Elastic random model prediction control method and system for resisting FDI attack
By introducing an adaptive input reconstruction mechanism and random control method in elastic MPC, the prediction time domain and control input are dynamically adjusted, and the problem of FDI attacks and system uncertainty is solved, and the stable operation of the system and the optimization of control performance is achieved. .
Patent Information
- Application Number
- CN202411584279.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-07
- Publication Date
- 2025-02-14
AI Technical Summary
The prior art fails to effectively handle system uncertainty in the elastic MPC that resists FDI attacks, resulting in too conservative control strategies and it is difficult to achieve optimal performance of the system.
A flexible random model prediction control method based on adaptive input reconstruction is proposed. By determining the controlled system model and FDI attack model, the relevant data is calculated and the controller is initialized, and the prediction time domain and control input are dynamically adjusted to resist FDI attacks and Handle system uncertainty.
This method can ensure the stable operation of the system and optimize the control performance when facing FDI attacks, reduce the conservatism of existing elastic MPCs, and improve the robustness and security of the system.
Smart Images
Figure CN119439744A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of computer control technology, and in particular to a flexible random model predictive control method and system for resisting FDI attacks. Background Art
[0002] With the rapid development of information science and technology, the Cyber-Physical System (CPS), which is the result of the deep integration of industrialization and informatization, has become the core technology that supports and leads the transformation of the new generation of industries. CPS is an advanced intelligent system that integrates computer, communication and control technologies, and is widely used in key infrastructure such as smart grids, smart transportation, and smart cities. Model Predictive Control (MPC) is an advanced computer control technology that predicts the future response of a system by using an explicit process model. Based on the system model and historical information, MPC obtains a series of control inputs at each sampling moment by solving an optimal control problem (OCP) with input\output constraints, and then applies the first control sequence obtained to the controlled system to complete the control action, and repeats the above process at the next sampling moment to achieve rolling optimization. Therefore, MPC is also called backward time domain control. Under such a rolling optimization mechanism, MPC can not only ensure that the state of the controlled system and the input constraints are met, but also maintain the CPS in the optimal state. Therefore, MPC is widely used as a decision module in key CPS facilities such as intelligent driving, smart grids, and smart cities.
[0003] However, since CPS needs to realize real-time data sharing between the physical layer and the control layer through wireless networks, the controlled system is extremely vulnerable to network attacks. Currently, frequent network attacks include false data injection (FDI) attacks, replay attacks, and denial-of-service (DoS) attacks. Among them, FDI attacks have attracted much attention in recent years because they can not only directly jump from the network layer to the physical layer to destroy the performance of CPS, but also have certain hidden characteristics. Therefore, there is an urgent need to develop resilient MPC methods to resist the damage of FDI attacks to CPS.
[0004] In addition to cyber attacks, system uncertainty is another major challenge facing CPS, because almost all systems under actual control are affected by uncertainty, such as interference and noise. In order to deal with the uncertainty of CPS and FDI attacks at the same time, robust control methods have been widely used in resilient MPC. Robust control methods aim to ensure that the control strategy is effective for all possible uncertainties by considering the worst case of model uncertainty. It is worth noting that robust control methods do not fully consider the uncertainty information of the system, so robust control methods may lead to extremely conservative or even infeasible designs of MPC. Compared with robust control methods, stochastic control methods only ensure that system constraints are satisfied under certain probability conditions by considering the probabilistic characteristics of uncertainty distribution. Therefore, compared with robust control methods, stochastic control methods can reduce the conservatism brought by hard constraints, thereby reducing operating costs while ensuring system performance. However, in the resilient MPC against FDI attacks, stochastic control methods have not been considered to deal with system uncertainties. Therefore, in order to reduce the conservatism of existing resilient MPC methods, it is necessary to propose a resilient stochastic model predictive control method based on adaptive input reconstruction. Summary of the invention
[0005] In order to overcome the defects of the above-mentioned prior art, the purpose of the present invention is to provide a resilient stochastic model predictive control method and system for resisting FDI attacks, so as to solve the technical problem of how to deal with the uncertainty of the system when resisting FDI attacks in the resilient MPC in the prior art.
[0006] The present invention is achieved through the following technical solutions: In a first aspect, the present invention provides a resilient stochastic model predictive control method for resisting FDI attacks, comprising: Determine the controlled system model and the FDI attack model, and calculate the relevant data of the elastic random model predictive control according to the determined controlled system model and the FDI attack model, wherein the relevant data includes the adjustment parameters , positive definite weight matrix , stage cost function and constraint parameters and terminal sets ; Initialize the controller update time according to the relevant data of the elastic stochastic model predictive control , and the initial state of the controlled system model Sampling is performed to determine the initial prediction time domain , obtain key reconstruction parameters and key information ; Determine the next update time through the adaptive prediction time domain update mechanism Prediction time domain , and key information Transmit to the reconstructor; The reconstructor reconstructs the mechanism and key information based on the input Reconstructing control input , and the state of the controlled system model Take samples and get key information Transmitting critical information to the controller and update the controller's update time, so , completing a working cycle of resilient stochastic model predictive control for defending against FDI attacks.
[0007] Preferably, the expression of the controlled system model is as follows:
[0008] in, is discrete time; and are the system state and control input respectively; is the system decision variable; is a random disturbance; is the system dynamic matrix; is the input matrix, is the feedback matrix; The FDI attack model expression is as follows:
[0009] in, is the decision variable actually received by the controlled system; The state of the system after being attacked; and False data injected from controller to actuator and from sensor to controller respectively; Or 0 to indicate whether an attack occurred.
[0010] Preferably, the controller update time is initialized according to the relevant data of the elastic stochastic model predictive control In the steps, when Based on key information Online solution of the optimal control problem (OCP) with input reconstruction mechanism , where for the optimal control problem OCP Initialization settings, the expression is as follows:
[0011] ; in, Cost Function ; is the reconstruction interval; is the expectation symbol; Indicates a constraint symbol; is the sampling time; is the prediction step length; is the stage cost function; is the nominal state of the system; [1, ] is the adjustment parameter; is a system opportunity constraint; and [0, ]; is the system dynamic matrix; The system at the sampling moment Actual status; is a set of integers, middle is the state coefficient vector, Represents the vector transpose symbol.
[0012] Preferably, the optimal control problem OCP The solution expression is as follows: ; in, To ensure the deterministic constraints that hold true for the chance constraints; is the reconstruction interval; For the prediction time domain; represents the empty set; It means that under the deterministic constraint, the reconstruction interval is Minimize the cost function; represents the minimization cost function with a reconstruction interval of 1 under deterministic constraints; To take the maximum value symbol; For the The optimal reconstruction interval of times; For Under the constraint of The optimal decision variable obtained when .
[0013] Furthermore, constraints The formula is as follows:
[0014] In the formula, are the decision variables obtained by solving the optimal control problem; is the Shure matrix; is the slope of the decision variable; For the Step prediction time The weight coefficient of For the Step prediction time The weight coefficient of is the chance constraint value that the system needs to satisfy; is a deterministic constraint parameter; Prediction time domain; For terminal sets.
[0015] Preferably, the expression of the input reconstruction mechanism is as follows:
[0016] in, is the reconstruction interval; and define ; is the reconstructed decision variable; is the reconstructed control input.
[0017] Preferred, key information and The expression is as follows:
[0018] in, is the reconstruction interval; and is the key decision variable; Critical system status.
[0019] Preferably, the adaptive prediction time domain update mechanism dynamically adjusts the prediction time domain according to the operating state of the controlled system model and / or the impact of the FDI attack .
[0020] Preferably, the next update time is determined by an adaptive prediction time domain update mechanism Prediction time domain In the step, the adaptive prediction time domain update mechanism expression is as follows:
[0021] in, is the reconstruction interval; Ensure that the prediction horizon changes with the reconstruction interval; To take the minimum symbol; To remove the lower bound symbol; Ensure nominal terminal state The terminal constraints are still met; for The prediction time domain of the moment; The reconstruction interval is Terminal constraints when is the terminal time step.
[0022] In a second aspect, the present invention also provides a system for resisting FDI attacks based on input reconstruction elastic random model predictive control, comprising: The first processing module is used to determine the controlled system model and the FDI attack model, and calculate the relevant data of the elastic random model predictive control according to the determined controlled system model and the FDI attack model, wherein the relevant data includes the adjustment parameters , positive definite weight matrix , stage cost function and constraint parameters and terminal sets ; The second processing module is used to initialize the update time of the controller according to the relevant data of the elastic random model predictive control , and the initial state of the controlled system model Sampling is performed to determine the initial prediction time domain , obtain key reconstruction parameters and key information ; The third processing module is used to determine the next update time through the adaptive prediction time domain update mechanism Prediction time domain , and key information Transmit to the reconstructor; The fourth processing module is used for the reconstructor to reconstruct the mechanism and key information based on the input Reconstructing control input , and the state of the controlled system model Take samples and get key information Transmitting critical information to the controller and update the controller's update time, so , completing a working cycle of resilient stochastic model predictive control for defending against FDI attacks.
[0023] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention provides a method for elastic random model predictive control for resisting FDI attacks. By determining the controlled system model and the FDI attack model, and calculating the relevant data of the elastic random model predictive control, the control system can still maintain stable operation when facing FDI attacks. Through the input reconstruction mechanism, the method can dynamically adjust the control input, thereby effectively resisting the interference caused by the FDI attack to the system, and improving the robustness and security of the system. The elastic random model predictive control can optimize the control performance by adjusting the parameters σ, the positive definite weight matrix Q, R and the stage cost function F. When facing FDI attacks, the method can ensure that the control performance of the system is optimized under the premise of satisfying the system constraints.
[0024] Furthermore, the present invention adopts an adaptive prediction time domain update mechanism, which can dynamically adjust the prediction time domain according to the actual operation of the system, thereby improving the adaptability and flexibility of the control system. The adaptive mechanism enables the control system to better cope with the uncertainty brought by FDI attacks and ensure the stable operation of the system.
[0025] Furthermore, by reconstructing the control input and sampling the system state through the reconstructor, this method can obtain the key information of the system in real time and adjust the control strategy accordingly; ensuring that the control system can respond quickly when facing FDI attacks and improving the reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] Figure 1 It is a flow chart of a resilient stochastic model predictive control method for resisting FDI attacks in an embodiment of the present invention; Figure 2 This is a structural diagram of a resilient stochastic MPC control system based on input reconstruction in an embodiment of the present invention; Figure 3 It is a state trajectory diagram of a closed-loop system controlled by elastic random MPC under FDI attack in an embodiment of the present invention; Figure 4 1 is a state trajectory diagram of a closed-loop system controlled by PSMPC in an embodiment of the present invention; wherein (a) is a schematic diagram of a FDI attack not being activated, and (b) is a schematic diagram of a FDI attack being activated; Figure 5 The simulation results of different control mechanisms under the same uncertain event in the embodiment of the present invention are shown in Figure 2. (a) is the comparison of state trajectories; (b) is the comparison of control inputs; (c) is the reconstruction interval of elastic random MPC ; (d) is the prediction time domain comparison. DETAILED DESCRIPTION
[0027] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.
[0028] The present invention is further described in detail below in conjunction with the accompanying drawings: The purpose of the present invention is to provide a resilient stochastic model predictive control method and system for resisting FDI attacks, so as to solve the technical problem of how to deal with the uncertainty of the system when resisting FDI attacks in the resilient MPC in the prior art.
[0029] Example 1 See also Figure 1 In one embodiment of the present invention, a resilient stochastic model predictive control method for resisting FDI attacks is provided, comprising: Step 1: determine the controlled system model and the FDI attack model, and calculate the relevant data of the elastic random model predictive control according to the determined controlled system model and the FDI attack model, wherein the relevant data includes the adjustment parameters , positive definite weight matrix , stage cost function and constraint parameters and terminal sets ; In this embodiment, the structure of the elastic random MPC control system based on input reconstruction is as follows: Figure 2 shown.
[0030] Specifically, the expression of the controlled system model is as follows:
[0031] in, is discrete time; and are the system state and control input respectively; is the system decision variable; is a random disturbance; is the system dynamic matrix; is the input matrix, is the feedback matrix; The FDI attack model expression is as follows:
[0032] in, is the decision variable actually received by the controlled system; The state of the system after being attacked; and False data injected from controller to actuator and from sensor to controller respectively; Or 0 to indicate whether an attack occurred.
[0033] when hour, ,otherwise .
[0034] in, and denote the set of non-negative integers and the set of real numbers respectively. and Description Euclidean space and dimension real matrix. Given a non-negative integer and satisfy , , and Respectively represent sets , and . Given a real number and satisfy , , and Respectively represent sets , and The zero matrix is defined as . Given a positive definite matrix ,vector of The norm is described as .event The probability is defined as , and its time The expectation is defined as .
[0035] In this embodiment is satisfied and an unknown additional disturbance with zero mean independent and identical distribution, where is the upper bound of disturbance.
[0036] The predictive control input is described as: , where the state feedback matrix By Shure Matrix design. And, when hour, is the optimal decision variable obtained by solving OCP. hour, .
[0037] The probability constraints that the controlled system needs to satisfy are: ,in, and is the probability constraint parameter.
[0038] In this embodiment, the constraint parameters Determined based on:
[0039] is calculated by:
[0040] In the formula, .
[0041] is calculated by: ; Calculated by ; is calculated by:
[0042] In the formula for , and For the satisfaction of being chosen The parameters divide the infinite time domain into a finite time domain.
[0043] is calculated by: , In the formula is any integer, Defined by . and This parameter is optional.
[0044] The stage cost function is , In the formula, Calculated by .
[0045] Step 2: Initialize the controller update time according to the relevant data of the elastic stochastic model predictive control , and the initial state of the controlled system model Sampling is performed to determine the initial prediction time domain , obtain key reconstruction parameters and key information ; Specifically, the controller update time is initialized according to the relevant data of the elastic stochastic model predictive control In the steps, when Based on key information Online solution of the optimal control problem (OCP) with input reconstruction mechanism , where for the optimal control problem OCP Initialization settings, the expression is as follows:
[0046]
[0047] in, Cost Function ; is the reconstruction interval; is the expectation symbol; Indicates a constraint symbol; is the sampling time; is the prediction step length; is the stage cost function; is the nominal state of the system; [1, ] is the adjustment parameter; is a system opportunity constraint; and [0, ]; is the system dynamic matrix; The system at the sampling moment Actual status; is a set of integers, middle is the state coefficient vector, Represents the vector transpose symbol.
[0048] Among them, the input reconstruction mechanism is described as:
[0049] in, is the reconstruction interval; and define ; is the reconstructed decision variable; is the reconstructed control input.
[0050] Among them, the optimal reconstruction interval Calculated by ; Specifically, the predictive control input is described as:
[0051] The key information is .
[0052] Among them, the actual solved OCP for
[0053] Among them, the constraints The formula is as follows:
[0054] In the formula, are the decision variables obtained by solving the optimal control problem, , , is a deterministic constraint parameter; Prediction time domain; For terminal sets.
[0055] Step 3: Determine the next update time through the adaptive prediction time domain update mechanism Prediction time domain , and key information Transmit to the reconstructor; Specifically, the adaptive prediction time domain update mechanism is expressed as:
[0056] in, is the reconstruction interval; Ensure that the prediction horizon changes with the reconstruction interval; To take the minimum symbol; To remove the lower bound symbol; Ensure nominal terminal state The terminal constraints are still met; for The prediction time domain of the moment; The reconstruction interval is Terminal constraints when is the terminal time step.
[0057] Step 4: The reconstructor reconstructs the mechanism and key information based on the input Reconstructing control input , and the state of the controlled system model Take samples and get key information Transmitting critical information to the controller and update the controller's update time, so , completing a working cycle of resilient stochastic model predictive control for defending against FDI attacks.
[0058] Specific, key information The expression is as follows:
[0059] In the formula, To reconstruct the interval, and is the key decision variable, Critical system status.
[0060] Among them, the adaptive prediction time domain update mechanism dynamically adjusts the prediction time domain according to the operating status of the controlled system model and / or the impact of FDI attacks ; Among them, the input reconstruction mechanism is described as:
[0061] In the formula, is the reconstruction interval.
[0062] In this embodiment, the following linearized DC-DC conversion system is considered: , In the formula, is the system status, For control input. is obtained by truncating the mean to 0 and the variance to The system under consideration needs to satisfy the probability constraint The state feedback matrix is calculated by the linear quadratic regulation method as The parameters of the FDI attack model without energy constraints are: ,and In other words, the FDI attack exists in the entire operation process of the controlled system. The parameters of the offline calculation are determined as: and ; Constraint parameters and terminal sets Calculated using the following parameters: and . The initialization parameters are: initial position , initial prediction time domain The entire operation step of the system is: , adjust the parameters In order to verify the effectiveness of the input-reconstruction-based elastic stochastic MPC method and system (hereinafter referred to as elastic stochastic MPC), a comparative verification was conducted with the periodically-triggered stochastic MPC (PSMPC) method.
[0063] Figure 3 and Figure 4 The results of 100 of the 2000 Monte Carlo experiments are randomly displayed. More specifically, Figure 3 The closed-loop trajectory of the system under resilient stochastic MPC control when the FDI attack is activated is shown. Figure 4 (a) is the closed-loop trajectory of the system under PSMPC control when the FDI attack is not activated. Figure 4 (b) shows the closed-loop trajectory of the system under PSMPC control when the FDI attack is activated. Note that to ensure the scientific validity of the simulation experiment, the defense resources consumed by PSMPC and elastic random MPC are the same when the FDI attack is activated. Table 1 records the average operating data of the system controlled by elastic random MPC and PSMPC in 2000 random experiments, including the prediction time domain, the number of OCP solutions, and the OCP solution time.
[0064] Defense effect: From Figure 3 It can be seen that under the control of elastic random MPC, the closed-loop system can operate stably under FDI attack without energy constraints. Figure 3 It can also be seen that the probability of the controlled system violating the constraint is 27:3%, which meets the preset probability constraint. Figure 4 (b) It can be seen that under PSMPC control, even if the same defense resources as those of elastic stochastic MPC are used, the convergence performance of the closed-loop system cannot be guaranteed when the system is attacked by FDI.
[0065] Resource saving: As shown in Table 1, elastic random MPC only needs to solve 11.2485 OCPs on average to ensure that the closed-loop system converges to a neighborhood of the origin, and the average solution time of OCP is only 0.0776s. Compared with PSMPC, due to the introduction of the adaptive input reconstruction mechanism, the OCP triggering frequency and average solution time of elastic random MPC are reduced by 37.51% and 17.62% respectively.
[0066] Table 1 Average running data of 2000 Monte Carlo experiments
[0067] To more clearly demonstrate the advantages of elastic stochastic MPC, Figure 5 The simulation results of different control mechanisms under the same uncertain events are given. Figure 5 In (a), (b), (c) and (d), the state trajectory, control input, reconstruction interval and prediction time domain are shown respectively. The solid line and dashed line are the simulation results of elastic stochastic MPC control and PSMPC control when the controlled system is attacked by FDI under the same defense resources. The dotted line is the simulation result of the PSMPC control system when the FDI attack is not activated. Figure 5 It can be seen that compared with PSMPC, elastic random MPC only needs to solve 10 OCPs to ensure the stability of the controlled system under FDI attack. However, once the PSMPC system is attacked by FDI, its stability cannot be guaranteed.
[0068] In addition, in this simulation experiment, when the system is attacked by FDI, the average time for elastic random MPC to solve OCP is 0.0926s, and the average time for PSMPC to solve OCP is 0.1921s. This is because Figure 5 As shown by the solid line in (d), the prediction horizon in elastic stochastic MPC can be continuously adjusted, thereby reducing the computational complexity of OCP.
[0069] Note that by Figure 3 and Figure 5 It can be seen that when the controlled system is attacked by FDI without energy constraints, the resilient random MPC still ensures that the controlled system converges to the neighborhood of the origin, which shows that the effectiveness of the developed algorithm is not affected by the energy of the FDI attack. Figure 3 It can be seen from Table 1 that since the controlled system constraints are satisfied in a probabilistic form, the conservatism of the existing elastic MPC due to hard constraints is reduced.
[0070] In summary, this embodiment provides a resilient random model predictive control method for resisting FDI attacks, which reduces the conservatism of the existing resilient MPC. The introduction of an adaptive input reconstruction mechanism in OCP not only reduces the assumptions of the existing resilient MPC about the FDI attack energy, but also reduces the solution frequency of OCP. The adaptive prediction time domain update mechanism and the terminal set are jointly designed to reduce the computational complexity of the developed algorithm. By converting fixed hard constraints into random constraints, the conservatism of the existing resilient MPC due to hard constraints is reduced.
[0071] Example 2 This embodiment also provides a system for resisting FDI attacks based on input reconstruction elastic random model predictive control, including: The first processing module is used to determine the controlled system model and the FDI attack model, and calculate the relevant data of the elastic random model predictive control according to the determined controlled system model and the FDI attack model, wherein the relevant data includes the adjustment parameters , positive definite weight matrix , stage cost function and constraint parameters and terminal sets ; The second processing module is used to initialize the update time of the controller according to the relevant data of the elastic random model predictive control , and the initial state of the controlled system model Sampling is performed to determine the initial prediction time domain , obtain key reconstruction parameters and key information ;.
[0072] The third processing module is used to determine the next update time through the adaptive prediction time domain update mechanism Prediction time domain , and key information Transmit to the reconstructor; The fourth processing module is used for the reconstructor to reconstruct the mechanism and key information based on the input Reconstructing control input , and the state of the controlled system model Take samples and get key information Transmitting critical information to the controller and update the controller's update time, so , completing a working cycle of resilient stochastic model predictive control for defending against FDI attacks.
[0073] 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 above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.
Claims
1. A resilient stochastic model predictive control method for resisting FDI attacks, characterized in that: include: Determine the controlled system model and the FDI attack model, and calculate the relevant data of the elastic random model predictive control according to the determined controlled system model and the FDI attack model, wherein the relevant data includes the adjustment parameters , positive definite weight matrix , stage cost function and constraint parameters and terminal sets ; Initialize the controller update time according to the relevant data of the elastic stochastic model predictive control , and the initial state of the controlled system model Sampling to determine the initial prediction time domain , obtain key reconstruction parameters and key information ; Determine the next update time through the adaptive prediction time domain update mechanism Prediction time domain , and key information Transmit to the reconstructor; The reconstructor reconstructs the mechanism and key information based on the input Reconstructing control input , and the state of the controlled system model Take samples and get key information Transmitting critical information to the controller and update the controller's update time, so , completing a working cycle of resilient stochastic model predictive control for defending against FDI attacks.
2. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 1, characterized in that: The expression of the controlled system model is as follows: in, is discrete time; and are the system state and control input respectively; is the system decision variable; is a random disturbance; is the system dynamic matrix; is the input matrix, is the feedback matrix; The FDI attack model expression is as follows: in, is the decision variable actually received by the controlled system; The state of the system after being attacked; and False data injected from controller to actuator and from sensor to controller respectively; Or 0 to indicate whether an attack occurred.
3. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 1, characterized in that: Initialize the controller update time according to the relevant data of the elastic stochastic model predictive control In the steps, when Based on key information Online solution of the optimal control problem (OCP) with input reconstruction mechanism , where for the optimal control problem OCP Initialization settings, the expression is as follows: ； in, Cost Function ; is the reconstruction interval; is the expectation symbol; Indicates a constraint symbol; is the sampling time; is the prediction step length; is the stage cost function; is the nominal state of the system; [1, ] is the adjustment parameter; is a system opportunity constraint; and [0, ]; is the system dynamic matrix; The system at the sampling moment Actual status; is a set of integers, middle is the state coefficient vector, Represents the vector transpose symbol.
4. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 1, characterized in that: The optimal control problem OCP The solution expression is as follows: ； in, To ensure the deterministic constraints that hold for chance constraints; is the reconstruction interval; For the prediction time domain; represents the empty set; It means that under the deterministic constraint, the reconstruction interval is Minimize the cost function; represents the minimization cost function with a reconstruction interval of 1 under deterministic constraints; To take the maximum value symbol; For the The optimal reconstruction interval of times; For Under the constraint of The optimal decision variable obtained when .
5. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 4, characterized in that: The constraints The formula is as follows: In the formula, are the decision variables obtained by solving the optimal control problem; is the Shure matrix; is the slope of the decision variable; For the Step prediction time The weight coefficient of For the Step prediction time The weight coefficient of is the chance constraint value that the system needs to satisfy; is a deterministic constraint parameter; Prediction time domain; For terminal sets.
6. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 1, characterized in that: The expression of the input reconstruction mechanism is as follows: in, is the reconstruction interval; and define ; is the reconstructed decision variable; is the reconstructed control input.
7. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 1, characterized in that: The key information and The expression is as follows: in, is the reconstruction interval; and is the key decision variable; Critical system status.
8. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 1, characterized in that: The adaptive prediction time domain update mechanism dynamically adjusts the prediction time domain according to the operating state of the controlled system model and / or the impact of the FDI attack .
9. The resilient stochastic model predictive control method for resisting FDI attacks according to claim 1, characterized in that: The next update time is determined by the adaptive prediction time domain update mechanism Prediction time domain In the step, the adaptive prediction time domain update mechanism expression is as follows: in, is the reconstruction interval; Ensure that the prediction horizon changes with the reconstruction interval; To take the minimum value symbol; To remove the lower bound symbol; Ensure nominal terminal state The terminal constraints are still met; for The prediction time domain of the moment; The reconstruction interval is Terminal constraints when is the terminal time step.
10. A system for resisting FDI attacks based on input reconstruction elastic random model predictive control, characterized in that: include: The first processing module is used to determine the controlled system model and the FDI attack model, and calculate the relevant data of the elastic random model predictive control according to the determined controlled system model and the FDI attack model, wherein the relevant data includes the adjustment parameters , positive definite weight matrix , stage cost function and constraint parameters and terminal sets ; The second processing module is used to initialize the update time of the controller according to the relevant data of the elastic random model predictive control , and the initial state of the controlled system model Sampling to determine the initial prediction time domain , obtain key reconstruction parameters and key information ; The third processing module is used to determine the next update time through the adaptive prediction time domain update mechanism Prediction time domain , and key information Transmit to the reconstructor; The fourth processing module is used for the reconstructor to reconstruct the mechanism and key information based on the input Reconstructing control input , and the state of the controlled system model Take samples and get key information Transmitting critical information to the controller and update the controller's update time, so , completing a working cycle of resilient stochastic model predictive control for defending against FDI attacks.