attached Figure Description
[0034] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0035] Figure 1 This is a flowchart of a system control method provided in an embodiment of this application;
[0036] Figure 2 This is a schematic diagram illustrating an FDI attack and a DoS attack within a preset time range, provided in an embodiment of this application.
[0037] Figure 3 This is a schematic diagram of a cyber-physical system under a hybrid FDI and DoS attack, provided in an embodiment of this application.
[0038] Figure 4 This is a schematic diagram of the overall process of a system control method provided in an embodiment of this application;
[0039] Figure 5 This is a schematic diagram of the structure of a system control device provided in an embodiment of this application;
[0040] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation
[0041] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0042] The terms "first," "second," etc., used in this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first" and "second" are generally of the same class, not limited in number; for example, the first object can be one or more. Furthermore, "and / or" in this application indicates at least one of the connected objects. For example, the scope of protection of "A and / or B" covers at least three scenarios: Scenario 1: including A but not B; Scenario 2: including B but not A; Scenario 3: including both A and B. Additionally, the character " / " generally indicates that the preceding and following objects are in an "or" relationship.
[0043] See Figure 1 , Figure 1 This is a flowchart of a system control method provided in an embodiment of this application, such as... Figure 1 As shown, the method includes the following steps:
[0044] Step 101: Obtain the minimum dormancy period of the cyber-physical system under a denial-of-service (DoS) attack within a preset time range, and obtain the state estimate of the cyber-physical system and the estimate of the spoofed data injection (FDI) attack suffered by the actuator of the cyber-physical system during the dormancy period of the DoS attack.
[0045] The preset time range can be a network attack test time range specified by those skilled in the art as needed, or it can be a time range of suffering from real false data injection (FDI) attacks and / or DoS attacks, without any limitation.
[0046] For details, please see Figure 2 , Figure 2 This is a schematic diagram illustrating an FDI attack and a DoS attack within a preset time range, as provided in an embodiment of this application. Figure 2 As shown:
[0047] Within the preset time range, the cyber-physical system is subjected to a hybrid FDI and DoS attack. Within this preset time range, the DoS attack exhibits an alternating pattern of "dormant period - active period". The preset time range may include the dormant period of multiple DoS attacks and the active period of multiple DoS attacks.
[0048] It is understood that the dormancy period of the DoS attack can be any one or more DoS attack dormancy periods within the preset time range; the minimum dormancy period of the DoS attack can be the dormancy period of the shortest DoS attack among the multiple DoS attack dormancy periods within the preset time range.
[0049] The cyber-physical system can include general-form cyber-physical systems or discrete linear cyber-physical systems. For details, please refer to [link to relevant documentation]. Figure 3 , Figure 3 This is a schematic diagram of a cyber-physical system under a hybrid FDI and DoS attack, provided in an embodiment of this application, as shown in the figure:
[0050] The cyber-physical system may include actuators, controlled systems, sensors, observers, controllers, and communication networks; wherein,
[0051] Actuators can be used to apply corresponding control actions to the controlled system based on the output of the controller (such as control commands);
[0052] The controlled system can be a specific physical object or physical process, such as an industrial production device, a power system, a transportation system, or mechanical equipment; the controlled system can change with the control action of the actuator, external disturbances, and the state transition of the cyber-physical system itself;
[0053] Sensors can be used to measure specified physical quantities in controlled systems and / or cyber-physical systems;
[0054] The controller can be used to control the controlled system according to its own output and / or preset algorithm; in this application, the controller can directly control the controlled system or control the controlled system through an actuator.
[0055] Communication networks can be used to transmit measurement data, estimation results, and control commands between sensors, observers, controllers, and actuators;
[0056] Under FDI and / or DoS attacks, communication networks, actuators, and sensors may suffer from abnormal behaviors such as data tampering, forgery, or packet loss. The controlled system may become unstable and malfunction, thereby affecting the normal operation of the entire cyber-physical system.
[0057] The state estimate of the cyber-physical system can be an estimate of a state vector formed by uniformly abstracting a portion of the physical and / or logical quantities of the cyber-physical system. The state vector of the cyber-physical system can be a physical process-related quantity (e.g., physical quantities such as position, velocity, and acceleration), a discrete / logic state (e.g., valve open / close and switching states), or a network and computation-related quantity, etc., used to characterize the state of the cyber-physical system in order to achieve stable control of the cyber-physical system.
[0058] The estimate of the FDI attack suffered by the actuators of the cyber-physical system can be an estimate used to characterize the extent of the impact of an FDI attack on the actuators of the cyber-physical system.
[0059] In this step, the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the estimate of the FDI attack suffered by the actuator of the cyber-physical system are obtained; this ensures that the data for constructing the controller model of the cyber-physical system described later comes from a relatively normal time period, reducing the impact of data interruption and distortion caused by the DoS attack; and the minimum dormancy period of the cyber-physical system suffering from a denial-of-service DoS attack within a preset time range is obtained, providing a data foundation for constructing the controller model of the cyber-physical system described later.
[0060] Step 102: Construct the controller model of the cyber-physical system based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate;
[0061] In this step, since the minimum dormancy period of the DoS attack is the shortest time for the cyber-physical system to function normally under a DoS attack, on the one hand, when constructing the controller model, the controller model is made to complete the control of the controlled system within this minimum dormancy period. As long as the actual doS attack dormancy period is not less than this minimum dormancy period, the stability of the linear cyber-physical system can be guaranteed. On the other hand, the minimum dormancy period can also be used to determine the key parameters of the controller model and make the controller model's control process of the controlled system match the minimum dormancy period, thereby improving the stable operation capability of the cyber-physical system under a DoS attack.
[0062] Furthermore, in this step, a controller model of the cyber-physical system is constructed based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate. This ensures that the controller model takes into account the temporal characteristics of the DoS attack and the characteristics of the spoofed data injection attack, thereby significantly reducing the disturbance of the linear physical system by network attacks (including FDI attacks and DoS attacks) and improving the stability of the linear physical system.
[0063] Step 103: Control the controlled system according to the controller model.
[0064] The controlled system can be the specific physical object or physical process described above.
[0065] In this step, the control system is controlled using the controller model, which can improve the stability of the cyber-physical system.
[0066] In this embodiment, since the controller model construction process incorporates the time characteristics of DoS attacks and the tampering characteristics of FDI attacks, the controller model's control process over the controlled system matches the minimum dormancy period of a DoS attack, reducing the disturbance of FDI attacks and / or DoS attacks on the linear cyber-physical system and improving the stability of the cyber-physical system.
[0067] In some embodiments, the method further includes one of the following:
[0068] Within the time range from the initial moment of the DoS attack's dormancy period to the expiration of the minimum dormancy period of the DoS attack, the first gain of the controller model is obtained; based on the negative value of the product of the first gain and the state estimate, a first intermediate quantity is determined; and based on the difference between the first intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined.
[0069] Within the time range from the expiration of the minimum dormancy period of the DoS attack to the end of the dormancy period of the DoS attack, the second gain of the controller model is obtained; based on the negative value of the product of the second gain and the state estimate, the second intermediate quantity is determined; and based on the difference between the second intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined.
[0070] During the active period of the DoS attack on the cyber-physical system within the preset time range, the output of the controller model is determined based on the negative value of the FDI attack estimate.
[0071] The output of the controller model is used to control the controlled system.
[0072] For example, the division of the active period and the dormant period of the DoS attack suffered by the cyber-physical system within the preset time range, that is, the network attack model constructed later based on the DoS attacks suffered by the cyber-physical system within the preset time range, can be expressed by the following first formula:
[0073]
[0074] In the first formula, A network attack model used to represent DoS attacks. Indicates the dormancy period of a DoS attack. This indicates the active period of the DoS attack; t represents the duration of the DoS attack. This represents the (n+1)th dormant period of a DoS attack; This indicates the (n+1)th active period of a DoS attack; n is an integer greater than or equal to 0, for example: n=0,1,2….;
[0075] … , , This indicates a point in time or a time step within a preset time range; for details, please refer to [link / reference]. Figure 2 ,like Figure 2 As shown: Within this preset time range, the first dormant period of a DoS attack starts from time [time value missing]. Beginning, from moment End; the first active period of a DoS attack begins at time [time missing]. Beginning, from moment End; and so on, the (n+1)th dormant period of a DoS attack begins at time [time]. Beginning, from moment End; the (n+1)th active period of the DoS attack begins at time [time]. Beginning, from moment End. It can be seen that DoS attacks exhibit an alternating pattern of "dormant period - active period"; the preset time range may include the dormant periods of multiple DoS attacks and the active periods of multiple DoS attacks.
[0076] Understandably, the minimum dormancy period for a DoS attack can be denoted as... The maximum dormancy period of a DoS attack can be denoted as... The dormancy period for DoS attacks ,satisfy The minimum active period of a DoS attack can be denoted as... The peak activity period of a DoS attack can be denoted as... For the active period of DoS attacks ,satisfy . and This means that a DoS attack cannot last too short (to fail to achieve its attack objective) or too long (to be easily detected); and since the capabilities of a DoS attacker are limited, the parameters... and Its existence is guaranteed.
[0077] It is worth noting that, , , and All can be rounded down, and the specific rounding method can be set by those skilled in the art as needed to better adapt to discrete linear cyber-physical systems; for example: You can round down. It can be rounded up.
[0078] Specifically, in the (n+1)th dormant period, the time range from the initial time of the doS attack's dormant period to the expiration of the minimum dormant period of the doS attack can be denoted as... That is In the (n+1)th dormant period, the time range from the expiration of the minimum dormant period of the DoS attack to the end of the dormant period of the DoS attack can be denoted as... That is In the (n+1)th active period, the active period during which the cyber-physical system suffers a DoS attack within the preset time range can be as described above. That is .
[0079] For example, the output of the controller model can be expressed by the following second formula:
[0080]
[0081] In the second formula, Used to indicate time The output of the controller model; This refers to a specific time within the preset time range; time This represents the time variable during the dormant period of the DoS attack; This represents the first gain of the controller model; This represents the second gain of the controller model; Used to indicate time The state estimate; Used to indicate time The estimated FDI attack quantity; , and The quantities are the same as those in the first formula above, and will not be repeated here.
[0082] In this embodiment, by configuring and determining the controller gain in segments according to the time characteristics of DoS attacks and compensating for FDI attacks, the controller model is adapted to control under DoS and FDI attacks, effectively suppressing the disturbance of the cyber-physical system by the attacks, ensuring that the output of the controller model always matches the stability requirements of the cyber-physical system, and further improving the stability of the linear physical system.
[0083] In some embodiments, the method further includes:
[0084] Based on the DoS attacks suffered by the cyber-physical system within the preset time range, construct a network attack model;
[0085] Based on the model of the cyber-physical system and the network attack model, construct an estimator model for the cyber-physical system;
[0086] The process of obtaining the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuators of the cyber-physical system includes:
[0087] Based on the model of the cyber-physical system and the estimator model, obtain the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuator of the cyber-physical system.
[0088] The network attack model is constructed based on the DoS attacks suffered by the cyber-physical system within the preset time range, as shown in the first formula.
[0089] The estimator of the cyber-physical system described in this application may also be referred to as the observer of the cyber-physical system; the estimator model of the cyber-physical system may also be referred to as the observer model of the cyber-physical system.
[0090] The model of the cyber-physical system can be a model of the cyber-physical system under FDI attack.
[0091] For example, the model of the cyber-physical system can be found in [reference needed]. Figure 2 And expressed by the following third formula:
[0092]
[0093] In the third formula, Used to indicate time The next step is the state variables of the linear cyber-physical system; Used to indicate time The state variables of the linear cyber-physical system; Used to indicate time The input quantities of the linear cyber-physical system; Used to indicate time The amount of FDI attacks suffered by the actuators of the linear cyber-physical system; Used in time The disturbance amount of the linear cyber-physical system; Used to indicate time The output of the linear cyber-physical system; Used to indicate time The amount of FDI attacks suffered by the sensors of the linear cyber-physical system; , , and These represent the system matrices of the linear cyber-physical system, respectively. and Related, it can be the state transition matrix; and( Related, it can be an input matrix; and Correlation can be a perturbation matrix; and The correlation can be the output matrix; It can be with The relevant constant matrix can be specifically derived from... And the characteristics of the linear cyber-physical system itself are determined.
[0094] For example, the estimator model of the cyber-physical system can be constructed using the first formula and the third formula, based on the model of the cyber-physical system and the network attack model.
[0095] Specifically, the estimator model of the cyber-physical system can be represented by the following fourth formula:
[0096]
[0097] In the fourth formula, Used to indicate time The next step is the first observation state quantity of the linear cyber-physical system; Used to indicate time The first observed state quantity of the linear cyber-physical system; Used to indicate time The next step is the second observation state quantity of the linear cyber-physical system; Used to indicate time The first observation state quantity of the linear cyber-physical system;
[0098] Used to indicate time The amount of FDI attacks suffered by the actuators of the linear cyber-physical system; Used to indicate time The amount of FDI attacks suffered by the sensors of the linear cyber-physical system; Used to indicate time The state variables of the linear cyber-physical system; Used to indicate time The output of the linear cyber-physical system;
[0099] , , , and They are respectively , , , and The estimator; and it satisfies, ; This indicates an adjustable parameter that can be set as needed by those skilled in the art;
[0100] and It is the estimator gain of the estimator model of the cyber-physical system, where Let the first-type gain of the estimator satisfy:
[0101]
[0102] The second-type gain of the estimator satisfies:
[0103]
[0104] in, , , , and The coefficients are the same as those in the first and second formulas above, and will not be repeated here; and They represent in and The first type gain of the estimator under the following conditions; and They represent in and The second type gain of the estimator under the following conditions;
[0105] The estimator gain of the estimator model of the cyber-physical system can also be represented in matrix form, including:
[0106] The first gain matrix of the estimator: And the second gain matrix of the estimator: ;
[0107] The remaining coefficients satisfy the following relationship:
[0108] , , , , , , , , , , , , , Among them, the coefficient , , , and The corresponding coefficients are the same as those in the third formula above, and will not be repeated here; matrix Represents an identity matrix of a preset dimension, used to expand the dimensions of the corresponding matrix.
[0109] In this embodiment, a network attack model is constructed based on the DoS attacks suffered by the cyber-physical system within the preset time range. Combined with the cyber-physical system model, an estimator model for the cyber-physical system is constructed. This estimator model can accurately estimate system state variables and actuator FDI attack volume during the dormant period of a DoS attack, providing a basis for determining the controller model and improving the stability of the cyber-physical system under mixed DoS and FDI attack scenarios.
[0110] In some embodiments, the method further includes:
[0111] Based on the estimator model, an augmented error model of the cyber-physical system is constructed. Based on the augmented error model and the model of the cyber-physical system, a closed-loop cyber-physical system model of the cyber-physical system under the DoS attack and the FDI attack is constructed.
[0112] The first gain and the second gain of the controller are obtained based on the stable operating conditions of the closed-loop cyber-physical system model.
[0113] For example, the augmented error model can be expressed by the following fifth formula:
[0114]
[0115] In the fifth formula, Used to indicate time The next step is to augment the error of the cyber-physical system; Used to indicate time The augmentation error of the cyber-physical system;
[0116] It can be the first gain matrix of the estimator corresponding to the fourth formula above. It can be the second gain matrix of the estimator corresponding to the fourth formula above;
[0117] coefficient and It can be the same as the corresponding coefficient in the third formula. It can be the perturbation quantity of the corresponding linear cyber-physical system in the third formula;
[0118] matrix Represents an identity matrix of a preset dimension, used to expand the dimensions of the corresponding matrix; These can be the adjustable parameters corresponding to those in the fourth formula above; coefficients , , , , , , and , can be the quantity corresponding to the fourth formula above; , , , and The coefficients are the same as those in the first and second formulas above, and will not be repeated here;
[0119] coefficient Sum of coefficients The fifth formula has been redefined, specifically: , ;
[0120] In the fifth formula, the remaining coefficients and quantities satisfy the following relationship:
[0121] ,in: , ;and, ;
[0122] , , , .
[0123] For example, the closed-loop cyber-physical system model of the cyber-physical system can be represented by the following sixth formula:
[0124]
[0125] In the sixth formula, , , , and The coefficients are the same as those in the first and second formulas above; and The quantity is the same as the one in the second formula above. Used to indicate time The state estimate, This represents the first gain of the controller model. The second gain of the controller model is represented by the coefficient. , and The corresponding coefficients are the same as those in the third formula above; , and The quantities are the same as those in the third formula; where, Used to indicate time The next step is the state variables of the linear cyber-physical system. Used to indicate time The state variables of the linear cyber-physical system. Used in time The disturbance amount of the linear cyber-physical system; The quantity is the same as the corresponding quantity in the fifth formula above; and it satisfies the following relationship: .
[0126] In this embodiment, the augmentation error of the cyber-physical system (including the error of the state quantity and the error of the FDI attack quantity) is incorporated into the augmentation model; and combined with the CPS model, a closed-loop cyber-physical system model covering DoS and FDI attacks is constructed; based on the stable operating conditions of the closed-loop cyber-physical system model (e.g., the Lyapunov function stability judgment criteria described later), the first gain and the second gain of the controller are determined, so that the first gain and the second gain adapt to the disturbance characteristics of the composite attack scenario, thereby making the augmentation error model and the closed-loop cyber-physical system model converge to a bounded range, improving the stability of the cyber-physical system.
[0127] In some implementations, obtaining the first gain and the second gain of the controller based on the stable operating conditions of the closed-loop cyber-physical system model includes:
[0128] Based on the first Lyapunov function constructed by the DoS attack and the stable operating conditions of the closed-loop cyber-physical system model, the first gain and the second gain of the controller are obtained.
[0129] For example, the first Lyapunov function constructed by the DoS attack can be seen in the following formula:
[0130]
[0131] The parameter i = 1 or 2 is used to distinguish the first Lyapunov function and the corresponding network attack model in different states;
[0132] The first Lyapunov function corresponding to a DoS attack can also be denoted as... To distinguish the first Lyapunov function in different time periods; Used to indicate time The state variables of the cyber-physical system; Specifically as follows:
[0133]
[0134] or,
[0135]
[0136] in, , , , and The coefficients are the same as those in the first and second formulas above; , and , respectively representing time , and DoS attack volume;
[0137] in, , , and , respectively with , , and equivalence.
[0138] Furthermore, through derivation, the conditions for the stable operation of the system can be obtained as follows:
[0139]
[0140]
[0141]
[0142]
[0143]
[0144] And includes:
[0145] in, , , , , , , , , , , All three are arbitrary scalars that satisfy the conditions; positive definite matrix , sum matrix The matrix to be solved is given, and the controller gain can be obtained. , ;
[0146] As mentioned above, where, , , and , respectively with , , and equivalence; , and These represent matrices related to the state variables of the cyber-physical system and / or the DoS attack volume and / or FDI attack volume at the corresponding time.
[0147] in," " represents a placeholder for any element; and The quantity is the same as that in the first formula; that is, the minimum dormancy period for a DoS attack can be denoted as... The peak activity period of a DoS attack can be denoted as... ;matrix Represents an identity matrix of a preset dimension; and They are the same as the corresponding coefficients in the sixth formula.
[0148] In this embodiment, by introducing the Lyapunov stability condition and DoS attack characteristics, and under the stable operating conditions of the closed-loop cyber-physical system model, the first gain and the second gain are determined. This ensures that the obtained first gain and second gain can guarantee the stable operation of the cyber-physical system even when subjected to a DoS attack, further improving the stability of the cyber-physical system.
[0149] In some implementations, constructing an estimator model for the cyber-physical system based on the model of the cyber-physical system and the network attack model includes:
[0150] Determine the estimator gain based on the stable operating conditions of the augmented error model;
[0151] Based on the estimator gain, the cyber-physical system model, and the network attack model, an estimator model for the cyber-physical system is constructed.
[0152] For example, to ensure the stable operation of the elastic augmentation error system, a second Lyapunov function corresponding to a DoS attack is proposed, as shown in the following formula:
[0153]
[0154] The parameter i = 1 or 2 is used to distinguish the second Lyapunov function and the corresponding network attack model in different states;
[0155] The second Lyapunov function corresponding to a DoS attack can also be denoted as... To distinguish the second Lyapunov function in different time periods; Used to indicate time The augmentation error of the cyber-physical system; Specifically as follows:
[0156]
[0157] or,
[0158] .
[0159] in, , , , and The coefficients are the same as those in the first and second formulas above; , and , respectively representing time , and DoS attack volume;
[0160] Furthermore, through derivation, the conditions for the stable operation of the system can be obtained as follows:
[0161]
[0162]
[0163]
[0164]
[0165]
[0166] And includes: ;
[0167] in, , , , , , , , , , The three are any scalars that satisfy the conditions, and positive definite matrices. , sum matrix Let be the matrix to be solved. Based on the linear matrix inequalities and the conditions for the stable operation of the elastic augmentation error system, the estimator gain can be calculated. , ;
[0168] in," " represents a placeholder for any element; and The quantity is the same as that in the first formula; that is, the minimum dormancy period for a DoS attack can be denoted as... The peak activity period of a DoS attack can be denoted as... ; , and The coefficients are the same as those in the fifth formula; matrix Represents an identity matrix of a preset dimension.
[0169] In this embodiment, the estimator gain is determined based on the stable operating conditions of the augmented error model, and then the estimator model of the cyber-physical system is constructed, which can improve the stability of the cyber-physical system in the presence of DoS attacks and / or FDI mixed attacks.
[0170] In some implementations, please refer to Figure 4 , Figure 4 This is a schematic diagram of the overall flow of a system control method provided in an embodiment of this application, such as... Figure 4 As shown, the system control method includes:
[0171] Based on the model of the cyber-physical system with actuators and sensors under FDI attack, and considering DoS attack, an estimator model of the cyber-physical system is constructed, and the augmented error system is further obtained.
[0172] Based on the stable operating conditions of the augmented error system, the estimator gain is further obtained; and a closed-loop cyber-physical system model of the cyber-physical system is constructed. Based on the stable operating conditions of the closed-loop cyber-physical system model, the first gain and the second gain of the control are further obtained.
[0173] Based on the first gain, the second gain, and the estimator model described above, a controller model is constructed, and the cyber-physical system is controlled using the controller model.
[0174] In this embodiment, in the presence of FDI and DoS attacks, both the augmented error system and the closed-loop cyber-physical model are made to meet stable operating conditions. Then, a controller model is constructed to control the cyber-physical system and improve its stability.
[0175] It should be noted that the system control method described above can be executed by an electronic device, that is, all steps included in the above method are executed by the electronic device, which can be an electronic device such as a server, computer or mobile phone.
[0176] See Figure 5 , Figure 5 This is a schematic diagram of the structure of a system control device provided in an embodiment of this application, as shown below. Figure 5 As shown, the system control device 500 includes:
[0177] The acquisition module 501 is used to acquire the minimum dormancy period of a cyber-physical system suffering a denial-of-service (DoS) attack within a preset time range, and to acquire the state estimate of the cyber-physical system and the estimate of the spoofed data injection (FDI) attack suffered by the actuator of the cyber-physical system during the dormancy period of the DoS attack.
[0178] The first processing module 502 is used to construct a controller model of the cyber-physical system based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate.
[0179] The execution module 503 is used to control the controlled system according to the controller model.
[0180] Optionally, the system control device 500 may also include one of the following:
[0181] The second processing module 504 is used to obtain a first gain of the controller model within the time range from the initial moment of the doS attack's dormancy period to the expiration of the minimum dormancy period of the DoS attack, determine a first intermediate quantity based on the negative value of the product of the first gain and the state estimate, and determine the output quantity of the controller model based on the difference between the first intermediate quantity and the FDI attack estimate.
[0182] The third processing module 505 is used to obtain the second gain of the controller model within the time range from the expiration of the minimum dormancy period of the DoS attack to the end of the dormancy period of the DoS attack, determine the second intermediate quantity based on the negative value of the product of the second gain and the state estimate, and determine the output quantity of the controller model based on the difference between the second intermediate quantity and the FDI attack estimate.
[0183] The fourth processing module 506 is used to determine the output of the controller model based on the negative value of the FDI attack estimate during the active period of the DoS attack on the cyber-physical system within the preset time range.
[0184] The output of the controller model is used to control the controlled system.
[0185] Optionally, the system control device 500 may further include: a fifth processing module 507;
[0186] The fifth processing module 507 is used to construct a network attack model based on the DoS attacks suffered by the cyber-physical system within the preset time range;
[0187] Based on the model of the cyber-physical system and the network attack model, construct an estimator model for the cyber-physical system;
[0188] The process of obtaining the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuators of the cyber-physical system includes:
[0189] Based on the model of the cyber-physical system and the estimator model, obtain the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuator of the cyber-physical system.
[0190] Optionally, the system control device 500 may further include: a sixth processing module 508;
[0191] The sixth processing module 508 is used to construct an augmented error model of the cyber-physical system based on the estimator model, and to construct a closed-loop cyber-physical system model of the cyber-physical system under the DoS attack and the FDI attack based on the augmented error model and the model of the cyber-physical system.
[0192] The first gain and the second gain of the controller are obtained based on the stable operating conditions of the closed-loop cyber-physical system model.
[0193] Optionally, obtaining the first gain and the second gain of the controller based on the stable operating conditions of the closed-loop cyber-physical system model includes:
[0194] Based on the first Lyapunov function constructed by the DoS attack and the stable operating conditions of the closed-loop cyber-physical system model, the first gain and the second gain of the controller are obtained.
[0195] Optionally, constructing the estimator model of the cyber-physical system based on the model of the cyber-physical system and the network attack model includes:
[0196] Determine the estimator gain based on the stable operating conditions of the augmented error model;
[0197] Based on the estimator gain, the cyber-physical system model, and the network attack model, an estimator model for the cyber-physical system is constructed.
[0198] The system control device 500 is capable of implementing each process of the above-described system control method embodiments. The technical features are one-to-one and can achieve the same technical effect. To avoid repetition, it will not be described again here.
[0199] This application also provides an electronic device, including: a processor, a memory, and a program stored in the memory and executable on the processor. When the program is executed by the processor, it implements the various processes of the above-described system control method embodiments and achieves the same technical effects. To avoid repetition, it will not be described again here.
[0200] For details, see Figure 6This application also provides an electronic device, including a bus 601, a transceiver 602, an antenna 603, a bus interface 604, a processor 605, and a memory 606.
[0201] The transceiver 602 is used to obtain the minimum dormancy period of a cyber-physical system under a denial-of-service (DoS) attack within a preset time range, and to obtain the state estimate of the cyber-physical system and the estimate of the spoofed data injection (FDI) attack suffered by the actuator of the cyber-physical system during the dormancy period of the DoS attack.
[0202] Processor 605 is configured to construct a controller model of the cyber-physical system based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate.
[0203] The controlled system is controlled according to the controller model.
[0204] Optionally, the processor 605 is also used for one of the following:
[0205] Within the time range from the initial moment of the DoS attack's dormancy period to the expiration of the minimum dormancy period of the DoS attack, the first gain of the controller model is obtained; based on the negative value of the product of the first gain and the state estimate, a first intermediate quantity is determined; and based on the difference between the first intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined.
[0206] Within the time range from the expiration of the minimum dormancy period of the DoS attack to the end of the dormancy period of the DoS attack, the second gain of the controller model is obtained; based on the negative value of the product of the second gain and the state estimate, the second intermediate quantity is determined; and based on the difference between the second intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined.
[0207] During the active period of the DoS attack on the cyber-physical system within the preset time range, the output of the controller model is determined based on the negative value of the FDI attack estimate.
[0208] The output of the controller model is used to control the controlled system.
[0209] Optionally, the processor 605 is also configured to construct a network attack model based on the DoS attacks suffered by the cyber-physical system within the preset time range;
[0210] Based on the model of the cyber-physical system and the network attack model, construct an estimator model for the cyber-physical system;
[0211] The process of obtaining the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuators of the cyber-physical system includes:
[0212] Based on the model of the cyber-physical system and the estimator model, obtain the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuator of the cyber-physical system.
[0213] Optionally, the processor 605 is further configured to construct an augmented error model of the cyber-physical system based on the estimator model, and to construct a closed-loop cyber-physical system model of the cyber-physical system under the DoS attack and the FDI attack based on the augmented error model and the model of the cyber-physical system.
[0214] The first gain and the second gain of the controller are obtained based on the stable operating conditions of the closed-loop cyber-physical system model.
[0215] Optionally, obtaining the first gain and the second gain of the controller based on the stable operating conditions of the closed-loop cyber-physical system model includes:
[0216] Based on the first Lyapunov function constructed by the DoS attack and the stable operating conditions of the closed-loop cyber-physical system model, the first gain and the second gain of the controller are obtained.
[0217] Optionally, constructing the estimator model of the cyber-physical system based on the model of the cyber-physical system and the network attack model includes:
[0218] Determine the estimator gain based on the stable operating conditions of the augmented error model;
[0219] Based on the estimator gain, the cyber-physical system model, and the network attack model, an estimator model for the cyber-physical system is constructed.
[0220] exist Figure 6In this document, a bus architecture (represented by bus 601) is used. Bus 601 may include any number of interconnected buses and bridges, linking various circuits including one or more processors represented by processor 605 and memory represented by memory 606. Bus 601 may also link various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. Bus interface 604 provides an interface between bus 601 and transceiver 602. Transceiver 602 may be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by processor 605 is transmitted over a wireless medium via antenna 603, which further receives data and transmits data to processor 605.
[0221] Processor 605 manages bus 601 and general processing, and also provides various functions, including timing, peripheral interface, voltage regulation, power management, and other control functions. Memory 606 can be used to store data used by processor 605 during operation.
[0222] Optionally, the processor 605 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a complex programmable logic device (CPLD).
[0223] This application also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the various processes of the above-described system control method embodiments and achieves the same technical effects. To avoid repetition, it will not be described again here. The computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc.
[0224] This application also provides a computer program product, including computer instructions. When these computer instructions are executed by a processor, they implement the various processes of the above-described system control method embodiments and achieve the same technical effects. To avoid repetition, they will not be described again here.
[0225] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.
[0226] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.
[0227] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.
Claims
1. A system control method, characterized in that, The method includes: Obtain the minimum dormancy period of a cyber-physical system under a denial-of-service (DoS) attack within a preset time range, and obtain the state estimate of the cyber-physical system and the estimate of the FDI (fictitious data injection) attack suffered by the actuators of the cyber-physical system during the dormancy period of the DoS attack. Based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate, a controller model for the cyber-physical system is constructed. The controlled system is controlled according to the controller model.
2. The method according to claim 1, characterized in that, The method also includes the following: Within the time range from the initial moment of the DoS attack's dormancy period to the expiration of the minimum dormancy period of the DoS attack, the first gain of the controller model is obtained; based on the negative value of the product of the first gain and the state estimate, a first intermediate quantity is determined; and based on the difference between the first intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined. Within the time range from the expiration of the minimum dormancy period of the DoS attack to the end of the dormancy period of the DoS attack, the second gain of the controller model is obtained; based on the negative value of the product of the second gain and the state estimate, the second intermediate quantity is determined; and based on the difference between the second intermediate quantity and the FDI attack estimate, the output quantity of the controller model is determined. During the active period of the DoS attack on the cyber-physical system within the preset time range, the output of the controller model is determined based on the negative value of the FDI attack estimate. The output of the controller model is used to control the controlled system.
3. The method according to claim 2, characterized in that, The method further includes: Based on the DoS attacks suffered by the cyber-physical system within the preset time range, construct a network attack model; Based on the model of the cyber-physical system and the network attack model, construct an estimator model for the cyber-physical system; The process of obtaining the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuators of the cyber-physical system includes: Based on the model of the cyber-physical system and the estimator model, obtain the state estimate of the cyber-physical system during the dormancy period of the DoS attack and the FDI attack estimate suffered by the actuator of the cyber-physical system.
4. The method according to claim 3, characterized in that, The method further includes: Based on the estimator model, an augmented error model of the cyber-physical system is constructed. Based on the augmented error model and the model of the cyber-physical system, a closed-loop cyber-physical system model of the cyber-physical system under the DoS attack and the FDI attack is constructed. The first gain and the second gain of the controller are obtained based on the stable operating conditions of the closed-loop cyber-physical system model.
5. The method according to claim 4, characterized in that, The step of obtaining the first gain and the second gain of the controller based on the stable operating conditions of the closed-loop cyber-physical system model includes: Based on the first Lyapunov function constructed by the DoS attack and the stable operating conditions of the closed-loop cyber-physical system model, the first gain and the second gain of the controller are obtained.
6. The method according to claim 4, characterized in that, The step of constructing an estimator model for the cyber-physical system based on the model of the cyber-physical system and the network attack model includes: Determine the estimator gain based on the stable operating conditions of the augmented error model; Based on the estimator gain, the cyber-physical system model, and the network attack model, an estimator model for the cyber-physical system is constructed.
7. A system control device, characterized in that, The device includes: The acquisition module is used to acquire the minimum dormancy period of a cyber-physical system under a denial-of-service (DoS) attack within a preset time range, and to acquire the state estimate of the cyber-physical system and the estimate of the spoofed data injection (FDI) attack suffered by the actuators of the cyber-physical system during the dormancy period of the DoS attack. The first processing module is used to construct a controller model of the cyber-physical system based on the dormancy period of the DoS attack, the minimum dormancy period of the DoS attack, the state estimate, and the FDI attack estimate. The execution module is used to control the controlled system according to the controller model.
8. An electronic device, characterized in that, include: A processor, a memory, and a program stored in the memory and executable on the processor, wherein the program, when executed by the processor, implements the steps of the method as described in any one of claims 1 to 6.
9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 6.
10. A computer program product, characterized in that, Includes computer instructions that, when executed by a processor, implement the steps of the method as described in any one of claims 1 to 6.