Reservoir level system control method under denial of service attack

Abstract

The invention discloses a reservoir level system control method under denial of service attack. The method comprises the steps of establishing a reservoir level system state space model, designing a hybrid event triggering strategy, designing a controller, establishing a denial of service attack model, analyzing the stability of a closed-loop system, and solving a controller gain and an event triggering matrix. Based on an event triggering theory, an average residence time method and a linear matrix inequality, a state feedback controller is designed through the linear matrix inequality by considering that a data transmission channel from a system sensor to a controller is subjected to denial of service attack, and effective control over a reservoir level system is achieved. According to the method, mixed event triggering control is adopted, network resources are effectively saved, meanwhile, the controller can be quickly updated after the denial of service attack disappears, and therefore the influence of the denial of service attack on the system stability is more effectively reduced.

Description

Technical Field

[0001] The invention belongs to the field of modern control technology, and in particular relates to a reservoir water level system control method under a denial of service attack. Background Art

[0002] Reservoirs are important structures in modern water conservancy projects, which play an important role in hydropower generation, agricultural irrigation, river flood control, urban water supply, etc. With the continuous development of science and technology, modern reservoir water level control systems generally communicate data through wired or wireless networks, which not only saves labor costs but also greatly improves control efficiency. However, due to the openness of the network, the system is also vulnerable to network attacks.

[0003] Denial of service attack is a common network attack that attempts to exhaust the resources of the network or server of the reservoir water level system by sending a large number of requests to it, so that the system cannot process the requests of legitimate users, resulting in service interruption. The reservoir water level system that suffers from denial of service attack may be unable to monitor the water level, flow or other key parameters, thus affecting the scheduling and safe operation of the reservoir. Therefore, designing a safe and effective control method for the reservoir water level system is crucial to the safe operation of modern industry and agriculture and the safety of water conservancy facilities such as reservoirs and rivers.

[0004] Taking into account the actual situation, the modern reservoir water level system will automatically adjust the operation mode of the reservoir according to time, which greatly increases the complexity of the entire reservoir system. On the other hand, due to global climate change, frequent rainstorms and other extreme weather conditions, these have increased the performance requirements for reservoir water storage and drainage. As for the control of reservoir water level systems, existing research methods rarely consider the impact of denial of service attacks on the system. Although the probability of a successful attack on the system is very low under various network security measures such as encryption and firewalls, once it is attacked, the consequences will be very serious. For this reason, it is necessary to design a new method that can safely and effectively control the reservoir water level even under denial of service attacks. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes a reservoir water level system control method under a denial of service attack, which is based on the average residence time method, hybrid event trigger control, and the linear matrix inequality to design the event trigger matrix and state feedback controller. While effectively saving network resources, the controller can also be quickly updated after the denial of service attack disappears. The effective control of the reservoir water level system is achieved, and it is suitable for modern reservoir water level systems.

[0006] A reservoir water level system control method under a denial of service attack specifically comprises the following steps:

[0007] Step 1: Establish a state space model of the reservoir water level system

[0008] Model the state space of the reservoir level system using the switching system formalism:

[0009]

[0010] Among them, x(t) represents the system state at time t. σ(t)→Ι={1,2,3.....m} is the switching signal of the reservoir water level system, indicating the operating mode of the reservoir water level system at time t, and m represents the number of switchable operating modes. σ(t) , B σ(t) They represent the state matrix and control input matrix of the reservoir water level system under the σ(t)th operation mode. u(t) represents the gate opening of the reservoir outlet at time t. represents a first derivative.

[0011] Step 2: Design a hybrid event trigger strategy

[0012] Define the following hybrid event triggering strategy:

[0013]

[0014] Where inf represents the infimum. k ,t k+1 They represent the kth and k+1th event triggering times respectively. The superscript T represents the transpose of the matrix, Φ σ(t) is the event trigger positive definite matrix to be designed in the σ(t)th operation mode. δ is a positive constant, and △ represents a positive constant related to the sampling period. e(t)=x(t k )-x(t), which indicates the error between the current system state and the last sampled system state. When the error e(t) is greater than the set trigger condition threshold, the system is sampled again. ACK=1 means that the signal is received successfully, and ACK=0 means that a denial of service attack has occurred during the signal transmission process.

[0015] Step 3: Establish a denial of service attack model

[0016] Considering that an attacker launches a denial of service attack on the data transmission channel from the system sensor to the controller, the following denial of service attack model is established:

[0017]

[0018]

[0019] Where n(t0,t1) represents the number of denial of service attacks that occur within (t0,t1), η, τ DAll are normal quantities. |Ξ(t0,t1)| represents the duration of the DoS attack within (t0,t1), κ is a normal quantity, and T is a normal quantity greater than 1.

[0020] Step 4: Controller Design

[0021] Based on state feedback, the following controller u(t) is designed:

[0022]

[0023] Among them, s k 、s k+1 They represent the triggering moments of the kth and k+1th successful transmissions under a denial of service attack, respectively. K represents the controller gain, which is obtained by solving the linear matrix inequality. Indicates the switching signal of the controller, Indicates k The switching signal of the moment controller, Indicates k The value of the controller gain at time instant.

[0024] Step 5: Stability analysis of closed-loop system

[0025] Substitute the error e(t) and controller u(t) into the state space model of the reservoir water level system to obtain the state space model of the closed-loop system:

[0026]

[0027] According to the Lyapunov stability theory, the exponential stability condition of the reservoir water level system is solved: for a given positive constant μ≥1, T, δ, α, β, T max , τ D , there is an average residence time τ a satisfy Among them, T max A positive number indicating the maximum allowed asynchronous time.

[0028] Step 6: Solve the controller gain and event trigger matrix

[0029] Under the condition of system stability, design the state feedback controller gain and event trigger matrix Matrix Y ij , Y ii and the positive definite matrix X ij , X ii , By solving the inequality Get, where

[0030] The present invention has the following beneficial effects:

[0031] In view of the shortcomings of the existing reservoir water level system and the lack of consideration of the impact of denial of service attacks on the system, a hybrid event trigger control method is proposed. Considering the possibility of the data transmission channel from the sensor to the controller being attacked by denial of service, an attack model that conforms to the actual situation is established by limiting the frequency and duration of denial of service attacks. On this basis, a hybrid event trigger control method is designed, which can not only improve system performance and save network resources. It can also quickly restore the stability of the reservoir water level system after the attack ends, and realize effective control of the water level. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a system status response diagram in the embodiment;

[0033] Figure 2 It is the system control input designed in the embodiment;

[0034] Figure 3 It is the event triggering interval of the hybrid event triggering strategy under the denial of service attack in the embodiment. DETAILED DESCRIPTION

[0035] The present invention will be further explained below with reference to the accompanying drawings;

[0036] A reservoir water level system control method under a denial of service attack specifically comprises the following steps:

[0037] Step 1: Establish a state space model of the reservoir water level system

[0038] Considering that the reservoir water level system will automatically adjust the operation mode of the reservoir according to time, the state space model of the reservoir water level system is modeled as a switching system:

[0039]

[0040] Where x(t) = [x1(t), x2(t), x3(t), x4(t)] T , x1(t), x2(t), x3(t), x4(t) respectively represent the flow velocity value of the reservoir outlet at time t, the water level value of the reservoir, the water pressure value of the reservoir surface and the water pressure value of the outlet. σ(t)→Ι={1,2,3.....m} is the switching signal of the reservoir water level system, indicating the operating mode of the reservoir water level system at time t, and m represents the number of switchable operating modes. A σ(t) ∈R 2×2 , B σ(t) ∈R 2×1are all constant matrices, representing the state matrix and control input matrix of the reservoir water level system under the σ(t)th operation mode. u(t) represents the gate opening of the reservoir outlet at time t. The symbol R represents Euclidean space, and the superscript T represents the transpose of the matrix. represents a first derivative.

[0041] Step 2: Design a hybrid event trigger strategy

[0042] Define the following hybrid event triggering strategy:

[0043]

[0044] Where inf represents the infimum. k ,t k+1 Respectively represent the kth and k+1th event triggering times. Φ σ(t) is the event trigger positive definite matrix to be designed in the σ(t)th operation mode. δ is a positive constant, and △ represents a positive constant related to the sampling period. e(t)=x(t k )-x(t), which indicates the error between the current system state and the last sampled system state. When the error e(t) is greater than the set trigger condition threshold, the system is sampled again. ACK is used to confirm whether the signal transmitted in the network has reached the destination. ACK=1 indicates that the signal has been successfully received, and ACK=0 indicates that a denial of service attack has occurred during the signal transmission process.

[0045] This hybrid event trigger strategy is the same as the traditional event trigger control when there is no denial of service attack, which can effectively save network resources. After suffering a denial of service attack, it will be converted into a periodic time trigger control to increase the number of data transmissions. Since the attacker's energy is limited, it can achieve the purpose of consuming the attack to hinder the number of data transmissions, so that the controller can be updated immediately after the denial of service attack disappears.

[0046] Step 3: Establish a denial of service attack model

[0047] Consider an attacker launching a denial of service attack on the data transmission channel from the system sensor to the controller. Since the attacker needs to consider the cost and practical significance when launching an attack, he will not launch continuous attacks or high-frequency attacks in a short period of time. Therefore, by limiting the frequency and duration of the denial of service attack, the following denial of service attack model is established:

[0048]

[0049]

[0050] Where n(t0,t1) represents the number of denial of service attacks that occur within (t0,t1), η, τ D All are normal quantities. |Ξ(t0,t1) represents the duration of the DoS attack within (t0,t1), κ is a normal quantity, and T is a normal quantity greater than 1.

[0051] Step 4: Controller Design

[0052] Based on state feedback, the following controller u(t) is designed:

[0053]

[0054] Among them, s k 、s k+1 They represent the triggering moments of the kth and k+1th successful transmissions under a denial of service attack, respectively. K represents the controller gain, which is obtained by solving the linear matrix inequality. Indicates the switching signal of the controller. Due to the influence of the denial of service attack, the switching signal of the controller It will lag behind the system’s switching signal σ(t).

[0055] Step 5: Stability analysis of closed-loop system

[0056] Substitute the error e(t) and controller u(t) into the state space model of the reservoir water level system to obtain the state space model of the closed-loop system:

[0057]

[0058]

[0059]

[0060] According to Lyapunov stability theory, the Lyapunov function V(t) is selected:

[0061]

[0062] For a given positive constant μ ≥ 1, T, δ, α, β, T max , τ D , if there is an average residence time τ a satisfy And there exists a positive definite matrix P ii , P ij , Φ i , Φ j satisfy And P ij ≤μP jj ,P ii ≤μP ij, so that the linear matrix inequality Established, where i, j∈Ι, substituting into V(t), discussing the stability of the reservoir water level system when it is subjected to a denial of service attack, we can get:

[0063]

[0064] Among them, T max is a positive constant, indicating the maximum asynchronous time allowed; * is the symmetric block of the matrix. c and ρ are both positive constants. Finally, we can deduce:

[0065]

[0066] ||·|| represents the Euclidean norm. v1 and v2 are positive constants. Therefore, under the controller u(t), the exponential stability of the reservoir water level system can be guaranteed.

[0067] Step 6: Solve the controller gain and event trigger matrix

[0068] Designing the state feedback controller gains and event trigger matrix Matrix Y ij , Y ii and the positive definite matrix X ij , X ii , By solving the inequality Get, where

[0069] The method is numerically simulated and the simulation parameters are set as follows:

[0070] m=2, α=0.75、

[0071] β=2.1, μ=1.25, T=3, T max =0.1, δ=0.5, Δ=0.1.

[0072] The average residence time τ can be obtained a =2, the corresponding controller gain and event trigger matrix are:

[0073] K1=[-5.4108 -2.6341], K2=[-0.9337 -1.3988],

[0075] Under this controller gain and event trigger matrix, the system state response is as follows Figure 1As shown, x1 and x2 represent two system states with different initial values, which tend to 0 in a finite time, indicating that the system is stable under this control method. Figure 2 is the system control input. As time goes by, the value of the control input u is balanced at 0. Figure 3 It is the event triggering interval under the denial of service attack. Its length is related to the sampling error. When the system state changes faster, the event triggering interval is shorter. When the system state changes slower, the event triggering interval will be longer.

Claims

1. A reservoir water level system control method under a denial of service attack, characterized in that: The specific steps include: Step 1: Model the state space of the reservoir water level system using the switching system form; Step 2: Define the following hybrid event triggering strategy: Among them, inf represents the infimum; t k ,t k+1 They represent the kth and k+1th event triggering times respectively; the superscript T represents the transpose of the matrix, Φ σ(t) is the event trigger positive definite matrix to be designed when the reservoir water level system switches to the σ(t)th operation mode; δ is a positive constant, △ represents a positive constant related to the sampling period; e(t) = x(t k )-x(t), which means the current system state x(t) is different from the last sampled system state x(t k ) between them; ACK=1 means the signal is received successfully, ACK=0 means a denial of service attack occurred during the signal transmission process; Step 3: Considering that the attacker launches a denial of service attack on the data transmission channel from the system sensor to the controller, the following denial of service attack model is established: Where n(t0,t1) represents the number of denial of service attacks that occur within (t0,t1), η, τ D All are normal quantities; |Ξ(t0,t1) represents the duration of the denial of service attack within (t0,t1), κ is a normal quantity, and T is a normal quantity greater than 1; Step 4: Design a state feedback controller u(t); Step 5: Substitute the error e(t) and the controller u(t) into the state space model of the reservoir water level system, and analyze the stability condition of the closed-loop system state space model according to the Lyapunov stability theory and the average residence time method; Step 6: Solve the controller gain and event trigger matrix under different operating modes.

2. A reservoir water level system control method under a denial of service attack as claimed in claim 1, characterized in that: The following reservoir water level system state space model is established: Where x(t) represents the system state at time t; σ(t)→Ι={1,2,3.....m} is the switching signal of the reservoir water level system, indicating the operation mode of the reservoir water level system at time t, and m represents the number of switchable operation modes; A σ(t) , B σ(t) They represent the state matrix and control input matrix of the reservoir water level system under the σ(t)th operation mode respectively; u(t) represents the gate opening of the reservoir outlet at time t; represents a first derivative.

3. A reservoir water level system control method under a denial of service attack as claimed in claim 2, characterized in that: x(t)=[x1(t),x2(t),x3(t),x4(t)] T , x1(t), x2(t), x3(t), and x4(t) respectively represent the water flow velocity value at the reservoir outlet, the water level height value of the reservoir, the water pressure value of the reservoir surface, and the water pressure value of the outlet at time t.

4. A reservoir water level system control method under a denial of service attack as claimed in claim 2, characterized in that: Based on state feedback, the following controller u(t) is designed: Among them, s k 、s k+1 They represent the triggering moments of the kth and k+1th successful transmissions under a denial of service attack respectively; K represents the controller gain, represents the switching signal of the controller, and m represents the number of switchable operating modes.

5. A reservoir water level system control method under a denial of service attack as claimed in claim 4, characterized in that: Substitute the error e(t) and controller u(t) into the state space model of the reservoir water level system to obtain the state space model of the closed-loop system: According to the Lyapunov stability theory, the exponential stability condition of the reservoir water level system is solved: for a given positive constant μ≥1, T, δ, α, β, T max , τ D , there is an average residence time τ a satisfy Among them, T max A positive number indicating the maximum allowed asynchronous time.

6. A reservoir water level system control method under a denial of service attack as claimed in claim 5, characterized in that: Under the condition of system stability, design the state feedback controller gain and event trigger matrix The matrix Y ij , Y ii and the positive definite matrix X ij , X ii , By solving the inequality get

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