Network attack resistance method considering robust actual stability

Abstract

The invention discloses a network attack resistance method considering robust actual stability. According to the method, a Lyapunov function is used to obtain sufficient conditions to ensure that a complex coupling network realizes robust event stability. The method is based on the thought of switching, two strategies exist to process the activity time of the controller under the nth network attack, namely, in one case, zero input is used, the service attack is denied to cause that the controller cannot be updated in time, and the controller is triggered immediately after the system is attacked; and the other method is that the latest released trigger data is stored to resist the influence generated by the attack when the attack does not occur, and a controller is used for controlling the state of the system. Successive behaviors are eliminated, resource consumption in a channel is reduced, and system performance is improved.

Description

Technical Field

[0001] The present invention relates to the field of network security, and in particular to a network attack resistance method taking robust practical stability into consideration. Background Art

[0002] The background of robust practical stability technology is a multidisciplinary field, including computer networks, information security, data science, system engineering, etc. Its development and application are crucial to ensure the safe operation of modern network and information systems. Robust practical stability under DoS (Denial of Service) attacks is part of the field of network security.

[0003] Regarding the problem of denial of service attacks, existing researchers have only modeled them as following the Bernoulli model, but in fact DoS attacks are carefully planned by attackers in order to reduce system performance. Therefore, it is inappropriate to consider the periodic model and Bernoulli distribution.

[0004] Due to the structural limitations of complex coupled networks, few researchers have considered studying stability issues under poor physical conditions, and have not considered issues such as attacks, time delays, resource consumption, and actuator saturation. At present, research on complex coupled network systems focuses on consistency, Lyapunov stability, and other issues, and no research results on robust practical stability have emerged. However, Lyapunov stability and consistency issues do not consider the boundedness of the system state. Therefore, in actual engineering applications, it is necessary to ensure that the system state is within a certain range to improve system performance. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a network attack resistance method taking robust practical stability into consideration, which solves the problem that the prior method does not take robust practical stability into consideration, resulting in poor attack resistance performance.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0007] A network attack resistance method considering robust practical stability is provided, which comprises the following steps:

[0008] S1. Construct a Lyapunov function; obtain a control gain K, an auxiliary gain matrix H and a trigger matrix W by deriving the Lyapunov function, and construct a controller based on the control gain K and the auxiliary gain matrix H;

[0009] S2, determine whether there is a network attack at present, if yes, proceed to step S3; otherwise, proceed to step S5;

[0010] S3, constructing an event trigger mechanism based on the error between the current system state and the system state at the previous moment, the trigger matrix, and the system state that triggered the attack resistance last time;

[0011] S4, determine whether it is currently in the attack range. If it is in the attack range, immediately obtain the trigger time through the event trigger mechanism when the attack ends, and bring the trigger time into the controller to update the controller parameters to offset the impact of the current attack, complete the resistance to the current DoS attack, and enter step S5; otherwise, enter step S6;

[0012] S5, determine whether to continue the network attack resistance, if yes, return to step S1; otherwise, end;

[0013] S6. Determine whether the error between the current system state and the system state at the previous moment meets the given conditions. If so, obtain the trigger moment through the event trigger mechanism, and bring the trigger moment into the controller to update the controller parameters, and return to step S5; otherwise, go directly to step S5.

[0014] Furthermore, the expression of Lyapunov function is:

[0015]

[0016] Where V δ (t) represents the Lyapunov function at time t; x(t) represents the system state at time t; x(s) represents the system state at time s; δ is a value function, if the current time t is a non-attack time, the value is 1, if the current time t is an attack time, the value is 2; is the sampling interval; e is a natural constant; Q δ and All are positive definite matrices; θ represents the time; the superscript T represents the transpose of the matrix; It means to find the first-order derivative of the transpose of x(s); Indicates the first-order derivative of x(s); ds and dθ are both integral elements; when δ is 1, a δ is 0.16, when δ is 2, a δ is 0.1.

[0017] Furthermore, the specific method of obtaining the control gain K, the auxiliary gain matrix H and the trigger matrix W by deriving the Lyapunov function is:

[0018] Derivative of the Lyapunov function:

[0019]

[0020] Solve Ψ1<0,Ψ2<0 through matlab to obtain the control gain K and trigger matrix W; represents the derivative of the Lyapunov function without attack; represents the derivative of the Lyapunov function under attack; τ k,n (t) represents the time of the kth trigger, x T (t-τ k,n (t)) is the n-dimensional state matrix containing time delay; It represents the segmentation error of the k-th trigger and the n-th attack; is the state matrix containing the adopted cycle; T (t,x(t)) is the n-dimensional nonlinear term;

[0021]

[0022]

[0023] All are positive definite matrices; Parameter θ l satisfy D l and All are prior matrices; is the coefficient matrix of nonlinear terms; U1 is the matrix that satisfies nonlinear terms; represents the Kroc inner product; M f represents the internal coupling matrix; * in the matrix represents the transposition of the symmetric position; c is the coupling strength; A, E and G are all constant matrices, G = [g ii ] N×N , N represents a set of positive integers; v is a constant;

[0024]

[0025]

[0026] U1 and U2 are both positive definite matrices; G1 and G2 are prior matrices.

[0027] Furthermore, the expression of the controller is:

[0028]

[0029] in represents the saturated actuator input variable at time t; x i (t) is the i-th state variable of the system at time t, i.e., the update object; F 1,nis the nth non-attack time period; F 2,n is the nth attack time period; f(t,x i (t)) represents the nonlinear term; x j (t) represents the jth state variable of the system at time t; B f is a constant matrix.

[0030] Furthermore, the expression of the event triggering mechanism in step S3 is:

[0031]

[0032] in is the trigger time of the kth trigger and the nth attack; represents the dth time period between the kth trigger and the k+1th trigger; Indicates the next trigger time; Represents the transpose of the error matrix between the current system state and the system state at the previous moment; represents the error matrix between the current system state and the system state at the previous moment; δ(t) is the trigger threshold; Indicates the time point The system parameter matrix when F 1,n-1 represents the n-1th non-attack time period; h n is the start time of the nth attack; express exist Under the circumstances.

[0033] Furthermore, matrix A, matrix E, matrix G, matrix M f , Matrix B f and matrix G2 are:

[0034]

[0035] The value of the coupling strength c is 9; the matrix G1 is a matrix whose element values ​​are all 0; The value of is 0.01; the value of v is 5.

[0036] Furthermore, the matrix F2, the auxiliary gain matrix H and the trigger matrix W are respectively:

[0037]

[0038]

[0039] The beneficial effects of the present invention are:

[0040] 1. This method takes into account factors that may affect system performance, such as uncertain nonlinearity, network delay, non-periodic network attack, actuator saturation and actuator error. This method can achieve robust actual stability under the condition of poor physical state of the system and has wider practical applications.

[0041] 2. This method is based on the idea of ​​switching. There are two strategies to deal with the active time of the controller in the nth network attack. One is to use zero input. Denial of service attacks will cause the controller to fail to update in time. The controller is triggered immediately after the system is attacked. The other is to save the latest released trigger data when there is no attack to resist the impact of the attack and use the controller to control the system state. Not only does it exclude Zeno behavior, but it also reduces resource consumption in the channel and improves system performance.

[0042] 3. This method uses Lyapunov function to derive sufficient conditions to ensure the robust event stability of complex coupled networks. The final system state reaches the predetermined robust design stability domain from the given initial domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of the process of this method;

[0044] Figure 2 It is a schematic diagram of the framework of the adaptive event triggering control scheme under a denial of service attack in the embodiment;

[0045] Figure 3 The first component of three nodes selected for the complex coupling network in the embodiment;

[0046] Figure 4 The second component of three nodes selected for the complex coupling network in the embodiment;

[0047] Figure 5 The third component of the three nodes selected for the complex coupling network in the embodiment;

[0048] Figure 6 A timing diagram of controller updates performed by three nodes in the embodiment;

[0049] Figure 7 Schematic diagram of DoS attack in the embodiment. DETAILED DESCRIPTION

[0050] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0051] like Figure 1 As shown, the network attack resistance method considering robust practical stability includes the following steps:

[0052] S1. Construct a Lyapunov function; obtain a control gain K, an auxiliary gain matrix H and a trigger matrix W by deriving the Lyapunov function, and construct a controller based on the control gain K and the auxiliary gain matrix H;

[0053] S2, determine whether there is a network attack at present, if yes, proceed to step S3; otherwise, proceed to step S5;

[0054] S3, constructing an event trigger mechanism based on the error between the current system state and the system state at the previous moment, the trigger matrix, and the system state that triggered the attack resistance last time;

[0055] S4, determine whether it is currently in the attack range. If it is in the attack range, immediately obtain the trigger time through the event trigger mechanism when the attack ends, and bring the trigger time into the controller to update the controller parameters to offset the impact of the current attack, complete the resistance to the current DoS attack, and enter step S5; otherwise, enter step S6;

[0056] S5, determine whether to continue the network attack resistance, if yes, return to step S1; otherwise, end;

[0057] S6. Determine whether the error between the current system state and the system state at the previous moment meets the given conditions. If so, obtain the trigger moment through the event trigger mechanism, and bring the trigger moment into the controller to update the controller parameters, and return to step S5; otherwise, go directly to step S5.

[0058] The expression of Lyapunov function is:

[0059]

[0060] Where V δ (t) represents the Lyapunov function at time t; x(t) represents the system state at time t; x(s) represents the system state at time s; δ is the value function, if the current time t is a non-attack time, the value is 1, if the current time t is an attack time, the value is 2; h is the sampling interval; e is a natural constant; and All are positive definite matrices; θ represents the time; the superscript T represents the transpose of the matrix; It means to find the first-order derivative of the transpose of x(s); Indicates the first-order derivative of x(s); ds and dθ are both integral elements; when δ is 1, a δis 0.16, when δ is 2, a δ is 0.1.

[0061] The specific method of obtaining the control gain K, auxiliary gain matrix H and trigger matrix W by deriving the Lyapunov function is:

[0062] Derivative of the Lyapunov function:

[0063]

[0064] Solve ψ1<0, ψ2<0 through matlab to obtain the control gain K and trigger matrix W; represents the derivative of the Lyapunov function without attack; represents the derivative of the Lyapunov function under attack; τ k,n (t) represents the time of the kth trigger, x T (t-τ k,n (t)) is the n-dimensional state matrix containing time delay; It represents the segmentation error of the k-th trigger and the n-th attack; is the state matrix containing the adopted cycle; T (t,x(t)) is the n-dimensional nonlinear term;

[0065]

[0066] All are positive definite matrices; Parameter θ l satisfy D l and All are prior matrices; is the coefficient matrix of nonlinear terms; U1 is the matrix that satisfies nonlinear terms; represents the Kroc inner product; M f represents the internal coupling matrix; * in the matrix represents the transposition of the symmetric position; c is the coupling strength; A, E and G are all constant matrices, G = [g ij ] N×N , N represents a set of positive integers; v is a constant;

[0067]

[0068] U1 and U2 are both positive definite matrices; g1 and G2 are prior matrices.

[0069] The expression of the controller is:

[0070]

[0071] in represents the saturated actuator input variable at time t; x i (t) is the i-th state variable of the system at time t, i.e., the update object; F 1,n is the nth non-attack time period; F 2,n is the nth attack time period; f(t,x i (t)) represents the nonlinear term; x j (t) represents the jth state variable of the system at time t; B f is a constant matrix.

[0072] The expression of the event trigger mechanism in step S3 is:

[0073]

[0074] in is the trigger time of the kth trigger and the nth attack; represents the dth time period between the kth trigger and the k+1th trigger; Indicates the next trigger time; Represents the transpose of the error matrix between the current system state and the system state at the previous moment; represents the error matrix between the current system state and the system state at the previous moment; δ(t) is the trigger threshold; Indicates the time point The system parameter matrix when F 1,n-1 represents the n-1th non-attack time period; h n is the start time of the nth attack; express exist Under the circumstances.

[0075] In the specific implementation process, the existing technical means of observing attacks are very mature and are not the focus of this method. The focus of this method is to resist attacks and minimize the impact of attacks on the system.

[0076] In one embodiment of the present invention, the framework of the adaptive event triggering control scheme under denial of service attack is as follows: Figure 2 As shown in the figure, assuming that an attacker attacks the network, the actuators in the system will be affected accordingly, and the impact will extend to the complex coupled network and be detected by the sensor. This method will then perform adaptive event triggering, obtain the corresponding triggering moment and bring it into the controller to update the controller parameters, offset the impact of the current attack, and complete the resistance to the current DoS attack.

[0077] This embodiment uses rand to generate a random non-periodic DoS attack sequence. Considering the system, we get Figure 7 In this embodiment, matrix A, matrix E, matrix G, matrix M f , Matrix B f and matrix G2 are:

[0078]

[0079] The value of the coupling strength c is 9; the matrix G1 is a matrix whose element values ​​are all 0; The value of is 0.01; the value of v is 5.

[0080] Based on the above parameters, the linear matrix inequality Ψ1<0,Ψ2<0 is solved by using the linear matrix inequality toolbox LMI in MATLAB to obtain the matrix F2 and the trigger matrix W. Substitute the matrix F2 into the controller and use ode45 in MATLAB to solve the system state x i (t), where i represents a node, i = 1, 2, 3, corresponding to Figure 3 , Figure 4 and Figure 5 .

[0081] The matrix F2, auxiliary gain matrix H and trigger matrix W are:

[0082]

[0083] The matrix W is the corresponding trigger matrix. When the trigger mechanism is introduced, the system state x at each moment is solved. i (t) determines whether to trigger. If the trigger condition is met, the controller is updated and the result is Figure 6 .from Figures 3 to 5 It can be seen that the controller designed by this method only controls the system at the color time point, which greatly saves channel resources and takes into account Figure 7 The existence of non-periodic DoS attacks can still achieve robust practical stability of the system.

[0084] In summary, the present invention takes into account factors that may affect system performance, such as uncertain nonlinearity, network lag, non-periodic network attacks, actuator saturation and actuator errors. The method can achieve robust actual stability when the system is in a poor physical state and has a wider range of practical applications.

Claims

1. A network attack resistance method considering robust practical stability, It is characterized in that The following steps are involved: S1. Construct a Lyapunov function; obtain a control gain K, an auxiliary gain matrix H and a trigger matrix W by deriving the Lyapunov function, and construct a controller based on the control gain K and the auxiliary gain matrix H; S2, determine whether there is a network attack at present, if so, proceed to step S3; Otherwise, proceed to step S5; S3, constructing an event trigger mechanism based on the error between the current system state and the system state at the previous moment, the trigger matrix, and the system state that triggered the attack resistance last time; S4, determine whether it is currently in the attack range. If it is in the attack range, immediately obtain the trigger time through the event trigger mechanism when the attack ends, and bring the trigger time into the controller to update the controller parameters to offset the impact of the current attack, complete the resistance to the current DoS attack, and enter step S5; Otherwise, proceed to step S6; S5, determine whether to continue the network attack resistance, if yes, return to step S1; otherwise, end; S6, judging whether the error between the current system state and the system state at the previous moment meets a given condition, if so, obtaining the triggering moment through the event triggering mechanism, and bringing the triggering moment into the controller to update the controller parameters, and returning to step S5; Otherwise, go directly to step S5.

2. The network attack resistance method considering robust practical stability according to claim 1, It is characterized in that The expression of Lyapunov function is: Where V δ (t) represents the Lyapunov function at time t; x(t) represents the system state at time t; x(s) represents the system state at time s; δ is a value function, if the current time t is a non-attack time, the value is 1, if the current time t is an attack time, the value is 2; is the sampling interval; e is a natural constant; and are all positive definite matrices; θ represents the time; the superscript T represents the transpose of the matrix; It means to find the first-order derivative of the transpose of x(s); Indicates the first-order derivative of x(s); ds and dθ are both integral elements; when δ is 1, a δ is 0.16, when δ is 2, a δ is 0.

1.

3. The network attack resistance method considering robust practical stability according to claim 2, It is characterized in that The specific method of obtaining the control gain K, auxiliary gain matrix H and trigger matrix W by deriving the Lyapunov function is: Derivative of the Lyapunov function: Solving Ψ by Matlab 1 <0,Ψ 2 <0, obtain the control gain K and trigger matrix W; represents the derivative of the Lyapunov function without attack; represents the derivative of the Lyapunov function under attack; τ k，n (t) represents the time of the kth trigger, x T (t-τ k，n (t)) is the n-dimensional state matrix containing time delay; It represents the segmentation error of the k-th trigger and the n-th attack; is the state matrix containing the adopted cycle; T (t, x(t)) is the n-dimensional nonlinear term; All are positive definite matrices; Parameter θ l satisfy D l and All are prior matrices; is the coefficient matrix of nonlinear terms; U 1 is the matrix that satisfies the nonlinear terms; represents the Kroc inner product; M f represents the internal coupling matrix; * in the matrix represents the transposition of the symmetric position; c is the coupling strength; A, E and G are all constant matrices, G = [g ij ] N×N , N represents a set of positive integers; v is a constant; U 1 , U 2 are all positive definite matrices; G 1 and G 2 is the prior matrix.

4. The network attack resistance method considering robust practical stability according to claim 3, It is characterized in that The expression of the controller is: in represents the saturated actuator input variable i at time t; x i (t) is the i-th state variable of the system at time t, i.e., the update object; F 1，n is the nth non-attack time period; F 2，n is the nth attack time period; f(t, x i (t)) represents the nonlinear term; x j (t) represents the jth state variable of the system at time t; B f is a constant matrix.

5. The network attack resistance method considering robust practical stability according to claim 3, It is characterized in that The expression of the event trigger mechanism in step S3 is: in is the trigger time of the kth trigger and the nth attack; represents the dth time period between the kth trigger and the k+1th trigger; Indicates the next trigger time; Represents the transpose of the error matrix between the current system state and the system state at the previous moment; represents the error matrix between the current system state and the system state at the previous moment; 6(t) is the trigger threshold; Indicates the time point The system parameter matrix when F 1，n-1 represents the n-1th non-attack time period; h n is the start time of the nth attack; express exist Under the circumstances.

6. The network attack resistance method considering robust practical stability according to claim 4, It is characterized in that Matrix A, Matrix E, Matrix G, Matrix M f , Matrix B f and the matrix G 2 They are: The value of coupling strength c is 9; the matrix G 1 is a matrix whose element values ​​are all 0; The value of is 0.01; the value of v is 5.

7. The network attack resistance method considering robust practical stability according to claim 6, It is characterized in that Matrix F 2 , the auxiliary gain matrix H and the trigger matrix W are:

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