Security data driven prediction control method for dual-channel DoS attack

Abstract

The invention discloses a security data-driven prediction control method aiming at a dual-channel DoS attack. The method comprises the following steps: firstly, constructing a linear control model based on a Koopman operator theory; thirdly, according to the linear control model, a finite time domain optimization control problem is constructed, solving is carried out based on historical data of a target nonlinear system, and an optimal control sequence at the moment k is obtained; and finally, according to a dual-communication channel asynchronous DoS attack state, selecting an optimal control input from the optimal control sequence at the moment k, and acting on the target nonlinear system. According to the method, linear modeling of an unknown dynamic system can be effectively realized, the influence caused by DoS attacks of double communication channels is compensated, and the system stability is ensured.

Description

Technical Field

[0001] The present invention is a secure data-driven predictive control method under malicious attacks, and specifically relates to a secure data-driven predictive control method for dual-communication channel DoS attacks. Background Art

[0002] Most existing control methods usually rely on accurate control models of the system. However, for complex coupled nonlinear systems, how to obtain accurate control models has always been a difficult problem. To address this problem, data-driven modeling methods have begun to be used more and more, especially when it is impossible to obtain an accurate system model or the system dynamics are highly nonlinear. The Koopman operator is a linearization tool that can convert a nonlinear dynamic system into a linear system that evolves in a high-dimensional space. By analyzing the input and output data of the system, the Koopman operator can extract the dynamic characteristics of the system and effectively model it. The key advantage of this method is that it constructs a linear control model, and the existing mature linear control theory can be used to design the control method.

[0003] The advantage of Model Predictive Control (MPC) lies in its ability to handle multi-input and multi-output systems and to naturally introduce constraints (such as input constraints, output constraints, and state constraints) into the control process. This makes MPC particularly suitable for complex, dynamic, and constrained systems, such as chemical processes, autonomous driving, energy systems, robotics, and other fields. The prediction model (i.e., the control model) is the key core of the MPC method. Using the Koopman linearized control model as the prediction model can improve the accuracy of the prediction model and effectively reduce the computational complexity of the MPC method.

[0004] With the transformation and upgrading of industrial systems towards informatization and intelligentization, cyberattacks (such as denial of service attacks and data injection attacks) have become a major threat to the security of modern infrastructure and critical systems. In particular, in the control system field, denial of service (DoS) attacks can disrupt data availability, thereby endangering the stability, reliability, and security of the system. Therefore, research on secure data-driven predictive control methods under dual-channel DoS attacks is of great significance. Currently, there are many security control methods for DoS attacks on a single sensor-controller communication channel, but there are fewer research results on security control methods for simultaneous DoS attacks on both sensor-controller and controller-actuator communication channels. Summary of the Invention

[0005] Taking into account the shortcomings and deficiencies in the current research on security control methods for simultaneous DoS attacks on sensor-controller and controller-actuator dual communication channels, the present invention provides a secure data-driven predictive control method for dual-channel DoS attacks to enhance the system's anti-attack and stability.

[0006] The object of the present invention is achieved through the following technical solutions:

[0007] 1. A secure data-driven predictive control method against dual-channel DoS attacks

[0008] 1) Construct a linear control model based on Koopman operator theory;

[0009] 2) According to the linear control model, a finite time domain optimization control problem is constructed and solved based on the historical data of the target nonlinear system to obtain the optimal control sequence at time k

[0010] 3) According to the dual communication channel asynchronous DoS attack state, the optimal control sequence at time k is The optimal control input is selected and applied to the target nonlinear system.

[0011] In 1), the linear control model satisfies the following formula:

[0012] z(k+1)=Az(k)+Bu(k)

[0013]

[0014] The matrix [AB] is the infinite-dimensional Koopman operator The approximate value of is calculated by the following formula:

[0015]

[0016] X lift =[x1,ψ(x1),…,ψ(x i ),…,ψ(x K )]

[0017] Y lift =[y1,ψ(y1),…,ψ(x i ),…,ψ(y K )]

[0018] Among them, z(k+1) is the system state of the Koopman space at time k+1, z(k) is the system state of the Koopman space at time k, is the predicted value of the actual state of the system after dimensionality reduction from the Koopman space, A and B are the first parameter matrix and the second parameter matrix respectively, and C is the mapping matrix from the Koopman space to the target system space. represents the pseudo-inverse of the matrix, represents matrix multiplication; X lift For different sampling states x i The matrix composed of the lifting functions of is the matrix X lift The pseudo-inverse of Y lift For different system states y i The matrix composed of the lifting function of ψ(x i ) represents the system state x i The corresponding lifting function; K is the number of collected system states; U is the vector composed of K control inputs; X is the vector composed of K system states.

[0019] In the above 2), the finite time domain optimization control problem satisfies the following formula:

[0020]

[0021] z(l+1)=Az(l)+Bu(l),l=0,…,N-1,

[0022]

[0023] Among them, U * (k) represents the optimal control sequence, which contains N optimal control inputs, satisfying U * (k)=[u * (0),u * (1),…,u * (N-1)],u * (0),u * (1),…,u * (N-1) represents the first control input, the second control input, and the Nth control input respectively. represents the cost function, is the system state stored in the controller at time k, u(l) represents the given control sequence, N represents the prediction time domain, z(l) and z(l+1) are the system states in the Koopman space at time l and time l+1 respectively, z(N) represents the system state in the Koopman space at time N, A and B are the first parameter matrix and the second parameter matrix respectively, C is the mapping matrix from the Koopman space to the target system space, z s represents the desired state of the system, Q is the state weight matrix, R is the control input weight matrix, ‖·‖ Q Represents the weight as the vector bi-norm operation of the state weight matrix Q, ‖·‖ RRepresents the weight as the vector two-norm operation that controls the input weight matrix R; is the input constraint, is the state constraint, is the latest system state stored by the controller; z(0) represents the system state in the Koopman space at time 0; Indicates that the system status Lifting function for upgrading to Koopman space.

[0024] Said 3) is specifically:

[0025] Detect whether a DoS attack on the sensor-controller channel occurs at time k; if the DoS attack does not occur, the controller obtains the latest state of the target system and updates the system state value stored in the controller; if the DoS attack occurs, the controller cannot obtain the actual state of the target system, and the stored system state value is equal to the value stored at the previous moment;

[0026] Detect whether the controller-actuator channel DoS attack occurs at time k; if the controller-actuator channel DoS attack does not occur, clear the memory of the actuator of the target nonlinear system and replace the optimal control sequence U at time k with the optimal control sequence U at time k. * (k) is passed to the actuator’s memory, and the first optimal control input u in the actuator’s memory is * (0) Act on the target nonlinear system;

[0027] If a DoS attack occurs on the controller-actuator channel, the lth optimal control input u in the actuator memory is * (l) Act on the target nonlinear system.

[0028] 2. A Secure Data-Driven Predictive Control Device Against Dual-Channel DoS Attacks

[0029] A linear control model building unit, used to build a linear control model based on Koopman operator theory;

[0030] The optimal control sequence generation unit is used to construct a finite time domain optimization control problem based on the linear control model and solve it based on the historical data of the target nonlinear system to obtain the optimal control sequence U at time k. * (k); optimal control input generation unit, used to generate the optimal control sequence U at time k according to the asynchronous DoS attack state of the dual communication channels * (k) The optimal control input is selected and applied to the target nonlinear system.

[0031] The beneficial effects of the present invention are:

[0032] This paper uses Koopman operator theory to construct a data-driven linear control model for discrete-time nonlinear systems with unknown dynamics. A secure model predictive control method with attack compensation is designed to address DoS attacks involving both sensor-controller and controller-actuator communication channels. The proposed secure Koopman model predictive control method can effectively compensate for attack effects and ensure system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the method of the present invention.

[0034] Figure 2 This is the system control block diagram under dual communication channel DoS attack.

[0035] Figure 3 Schematic diagram of the system state trajectory of the Van der Pol oscillator under the action of two control methods.

[0036] Figure 4 Schematic diagram of the control input trajectory of the Van der Pol oscillator under the two control methods.

[0037] Figure 5 Indicates the change of motor speed under the two control methods.

[0038] Figure 6 It shows the changes of the input stator current under the two control methods. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] This paper proposes a secure data-driven predictive control method for dual-channel DoS attacks. Figure 1 As shown, the method includes the following steps:

[0041] 1) Construct a linear control model based on Koopman operator theory;

[0042] The target nonlinear system is a discrete-time nonlinear model, and the formula is as follows:

[0043] x + =f(x,u)

[0044] Among them, x represents the current system state, u represents the control input, and x + represents the system state at the next moment, f represents an unknown function, which is used to represent the system state x +The relationship between the system state x and the control input u. Since f is unknown, the present invention uses the state data and the control input data based on the Koopman operator to construct an approximate linear control model. The construction process is as follows:

[0045] Randomly generate K control inputs to form a vector U, and generate K system states to form a vector X:

[0046] U=[u1,…,u i ,…,u K ],X=[x1,…,x i ,…,x K ]

[0047] Under the action of U, the system state vector Y is generated:

[0048] Y=[y1,…,y i ,…,y K ]

[0049] Satisfy condition y i =f(x i ,u i ),u i is the i-th control input, x i is the i-th system state, y i The target nonlinear system is u i The subsequent system state under the action.

[0050] The linear control model satisfies the following formula:

[0051] z(k+1)=Az(k)+Bu(k)

[0052]

[0053] Koopman operator theory points out that by properly selecting the lifting function ψ(x), the system state can be upgraded to a high-dimensional Koopman space, so that the high-dimensional space state z can be The matrix [AB] is the infinite-dimensional Koopman operator The approximate value of is calculated by the following formula:

[0054]

[0055] X lift =[x1,ψ(x1),…,ψ(x i ),…,ψ(x K )]

[0056] Y lift =[y1,ψ(y1),…,ψ(x i),…,ψ(y K )]

[0057] Among them, z(k+1) is the system state of the Koopman space at time k+1, z(k) is the system state of the Koopman space at time k, is the predicted value of the actual state of the system after dimensionality reduction from the Koopman space, A and B are the first parameter matrix and the second parameter matrix respectively, and C is the mapping matrix from the Koopman space to the target system space. represents the pseudo-inverse of the matrix, represents matrix multiplication; X lift For different sampling states x i The matrix composed of the lifting functions of is the matrix X lift The pseudo-inverse of Y lift For different system states y i The matrix composed of the lifting function of ψ(x i ) represents the system state x i The corresponding lifting function can be composed of a radial basis function and a Gaussian function; K is the number of collected system states; U is a vector composed of K control inputs; and X is a vector composed of K system states.

[0058] 2) According to the linear control model, a finite time domain optimization control problem is constructed and solved based on the historical data of the target nonlinear system to obtain the optimal control sequence U at time k * (k);

[0059] The finite-time domain optimization control problem satisfies the following formula:

[0060]

[0061] z(l+1)=Az(l)+Bu(l),l=0,…,N-1,

[0062]

[0063] Among them, U * (k) represents the optimal control sequence, which contains N optimal control inputs, satisfying U * (k)=[u * (0),u * (1),…,u * (N-1)],u * (0),u * (1),…,u * (N-1) represents the first control input, the second control input, and the Nth control input respectively. represents the cost function, is the system state stored in the controller at time k, u(l) represents the given control sequence, N represents the prediction time domain, z(l) and z(l+1) are the system states in the Koopman space at time l and time l+1 respectively, z(N) represents the system state in the Koopman space at time N, and z s represents the desired state of the system, Q is the state weight matrix, R is the control input weight matrix, ‖·‖ Q Represents the weight as the vector bi-norm operation of the state weight matrix Q, ‖·‖ R Represents the weight as the vector two-norm operation that controls the input weight matrix R; is the input constraint, is the state constraint, is the latest system state stored by the controller; z(0) represents the system state in the Koopman space at time 0; Indicates that the system status Lifting function for upgrading to Koopman space.

[0064] 3) According to the dual communication channel asynchronous DoS attack state with finite duration, the optimal control sequence U at time k is * (k) The actuator that selects the optimal control input and acts on the target nonlinear system.

[0065] 3) Specifically:

[0066] Detect whether the sensor-controller channel DoS attack occurs at time k; if the sensor-controller channel DoS attack does not occur, the controller can obtain the latest state of the target system and update the system state value stored in the controller (with symbol indicates), that is, If a DoS attack occurs on the sensor-controller channel, the controller cannot obtain the actual state of the target system, and the stored system state value is equal to the stored value at the previous moment, that is,

[0067] Detect whether the controller-actuator channel DoS attack occurs at time k; if the controller-actuator channel DoS attack does not occur, clear the memory of the actuator of the target nonlinear system and replace the optimal control sequence U at time k with the optimal control sequence U at time k. * (k) is passed to the actuator’s memory, and the first optimal control input u in the actuator’s memory is * (1) Acting on the target nonlinear system;

[0068] If a DoS attack occurs on the controller-actuator channel, the lth optimal control input u in the actuator memory is * (l) Act on the target nonlinear system.

[0069] The effects of the present invention are further described below with reference to two simulation examples.

[0070] 1) The target nonlinear system is a van der Pol oscillator, and its control block diagram is as follows Figure 2 The discrete-time system dynamic equation of the van der Pol oscillator is as follows:

[0071]

[0072] Among them, x 1,k represents the van der Pol oscillator displacement, x 2,k represents the van der Pol oscillator speed, u k represents the control input. The system state constraint is χ={x:-0.6≤x 1,k ≤0.6}. The system control input constraint is The weight matrix in the cost function is selected as Q = [1, 0; 0, 1], R = 0.01. The initial state of the system is selected as x0 = [0.5, -0.6] T .

[0073] With the help of Matlab / IPOPT, the Koopman model predictive control (K-MPC) method with attack compensation and the Koopman model predictive control method without attack compensation are simulated respectively. Figure 3 and Figure 4 It shows the changes of system state trajectory and control input trajectory under the two control methods. Figure 3 and Figure 4 It can be seen that the K-MPC method with DoS attack compensation stabilizes the system state and control input near the origin, while the K-MPC method without DoS attack compensation cannot drive the system state and control input near the origin. This shows that the secure data-driven predictive control method proposed in this paper against dual-channel DoS attacks can effectively ensure system stability.

[0074] 2) The target nonlinear system is a DC generator, and its continuous-time system dynamic equation is as follows:

[0075]

[0076] in, represents the differential of the DC motor current x1, The system state constraint is χ={x:-0.6≤x1≤0.6}. The system control input constraint is The weight matrix in the cost function is selected as Q = [1, 0; 0, 1], R = 0.01. The initial state of the system is selected as x0 = [0.5, -0.6] T The reference trajectory is a square wave signal.

[0077] The above continuous-time system is discretized using the fourth-order Runge-Kutta method with a period of T = 0.01s. Figure 5 and Figure 6 It shows the changes of motor speed and input stator current under the two control methods. Figure 5 It can be seen that the K-MPC method with DoS attack compensation allows the motor speed to quickly track the given square wave reference trajectory and meet the state constraints; while the K-MPC method without DoS attack compensation cannot allow the motor speed to track the non-fixed square wave reference trajectory and exceeds the state constraints. Figure 6 It can be seen that the K-MPC method without DoS attack compensation has a large stator current variation and cannot make the speed track the reference value. This shows that the event-triggered data-driven predictive control method proposed in this invention can effectively ensure system stability under DoS attacks.

[0078] The above embodiments are used to illustrate the present invention rather than to limit the present invention. Any modifications and changes made to the present invention within the spirit of the present invention and the protection scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A secure data-driven predictive control method for dual-channel DoS attacks, characterized in that: The following steps are involved: 1) Construct a linear control model based on Koopman operator theory; 2) According to the linear control model, a finite time domain optimization control problem is constructed and solved based on the historical data of the target nonlinear system to obtain the optimal control sequence at time k 3) According to the dual communication channel asynchronous DoS attack state, the optimal control sequence at time k is The optimal control input is selected and applied to the target nonlinear system.

2. A secure data-driven predictive control method for dual-channel DoS attacks according to claim 1, characterized in that: In 1), the linear control model satisfies the following formula: z(k+1)=Az(k)+Bu(k) The matrix [AB] is the infinite-dimensional Koopman operator The approximate value of is calculated by the following formula: X lift =[x1,ψ(x1),…,ψ(x i ),…,ψ(x K )] Y lift =[y1,ψ(y1),…,ψ(x i ),…,ψ(y K )] Among them, z(k+1) is the system state of the Koopman space at time k+1, z(k) is the system state of the Koopman space at time k, is the predicted value of the actual state of the system after dimensionality reduction from the Koopman space, A and B are the first parameter matrix and the second parameter matrix respectively, and C is the mapping matrix from the Koopman space to the target system space. represents the pseudo-inverse of the matrix, represents matrix multiplication; X lift For different sampling states x i The matrix composed of the lifting functions of is the matrix X lift The pseudo-inverse of Y lift For different system states y i The matrix composed of the lifting function of ψ(x i ) represents the system state x i The corresponding lifting function; K is the number of collected system states; U is the vector composed of K control inputs; X is the vector composed of K system states.

3. The secure data-driven predictive control method for dual-channel DoS attacks according to claim 1, characterized in that: In the above 2), the finite time domain optimization control problem satisfies the following formula: z(l+1)=Az(l)+Bu(l),l=0,…,N-1, Among them, U * (k) represents the optimal control sequence, which contains N optimal control inputs, satisfying U * (k)=[u * (0),u * (1),…,u * (N-1)],u * (0),u * (1),…,u * (N-1) represents the first control input, the second control input, and the Nth control input respectively. represents the cost function, is the system state stored in the controller at time k, u(l) represents the given control sequence, N represents the prediction time domain, z(l) and z(l+1) are the system states in the Koopman space at time l and time l+1 respectively, z(N) represents the system state in the Koopman space at time N, A and B are the first parameter matrix and the second parameter matrix respectively, C is the mapping matrix from the Koopman space to the target system space, z s represents the desired state of the system, Q is the state weight matrix, R is the control input weight matrix, ‖·‖ Q Represents the weight as the vector bi-norm operation of the state weight matrix Q, ‖·‖ R Represents the weight as the vector two-norm operation that controls the input weight matrix R; is the input constraint, is the state constraint, is the latest system state stored by the controller; z(0) represents the system state in the Koopman space at time 0; Indicates that the system status Lifting function for upgrading to Koopman space.

4. The secure data-driven predictive control method for dual-channel DoS attacks according to claim 1, characterized in that: Said 3) is specifically: Detect whether a DoS attack on the sensor-controller channel occurs at time k; if a DoS attack on the sensor-controller channel does not occur, the controller obtains the latest state of the target system and updates the system state value stored in the controller; If a DoS attack occurs on the sensor-controller channel, the controller cannot obtain the actual state of the target system, and the stored system state value is equal to the stored value at the previous moment; Detect whether the controller-actuator channel DoS attack occurs at time k; if the controller-actuator channel DoS attack does not occur, clear the memory of the actuator of the target nonlinear system and replace the optimal control sequence U at time k with the optimal control sequence U at time k. * (k) is passed to the actuator’s memory, and the first optimal control input u in the actuator’s memory is * (0) Act on the target nonlinear system; If a DoS attack occurs on the controller-actuator channel, the lth optimal control input u in the actuator memory is * (l) Act on the target nonlinear system.

5. A secure data-driven predictive control device for dual-channel DoS attacks, characterized in that: include: A linear control model building unit, used to build a linear control model based on Koopman operator theory; The optimal control sequence generation unit is used to construct a finite time domain optimization control problem based on the linear control model and solve it based on the historical data of the target nonlinear system to obtain the optimal control sequence U at time k. * (k); optimal control input generation unit, used to generate the optimal control sequence U at time k according to the asynchronous DoS attack state of the dual communication channels * (k) The optimal control input is selected and applied to the target nonlinear system.

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