Network control system event trigger control method and device under DoS attack

Abstract

The invention discloses the field of wireless communication networks, and particularly relates to a network control system event trigger control method and device under DoS attacks. Comprising the following steps: S1, initializing a mathematical model of a network control system; s2, according to the mathematical model of the network control system, establishing a prediction model, setting constraint conditions, and solving an optimization result at each prediction moment; s3, detecting random disturbance, and monitoring the state of a communication link; s4, on the basis of an event triggering mechanism, whether random disturbance triggers sampling of a network control system or not is judged; s5, updating the control input of the network control system according to the optimization result of the prediction model when the sampling triggering condition is met; and S6, according to an optimization result, when the communication link is interrupted, compensating the network control system by adopting the predictive control sequence. By establishing the prediction model and the event triggering mechanism, the response speed and stability of the network control system under the DoS attack are effectively improved, the data sampling frequency can be optimized, and the energy consumption can be reduced.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication networks, and particularly to a method and device for event-triggered control of a network control system under a DoS attack. Background Art

[0002] As a main category of Cyber-physical Systems (CPS), Network control systems (NCSs) have been one of the research hotspots in the control field in recent years. The main advantages of NCSs include less wiring, low installation cost, easy maintenance, flexibility and reliability, etc. Therefore, the application of NCSs plays an important role in all aspects of real life and production, such as medical treatment, aerospace, process industry, vehicle engineering and power systems. The main structure of NCSs includes a controller, an actuator and a sensor, which are connected through a digital communication network. The digital communication network can be a Controller Area Network (CAN), BACnet, fieldbus, existing Ethernet and Internet. The communication quality between the components of the network control system plays a decisive role in the control performance of the system.

[0003] In the face of malicious attacks such as spoofing attacks, False-Data Injection (FDI) and Denial of Service (DoS) attacks, it is very necessary to design an effective control algorithm to ensure the security and stability of the network control system. Malicious attackers can inject a large amount of redundant data to occupy storage, computing units and physical units, thereby destroying the stable operation of the network control system under a DoS attack. In addition, data transmission can be interrupted by a communication link in the middle, resulting in control instructions for the controller and the actuator, thus causing the information between the components of the network control system to be completely asynchronous, resulting in a decline in control performance and even paralysis of the control system.

[0004] Y. Zhu and W. Zheng studied the DoS attacks with a fixed period in "Observer-based control for cyber-physical systems with periodic DoS attacks via a cyclic switching strategy". This method attacks the NCSs within a certain time period, causing the interruption of data transmission in the communication link and reducing the security of system control. Another type is the random constraint model, which means that the networked control system can be attacked at every instant. The common processing method for both models is to introduce Bernoulli variables to represent the DoS attack signal. Y. Deng et al. studied the time-limited DoS attacks in "Event-triggered predictive control for networked control systems with DoS attacks", that is, each active or dormant period of the DoS attack is different, but the frequency and duration of the DoS attack are active within a certain time period. The state information and control commands are asynchronous, and the update frequencies of both are very slow, so the stability of the system cannot be guaranteed, which poses a great challenge to the existing control methods. Most of the existing research on NCSs algorithms has drawbacks such as non-update of system control commands and state information, data freezing adopted by the system, system control input being zero, and the system belonging to an open-loop control system when suffering from DoS attacks.

[0005] To ensure the stability of the system, L. Qiu et al. adopted the model predictive control (MPC) method to calculate the predictive control commands and the corresponding state information in "Model predictive control for networked multiple linear motors system under DoS attack and time delay". Since MPC can handle both the physical constraints of the hardware and the uncertainties of system parameters and has strong robustness, MPC is an effective optimal control method and is widely used in NCSs.

[0006] In practical industrial applications, event-triggered control MPC is an effective method to save communication resources and has a trend of large-scale application in networked control systems. For example, event-triggered, self-triggered, adaptive event-triggered, and intermittent dynamic event-triggered. The characteristic of event-triggered control MPC is that when a certain performance exceeds a preset threshold, the system only samples or updates the control command. The biggest advantage of this method is that it can save communication resources in networked control systems, reduce the computational and hardware load of the system, and the risk of the communication network being attacked, but it cannot handle probabilistic constraints. For network security control under DoS attacks, the present invention not only considers the balance between system constraints and control performance, that is, the system is subject to probabilistic constraints, but also studies how to save communication costs, reduce unnecessary sampling, reduce the computational burden, and compensate the system with a certain predictive control sequence when the system is attacked, so that the system has better control performance. Summary of the Invention

[0007] The present invention provides an event-triggered control method for a networked control system under DoS attacks, which can optimize the control of networked control systems (NCSs) affected by random disturbances and DoS attacks, and obtain the technical effects of reducing communication resource consumption, improving system stability and robustness. During the operation of the networked control system, event-triggered sampling and control input optimization can be performed according to system states and disturbance information. By introducing an event-triggered mechanism to reduce the sampling frequency, transforming probabilistic constraints into second-order cone constraints to enhance the solution efficiency, and designing a predictive control compensation strategy to cope with communication link interruptions, the anti-attack ability and stability of the system can be improved while reducing communication overhead and computational burden, thereby ensuring the recursive feasibility and exponential mean-square stability of the system and meeting the technical requirements of actual engineering applications.

[0008] To achieve the above-mentioned invention objectives, the present invention provides the following technical solutions:

[0009] In a first aspect, the present embodiment provides an event-triggered control method for a networked control system under DoS attacks, including the following steps:

[0010] S1. Initialize the mathematical model of the networked control system;

[0011] S2. According to the mathematical model of the networked control system, establish a prediction model, set constraint conditions, and solve the optimization results at each prediction time;

[0012] S3. Detect random disturbances and monitor the state of the communication link;

[0013] S4. Based on the event-triggered mechanism, determine whether the random disturbances trigger the sampling of the networked control system;

[0014] S5. When the triggering condition for sampling is satisfied, update the control input of the network control system according to the optimization result of the prediction model;

[0015] S6. According to the optimization result, when the communication link is interrupted, use the predictive control sequence to compensate the network control system.

[0016] Preferably, the mathematical model of the network control system in step S1 is a discrete-time linear model, including a state equation, a control input, and a stochastic disturbance, which is represented by the following formula:

[0017] x t+1 =Ax t +Bu t +B d w t

[0018] Wherein, respectively represent the state vector, the control input, and the stochastic disturbance; t represents the discrete-time step, and n represents the dimension; and are known constant matrices.

[0019] In the above implementation, by describing the mathematical model of the network control system as a discrete-time linear model, the technical effects of improving the system prediction accuracy and control precision are achieved. The accurate mathematical model helps to reduce the deviation of the system in actual operation and ensure higher operation accuracy.

[0020] Preferably, step S2 includes solving the objective optimization problem; the objective of the optimization problem is to minimize the system state; the constraint conditions include state constraints and terminal constraints.

[0021] In the above implementation, by setting the objective optimization problem, the technical effect of minimizing the system state is achieved, and the overall performance and efficiency of the system are enhanced. This strategy reduces the waste of energy and resources by precisely controlling the operation of the system.

[0022] Preferably, the stochastic disturbance includes a DoS attack; the DoS attack is represented by a random variable, and different states of the communication link are represented based on the value of the random variable: when the value of the random variable is 0, it means being under a DoS attack, indicating that the communication link is interrupted; when the value of the random variable is 1, it means not being under a DoS attack, indicating that the communication link is normal.

[0023] In the above implementation, by defining the stochastic disturbance as a DoS attack and representing the communication link state with a random variable, the technical effect of accurately identifying and coping with network attacks is achieved. This definition enables the system to detect attacks more sensitively and respond quickly, thereby protecting network security.

[0024] Preferably, the event triggering mechanism includes the following steps:

[0025] S31. Calculate the difference between the current state of the control system and the most recent triggered state;

[0026] S32. When the difference exceeds a preset triggering threshold, trigger sampling and update the control input.

[0027] In the above implementation, by calculating the difference between the current state of the control system and the most recent triggered state, and triggering sampling and updating the control input based on the fact that this difference exceeds a preset threshold, the technical effect of enhancing the response ability of the networked control system is achieved. This not only improves the sensitivity of the system to environmental changes but also optimizes the resource utilization efficiency.

[0028] Preferably, the calculation of the difference in the event triggering mechanism is based on a triggering function calculation, and triggering parameters are preset to control the triggering frequency.

[0029] In the above implementation, by presetting triggering parameters to control the triggering frequency, the technical effect of optimizing the event triggering mechanism to reduce unnecessary system activities and resource consumption is achieved. Such a control strategy reduces the burden on the system and extends the service life of the device.

[0030] Preferably, when the communication link is interrupted, the networked control system compensates the control input using a predictive control sequence based on the LQR solution.

[0031] In the above implementation, when the communication link is interrupted, by compensating the control input using a predictive control sequence based on the LQR solution, the technical effect of ensuring the continued stable operation of the networked control system in an unstable network environment is achieved. This ensures that the system can still maintain efficient operation in the face of network instability.

[0032] Preferably, the probabilistic constraint in the optimization problem is transformed into a distributionally robust constraint through a distributionally robust optimization method and further into a convex optimization problem in the form of a second-order cone constraint.

[0033] In the above implementation, by transforming the probabilistic constraint in the optimization problem into a distributionally robust constraint and further forming a convex optimization problem, the technical effects of improving the optimization solution efficiency and system stability are achieved. This transformation enhances the feasibility of problem solving, making the solution more reliable and efficient.

[0034] Preferably, the recursive feasibility and exponential mean-square stability of the predictive model are achieved in the following way:

[0035] By restricting the feasible region of the state vector x t through the terminal constraint;

[0036] Verify the stability of the state of the network control system by using the Lyapunov function and dynamically adjust the optimization result.

[0037] In the above implementation manner, by restricting the feasible region of the state vector and dynamically adjusting the optimization result by using the Lyapunov function, the technical effects of ensuring the stability and recursive feasibility of the network control system under DoS attacks are achieved. Through these technical measures, the system can maintain a stable state during long-term operation and prevent performance degradation caused by parameter changes.

[0038] In a second aspect, the present embodiment provides an event-triggered control device for a network control system under DoS attacks. The device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method described in the above description is implemented.

[0039] In the above implementation manner, by implementing a device including a processor and a memory to run a computer program, the technical effects of automating the above method and improving the convenience and practicality of system operation are achieved. The automated process not only reduces errors in manual operations but also significantly improves the system's response speed and processing capacity.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] The present invention proposes an event-triggered control method for a network control system under DoS attacks, aiming to solve several defects and limitations in the prior art. Compared with the prior art, this method shows significant advantages in dealing with DoS attacks and the resulting random disturbances and communication link instabilities. First, by initializing the mathematical model of the network control system and establishing a prediction model, the present invention can set effective constraint conditions to prevent possible system performance degradation in advance, which is often lacking in traditional systems. Second, this method can monitor random disturbances and communication link states in real time and quickly respond to environmental changes, thereby reducing the negative impacts caused by information asynchronization. In addition, by introducing an event-triggered mechanism, this method only updates the control input when specific conditions are met, greatly reducing the frequency of data sampling and communication, optimizing resource usage, reducing energy consumption, and significantly improving the system's anti-attack ability. In the case of a communication link interruption, the present invention can also compensate through a predicted control sequence to ensure that the system can maintain operation even in extreme cases, ensuring the continuity and stability of the system. These improvements not only enhance the stability and security of the network control system in the face of DoS attacks but also reduce performance losses caused by untimely or inaccurate responses, thus having higher practical value and a superior operation experience compared with the prior art in practical applications. Description of the Drawings

[0042] Figure 1 Schematic diagram of the steps of an event-triggered control method for a network control system under a DoS attack in Embodiment 1 of the present invention;

[0043] Figure 2 Structure diagram of the ETM-DR-SMPC method in Embodiment 2 of the present invention;

[0044] Figure 3 Algorithm flowchart of an event-triggered control method for a network control system under a DoS attack in Embodiment 3 of the present invention;

[0045] Figure 4 Schematic diagram of the DC-DC transformer in Embodiment 4 of the present invention;

[0046] Figure 5 Average state trajectory diagram of 1000 simulations of three algorithms in Embodiment 4 of the present invention;

[0047] Figure 6 DoS attack timing diagram in Embodiment 4 of the present invention;

[0048] Figure 7 Trigger interval timing diagram in Embodiment 4 of the present invention;

[0049] Figure 8 State response diagram under three algorithms in Embodiment 4 of the present invention;

[0050] Figure 9 Control input diagram under three algorithms in Embodiment 4 of the present invention. Detailed implementation manners

[0051] The following further elaborates in detail on an event-triggered control method and device for a network control system under a DoS attack provided by the present invention in conjunction with the accompanying drawings and specific embodiments. However, this should not be construed as limiting the scope of the above-mentioned subject matter of the present invention to the following embodiments. Any technology implemented based on the content of the present invention belongs to the scope of the present invention. In combination with the following description, the advantages and features of the present invention will be clearer. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise scales, only for conveniently and clearly assisting in explaining the purpose of the embodiments of the present invention.

[0052] Embodiment 1

[0053] During the research process, the applicant found that when using the traditional Stochastic Model Predictive Control (SMPC) method to deal with networked control systems (NCSs) affected by additive noise and suffering from DoS attacks and ensuring the stability and robustness of the system, frequent sampling and communication are required, and there is a high dependence on the probability distribution information of the disturbances. These steps are cumbersome and consume a large amount of resources. The existing technologies can only improve the system performance by increasing the computing and communication costs, but in practical engineering problems, this method is difficult to adapt to resource-constrained or vulnerable network environments.

[0054] When solving practical engineering problems, in order to achieve the technical objectives of reducing communication overhead, improving the robustness and stability of the system, the existing technologies cannot meet the requirements of dealing with unbounded disturbances and DoS attacks. Therefore, after in-depth research on this problem, the applicant proposed an Event-Triggered Model Predictive Control (ETM-DR-SMPC) method. When dealing with the technical problem of networked control systems affected by random disturbances and DoS attacks, by introducing an event-triggered mechanism, reformulating the probability constraints as second-order cone constraints, and designing a predictive control compensation strategy, the sampling frequency and communication overhead are reduced, while the robustness and stability of the system are enhanced, thus achieving the technical effects of optimizing resource utilization, ensuring the recursive feasibility and exponential mean-square stability of the system.

[0055] As Figure 1 shown, Figure 1 is a schematic diagram of the steps of an event-triggered control method for a networked control system under DoS attacks provided in this embodiment. The event-triggered control method for a networked control system under DoS attacks may include the following steps:

[0056] S1. Initialize the mathematical model of the networked control system;

[0057] S2. According to the mathematical model of the networked control system, establish a prediction model, set constraint conditions, and solve the optimization results at each prediction time;

[0058] S3. Detect random disturbances and monitor the state of the communication link;

[0059] S4. Based on the event-triggered mechanism, determine whether the random disturbances trigger the sampling of the networked control system;

[0060] S5. When the triggering condition for sampling is met, update the control input of the networked control system according to the optimization results of the prediction model;

[0061] S6. According to the optimization results, when the communication link is interrupted, use the predictive control sequence to compensate the networked control system.

[0062] The event-triggered control method for networked control systems under DoS attacks provided in this embodiment can be applied to many technical fields, such as medical systems, aerospace, vehicle engineering, process industry, and power systems, including optimal control of resource-constrained systems, robust control of systems under random disturbances, and security control of systems suffering from DoS attacks. In the above implementation, when controlling the coordinated operation of controllers, sensors, and actuators in a networked control system, the sampling frequency can be dynamically adjusted based on the event-triggering mechanism, the probability constraints can be optimized by using the first-order and second-order moment information of the disturbance distribution, and the communication link interruption problem can be addressed by designing a predictive control compensation strategy, achieving the reduction of sampling times and communication costs, enhancing the robustness and stability of the system, and thus achieving the effects of improving the anti-attack ability of the system, optimizing resource utilization, and ensuring the stable operation of the system.

[0063] In this embodiment, a specific implementation of an event-triggered control method for networked control systems under DoS attacks is proposed based on distributed robust optimization (DRO) event-triggered stochastic model predictive control (SMPC). First, in order to reduce the sampling times, save communication costs, and reduce the system computation amount, this embodiment designs an event-triggering mechanism to balance the sampling times and system performance. Second, considering a class of disturbances with less prior knowledge and assuming that only the first-order and second-order moment information of the random disturbance is known, the probability constraints related to the physical state are converted into second-order cone (SOC) constraints. This conversion enhances the traceability in the solution process. The security of the networked control system and the saving of communication and computing resources are two inseparable research tasks. Third, an event-based stochastic model predictive control (ETM-DR-SMPC) is proposed. In particular, compared with the existing research results, it can not only handle the probability constraints with unbounded disturbances, but also save communication and computing resources and resist DoS attacks. The results show that the optimization problem of the ETM-DR-SMPC method is recursively feasible and the system is exponentially mean-square stable. Finally, the effectiveness of the proposed algorithm is verified by numerical simulation results.

[0064] 1.1. Problem Description

[0065] Consider a discrete-time linear system with an additive random disturbance.

[0066] x t+1 = Ax t + Bu t + B d w t (1)

[0067] where, denote the state vector, control input, and stochastic disturbance respectively; \(t\) represents the discrete time step, and \(n\) represents the dimension; and are known constant matrices; \((A, B)\) is Schur stable; \(w\) t is a zero-mean, independent and identically distributed stochastic disturbance; the covariance matrix The predicted system model at time \(t\) is defined as follows

[0068] \(x\) i+1|t = \(Ax\) i|t + \(Bu\) i|t + \(B\) d \(w\) i|t , \(i = 0, 1, \ldots, N - 1\) (2)

[0069] where \(i|t\) represents \(i\) time after time \(t\), is the length of the prediction horizon and is a positive integer.

[0070] Assume that the system (2) follows the state probability constraint as

[0071]

[0072] where \(Pr\) [P] is the probability under the uncertain disturbance \(P\), is a constant vector, represents the constraint upper bound, \(\zeta\) x is a predefined constant representing the maximum probability of constraint violation. Since only partial distribution information of the disturbance can be obtained in this embodiment, the following fuzzy set of the disturbance is defined

[0073]

[0074] where is an \(n\) w dimensional zero vector, is the expectation under the distribution Any probability distribution of the disturbance \(w\) should belong to and timely consider the worst-case distribution in, so the state probability constraint (3) is equivalent to the distributionally robust constraint as follows:

[0075]

[0076] Such as Figure 2As shown in the figure, as the carrier of information transmission, the communication network is the link connecting each unit in the network control systems (NCSs), and plays an indispensable role in ensuring safety control and system performance. In actual systems, many hardware conditions are not sufficient to support a large amount of data transmission, such as being limited by the communication network bandwidth. Reducing unnecessary redundant information transmission is a very important research work. Event-triggered control is an effective method to reduce data transmission, save communication resources, and reduce the amount of calculation.

[0077] To represent the event-triggered communication scheme in detail, define {0, 1, 2, …, τ, …}, as the event-triggered sequence, and the corresponding instants are denoted as {t 0 , t 1 , t 2 , …, t τ , …}. The triggering function is designed according to the current state and the last triggered state , and its formula is

[0078]

[0079] where δ is the triggering parameter, and its value range is 0 < δ < 1. δ is the trade-off coefficient between the triggering interval and the control performance. If the sample is triggered at time tτ and its transmission and residual represent the triggering condition. and are both terminal weighting matrices, which will be described in detail later in this embodiment. Then, by combining the following two formulas, the next event-triggered instant can be obtained.

[0080]

[0081] According to the triggering condition (7), it can be seen that the next event-triggered moment of the system depends not only on the current state but also on the difference between the most recent event-triggered state and the triggering parameter δ. That is, when the triggering function (6) is greater than 0, the system is triggered to perform sampling and update of the control input sequence.

[0082] 1.2. Random DoS Attack Model

[0083] The DoS attack will generate a large number of interference signals and inject them into the communication network, resulting in serious consequences such as communication link blockage and packet loss. The channel from the controller to the actuator is at risk of being attacked at any time.

[0084] Therefore, a random variable ε is introduced t to represent the DoS attack.

[0085]

[0086] where the random variable ε t is used to adjust the control input and represents the impact of the DoS attack on the control system.

[0087]

[0088] where is a given scalar representing the expectation of the variable ε t The nominal system corresponding to system (2) is defined as follows

[0089] where

[0090]

[0091] where and represent the nominal state vector and the control input respectively. The state feedback controller of system (6) is designed as follows

[0092]

[0093] In Equation (12), K is the state feedback gain obtained from the LQR solution, which is the decision variable of the following optimization problem. Different from Equation (7), the controller of system (2) needs to consider the state feedback information with random disturbances under the DoS attack, and its design form is as follows:

[0094]

[0095] As Figure 2 shown, when the controlled object is affected by external disturbances, when the event trigger receives the sampling signal from the sensor, it performs a sampling trigger discrimination to determine whether it reaches the trigger condition and decides to update the control input, so as to reduce the computational load of the system and the data transmission volume of the wireless communication network. As shown in Equation (13), when the wireless network is under a DoS attack, the data transmission between the controller and the sensor channel is blocked. Therefore, the system uses the predictive control sequence under the nominal system to the actuator instead of operating in an open loop, so as to ensure the control system of the system to a certain extent.

[0096] 1.3. Objective Function, Terminal Constraint and Optimization Problem

[0097] In this embodiment, the objective function is considered:

[0098]

[0099] where and are positive definite weight matrices.

[0100]

[0101] where is the terminal weight matrix to be calculated. For the variable has randomness. It is assumed that it follows a Markov random jump process, and its transition probability is expressed as follows

[0102]

[0103] where, Π is the transition probability, λ represents the mode, and η represents the mode at time; π 11 is the probability of transitioning from mode 1 to mode 1, π 12 is the probability of transitioning from mode 1 to mode 2, π 21 is the probability of transitioning from mode 2 to mode 1, π 22 is the probability of transitioning from mode 2 to mode 2.

[0104] In this embodiment, the following terminal constraints are also imposed on the nominal state.

[0105]

[0106] where the subscript T represents the set of terminals;

[0107] Since is a positive invariant set that satisfies

[0108]

[0109] where Φ = A + BK, and moreover, for any the following conditions hold

[0110]

[0111] Based on equations (7) and (8), in order to obtain the predictive control u t , the system needs to solve the following optimization problem with the initial state :

[0112]

[0113] where, v tτ ={v 0|tτ , v 1|tτ , v 2|tτ ,…, v N-1|tτ}. Due to the probability constraint (20f), it is a non-convex optimization problem. Obviously, P 1It is usually difficult to handle. Therefore, it will be equivalently transformed into a convex optimization problem that is easy to solve in the following.

[0114] 1.4. Update Strategy for Control Input

[0115] To ensure the stability of the closed-loop system, the following conditions must be satisfied.

[0116]

[0117] Theorem 1: Under the stochastic event-triggering scheme in (7) and (8), if there exist two matrices and such that

[0118]

[0119] then condition (21) holds.

[0120] Proof: Substituting (2) into (21), we obtain the perturbation w with mean 0 and variance Σ.

[0121]

[0122] where is a Markov random jump process of a random variable. Therefore, the following results can be obtained

[0123]

[0124] According to (25) and (26), it can be obtained that (24) is equivalent to the following formula.

[0125]

[0126] Obviously, (27) is guaranteed by condition (22) and (23) because (27) is equivalent to condition (21) guaranteed by (22)-(23), and the proof is completed.

[0127] 1.5. Elastic Event-Triggered SMPC DoS Attack

[0128] The DoS attack interrupts the current data transmission in the network transmission channel, seriously affecting the stability of the network control system. This embodiment considers the DoS attack on the C-A channel. The ETM-DR-SMPC algorithm and its recursive feasibility and state convergence will be introduced in the following three theorems.

[0129] Theorem 2: Based on the method of handling the probabilistic constraint (20f) with a second-order cone, P1 is equivalently re-transformed into the following convex optimization problem, simply referred to as ETM-DR-SMPC.

[0130]

[0131] wherein represents the systematic error, is the corresponding variance, and

[0132]

[0133] Combining (2), (4), (6), (7) and (8), we can obtain

[0134]

[0135] In the formula is given by formulas (4) and (29)

[0136] Therefore, the following conclusion can be drawn.

[0137]

[0138] Substituting (32) and (34) into formula (14) and considering (33), it is known that the objective function J in (28a) is equivalent to the objective function in (20a) In addition, by using the following Lemma 1, the equivalence of the probability constraint (20f) is transformed into a second-order cone problem based on the distributionally robust optimization method.

[0139] Lemma 1: For any ε ∈ (0, 1), the probability constraint

[0140]

[0141] is equal to the following SOC constraint

[0142]

[0143] There is

[0144]

[0145] Define

[0146]

[0147] Therefore, we obtain

[0148]

[0149] The probability constraint (20f) is equivalent to the following

[0150]

[0151] Applying Lemma 1 to (41), we obtain

[0152]

[0153] The proof is completed.

[0154] The recursive feasibility of the ETM-DR-SMPC algorithm proposed in this embodiment is established by Theorem 3 below.

[0155] Theorem 3: If there exists a feasible solution at time t τ , then the optimization problem P2 has recursive feasibility, that is, for t τ+1 , the constraint (37) is satisfied. In this section, a proof of the recursive feasibility of P2 will be provided. The predicted state sequence of the system at time t τ is defined as and the corresponding optimal solution

[0156] This embodiment adopts a binary initialization strategy. is a feasible solution at the step size t τ+1 . If is defined as where

[0157] Given the structure of it is concluded that (37) is verified for i = 1,..., N - M τ , and thus it is subsequently proved that (38) is feasible for i = N - M τ+1 at time t τ + 1,..., i = N. And the terminal constraint is satisfied because there is

[0158]

[0159] Since is feasible at time t τ , there is Then, considering (17), (18) and (43), it can be obtained that

[0160]

[0161] satisfies the terminal constraint, and the proof is completed.

[0162] Definition 1: If there exist θ ∈ (0, 1) and σ > 0 such that then the system (1) is exponentially mean-square stable and has a feasible region and the initial state

[0163] Theorem 4: Under the event-triggered stochastic model predictive control, if the control law given in Algorithm 1 satisfies the following stability conditions, then the system (1) is exponentially mean-square stable.

[0164]

[0165] where

[0166] Proof: The main results regarding the convergence of the algorithm are established. In this embodiment, the objective function (14) is defined as the Lyaplov function and

[0167] Iterating i from t τ +N to t τ+1 +N through condition (21), we get

[0168]

[0169] Combining equations (46) and (47) gives the following result

[0170]

[0171] The value of the objective function V N (i|t τ+1 ) corresponding to the sub-optimal solution is the value of the Lyaplov function. Therefore, it should be less than or equal to the objective function corresponding to the optimal solution value

[0172]

[0173] Based on equation (49), we can obtain

[0174]

[0175] where β > 0. Iterating from t to 0 for t τ ending gives

[0176]

[0177] Therefore, it can be concluded that

[0178]

[0179] where σ > 0 and θ = e-β are constants. Therefore, the system (1) is exponentially convergent and it is exponentially mean-square stable. The proof is complete.

[0180] In this embodiment, an SMPC algorithm considering constraints, interference, and DoS attacks is established for the first time. Event-triggered control is introduced into SMPC, and a random event-triggering function is designed. At the same time, an SMPC compensation strategy for networked control systems under attacks is proposed, and using partial information of the disturbance distribution, the state probability constraint is reformulated as a second-order cone constraint. Finally, the feasibility and stability of the system recursion under the ETM-DR-SMPC method are proven. Compared with existing SMPC methods, the ETM-DR-SMPC method proposed in this embodiment can effectively reduce the number of sampling times and the number of constraint violations, and can also effectively defend against DoS attacks. Also, since ETM-DR-SMPC only requires the first and second moments of the process disturbance, the disturbance can be unbounded. These advantages make the proposed ETM-DR-SMPC method more suitable for NCSs.

[0181] Embodiment 3

[0182] This embodiment provides an implementation manner of an event-triggered control method for a networked control system under DoS attacks, aiming to ensure the stability and security of the networked control system in an attack environment through an efficient control strategy.

[0183] This algorithm receives input data including the current state of the system, the target state, and control parameters. At the start of the algorithm, these parameters are initialized, the starting time is set, and the initial state of the system is set as the current state. This stage is to ensure that the algorithm can start execution from an accurate starting point.

[0184] The algorithm first checks whether the current time step has reached the predetermined end time of operation. If so, the algorithm directly updates the current state to the target state, and at this time the algorithm terminates. This design ensures that the system can be in the desired safe state at the end moment.

[0185] If it has not reached the end time, the algorithm enters the recursive processing flow. The algorithm continuously checks whether the transition path from the current state to the target state is feasible. By dynamically evaluating and adapting to environmental changes, the algorithm searches for the optimal control strategy to approach the target state. The state update at each step takes into account external interference and the internal response of the system, ensuring that the decision is based on the latest and most comprehensive information.

[0186] The key event-triggering mechanism adjusts the control input according to preset conditions. These conditions are usually based on the deviation of the system state and its rate of change. When the actual state of the system deviates from the predetermined path by a certain threshold, the algorithm triggers a new control instruction to adjust the system state. This event-based control strategy significantly reduces the operating overhead of the system and improves the reaction efficiency and accuracy.

[0187] Upon each event trigger, the system updates its state according to the new control instructions. Additionally, the algorithm ensures that each update maintains or improves the system's performance and security through recursive adjustment. Each update of the system state aims to better adapt to external changes and optimize overall performance.

[0188] Once the system state successfully approaches or reaches the target state, or reaches the preset time limit, the algorithm finishes execution. Through this process, the system ensures stable operation and security in the face of network attacks such as DoS.

[0189] This control method can be widely applied in multiple fields such as medical systems, aerospace, vehicle engineering, process industry, and power systems, especially suitable for environments with resource constraints or extremely high security requirements.

[0190] This embodiment demonstrates an implementation of an efficient and secure event-triggered control method for network control systems by elaborating on the various steps and components of the algorithm, effectively addressing the challenges of complex and dynamic environments.

[0191] Embodiment 4

[0192] As a further optimization of the foregoing embodiment, this embodiment presents a specific implementation of the event-triggered control method for a network control system under DoS attacks according to the present invention. Based on the research by M. Lazar et al. in "Input-to-state stabilizing sub-optimal NMPC with an application to DC-DC converters", this embodiment further proposes a Buck-Boost DC-DC transformer. DC-DC converters are widely used in various electronic process industries, such as electric and hybrid vehicles, etc. Its structure diagram is as Figure 4 shown, and the corresponding DC-DC transformer system dynamic model is as follows:

[0193]

[0194] Among them, the state vector x k = [x 1,k x 2,k respectively represents the current flowing through the inductor and the circuit output voltage; u k represents the duty cycle. The parameters T, R, C, and L respectively represent the system sampling time, load resistance, capacitance, and inductance.

[0195] Based on the research of M. Cannon et al. in "Stochastic Tubes in Model Predictive Control With Probabilistic Constraints", this embodiment further considers a linearized DC-DC converter system, which has a linear form and the system matrix is shown as follows

[0196]

[0197] Parameter x 0 = [2.5 2.8] T is the initial state of the system. The control gain K is solved from the Ricatti equation in the LQR problem with Q = diag{1, 3.5}, R = 0.1, N = 8. Other parameters give ρ T = [1 0], δ = 0.2, g = 1.5, ζ x = 0.2. The disturbance w has the characteristics of distributional robustness. To compare and highlight the effectiveness and advantages of the ETM-DR-SMPC algorithm proposed in this embodiment, a periodic distributionally robust MPC (PDR-SMPC) algorithm (proposed by Y. Tan et al. in "A Distributionally Robust Optimization Approach to Two-Sided Chance-Constrained Stochastic Model Predictive Control With Unknown Noise Distribution") and a self-triggered stochastic model predictive control algorithm (SSMPC) (proposed by L. Dai et al. in “Stochastic selftriggered

[0198] model predictive control for linear systems with probabilistic constraints”) are designed and compared in the simulation when the system is under DoS attacks. The simulation of this embodiment will show the advantages of the algorithm of this embodiment from four aspects: statistical trigger interval, DoS attack frequency, number of constraint violations calculated, and generation of system state trajectories.

[0199] 5.1. Gaussian mixture distribution

[0200] It is considered that the disturbance w follows a Gaussian mixture distribution, and its probability density function is

[0201]

[0202] where λ 1= 0.6, λ 2 = 0.4, the parameter λ q can be regarded as the mixing percentage of Gaussian components in the model. The simulation results of the system state responses under the considered ETM-DR-SMPC and PDR-SMPC algorithms are as Figure 5 shown. It can be seen that the states of the closed-loop system converge under all algorithms. At the same time, the number of constraint violations of ETM-DR-SMPC, PDR-SMPC, and SSMPC are 115 times, 98 times, and 176 times respectively, and the results are in line with the preset violation probability. The results show that the ETM-DR-SMPC algorithm can keep the system state better in the safe region and hardly violates the constraints, indicating that ETM-DR-SMPC has good control effects in reducing the sampling times and defending against DoS attacks. Its performance indicators are calculated as follows.

[0203]

[0204] Table 1: J perf , Λ and Γ statistics

[0205]

[0206] To more clearly characterize the changes in physical quantities such as system state, control input, and triggering interval, the state response of one result randomly selected from 1000 simulations is as Figure 8 shown, the control input is as Figure 9 shown, and the corresponding key parameter statistics are shown in Table 1. Figure 5 and Figure 8 show that ETM-DR-SMPC, SSMPC, and PDR-SMPC can all make the control system converge in the state under the DoS attack as Figure 6 shown, and the convergence time and convergence amplitude are close. It can be known from Figure 7 and Table 1 that ETM-DR-SMPC has relatively fewer sampling times compared to the other two algorithms. It can be seen from Table 1 that the average sampling interval Λ = 2.5. Compared with the PDR-SMPC algorithm, the ETM-DR-SMPC algorithm can reduce the communication rate by 60.0% and make the system state converge to the stable region. To sum up, the ETM-DR-SMPC algorithm can reduce the sampling times, save communication costs, and achieve excellent control performance.

[0207] Example 5

[0208] This embodiment provides a network control system event-triggered control device under DoS attacks, which is used to implement the network control system event-triggered control method under DoS attacks. This device is specially designed to cope with random disturbances and potential DoS attacks in the network environment, and ensures the efficient and stable operation of the network control system through the following components:

[0209] Processor: Responsible for executing all computing tasks, including the initialization of mathematical models, the establishment of prediction models, the solution of optimization results, and the decision-making based on the event-triggered mechanism. The processor can quickly process data from the network, judge whether to trigger the sampling of the network control system, and update the control input accordingly.

[0210] Memory: Used to store the mathematical models, prediction models, optimization algorithms, historical data, and operating parameters of the network control system. The memory supports high-speed data access to ensure that the processor can instantly obtain all the information it needs.

[0211] Communication interface: Allows the device to exchange data with other components in the network (such as sensors, actuators, etc.). This interface supports multiple communication protocols to adapt to different network environments and maintain the stability and security of data transmission.

[0212] Event-triggered module: This core module dynamically adjusts the sampling frequency and control strategy based on the set trigger conditions. It monitors the system state and communication link status in real time, and when a defined trigger event is detected, it guides the processor to make corresponding control decisions.

[0213] Power management system: Ensures that the device can maintain stable power supply under various operating conditions, especially during DoS attacks, and can handle possible energy fluctuations or interruptions.

[0214] Security module: Protects the device from external attacks and internal failures. This module uses the latest encryption technologies and security protocols to prevent unauthorized access and data tampering.

[0215] The device provided in this embodiment not only optimizes the response strategy of the network control system, reduces the resource consumption caused by frequent sampling, but also enhances the robustness and stability of the system when facing DoS attacks through accurate and timely control input updates. This device is applicable to a variety of industrial and commercial applications, such as medical systems, aerospace equipment, vehicle engineering, and process control systems, and is particularly suitable for use in resource-constrained or high-security requirement environments.

[0216] Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects.

[0217] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as falling within the scope described in this specification.

[0218] The above-described embodiments only represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. A method for controlling network control system event triggering under DoS attack, characterized in that: The following steps are involved: S1. Initialize the mathematical model of the network control system; S2. According to the mathematical model of the network control system, a prediction model is established, constraints are set, and the optimization result of each prediction moment is solved; S3. Detect random disturbances and monitor the status of the communication link; S4. Based on the event triggering mechanism, it is determined whether the random disturbance triggers the sampling of the network control system; S5. When the triggering conditions for sampling are met, the control input of the network control system is updated according to the optimization results of the prediction model; S6. Based on the optimization results, when the communication link is interrupted, the network control system is compensated using a predictive control sequence.

2. According to the method for controlling a network control system under DoS attack according to claim 1, it is characterized in that: The mathematical model of the network control system in step S1 is a discrete time linear model, including state equations, control inputs and random disturbances, which is expressed by the following formula: x t+1 =Ax t +Bu t +B d w t in, Represent the state vector, control input and random disturbance respectively; t represents the discrete time step, and n represents the dimension; and is a known constant matrix.

3. According to the method for controlling a network control system under DoS attack, the method is characterized in that: Step S2 includes solving a target optimization problem; the goal of the optimization problem is to minimize the system state; the constraints include state constraints and terminal constraints.

4. According to the method for controlling a network control system under DoS attack according to claim 2, it is characterized in that: The random disturbance includes a DoS attack; the DoS attack is represented by a random variable, and different states of the communication link are represented based on the value of the random variable: when the value of the random variable is 0, it indicates that it is under a DoS attack and the communication link is interrupted; when the value of the random variable is 1, it indicates that it is not under a DoS attack and the communication link is normal.

5. According to the method for controlling a network control system under DoS attack according to claim 1, it is characterized in that: The event triggering mechanism comprises the following steps: S31. Calculate the difference between the current state of the control system and the most recent trigger state; S32. When the difference exceeds a preset trigger threshold, trigger sampling and update the control input.

6. According to the method for controlling a network control system under DoS attack according to claim 5, it is characterized in that: The calculation of the difference in the event trigger mechanism is based on the trigger function calculation, and the trigger parameters are preset to control the trigger frequency.

7. According to the method for controlling a network control system under DoS attack according to claim 1, it is characterized in that: When the communication link is interrupted, the network control system uses a predictive control sequence based on the LQR solution to compensate for the control input.

8. According to the method for controlling a network control system under DoS attack according to claim 3, it is characterized in that: The probability constraints in the optimization problem are transformed into distributionally robust constraints through a distributionally robust optimization method, and further transformed into a convex optimization problem through a second-order cone constraint form.

9. According to the method for controlling a network control system under DoS attack according to claim 4, it is characterized in that: The recursive feasibility and exponential mean square stability of the prediction model are achieved by: The state vector x is restricted by the terminal constraints t feasible area; The Lyapunov function is used to verify the stability of the network control system state and dynamically adjust the optimization results.

10. A network control system event trigger control device under DoS attack, characterized in that: The computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method according to any one of claims 1 to 9 when executing the computer program.

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