CN116614299B - Hybrid attack-based complex network dynamic event triggering traction control method - Google Patents
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Abstract
The invention discloses a complex network dynamic event triggering traction control method under hybrid attack. Firstly, establishing a complex network synchronous error model with N nodes, introducing a dynamic event triggering mechanism into the synchronous error model, and designing dynamic event triggering conditions; considering the influence of FDI attack and DOS attack on system input at the same time, and establishing a complex network synchronization error model with N nodes under the hybrid network attack; based on Lyapunov stability theory and Kronecker method, adopting a traction control strategy to obtain a sufficient condition for stabilizing a synchronous error system by utilizing partial nodes; and solving the inequality of the linear matrix, and obtaining the gain of the controller and the triggering parameters of the dynamic event. The controller provided by the invention can simultaneously cope with the condition that two attacks of FDI and DOS affect the system, effectively ensures the system safety, only needs to control part of nodes in the complex network, and reduces the realization cost for practical engineering.
Description
Technical Field
The invention belongs to the technical field of network control, and mainly relates to a complex network dynamic event triggering traction control method under hybrid attack.
Background
The complex network, also called complex power network, is formed by connecting a large number of dynamic nodes according to a certain topological relation. However, due to the limited network bandwidth, timeliness of information exchange is severely restricted, and a series of network induction problems such as network congestion, information delay, packet loss, disorder and the like are brought; moreover, data communication networks are extremely vulnerable, which all present challenges for the control of the network system.
The current research on complex network control has the following problems
(1) Most researches on complex network attacks are focused on processing a certain attack, ignoring the condition that multiple attacks exist simultaneously and cannot process mixed attacks, for example, chinese patent application CN112286051A (neural network quantization control method based on self-adaptive event triggering mechanism under complex network attack)
(2) Many related studies have often controlled all nodes when controlling a complex network with multiple nodes. For example, chinese patent application CN112995154a, "a complex network synchronization control method under aperiodic DoS attack". The method includes introducing an event triggering mechanism into the synchronization error model and analyzing synchronization problems under non-periodic DOS attacks. However, the above method only considers a single aperiodic DOS attack and the static event trigger mechanism threshold is fixed, and the control action is applied to all nodes, which is not easy in practical engineering application.
There is therefore a need in the art for a method that can handle multiple attacks simultaneously and control only for a portion of the nodes, and that can dynamically adjust the event trigger threshold to conserve network resources.
Disclosure of Invention
The invention aims to provide a complex network dynamic event triggering traction control method under hybrid attack, which is used for solving the problem that a synchronous error model is stable by adopting a traction control mode by utilizing a dynamic event triggering mechanism under the condition of hybrid network attack of a complex network system. The requirement of the system on network bandwidth is reduced, and the data transmission efficiency is improved.
The technical scheme is as follows:
a complex network dynamic event triggering traction control method under hybrid attack comprises the following steps:
s1: establishing a complex network synchronization error model with N nodes;
s2: introducing a dynamic event triggering mechanism into the synchronous error model, and designing dynamic event triggering conditions;
s3: considering the influence of FDI attack and DOS attack on system input at the same time, and establishing a complex network synchronization error model with N nodes under the hybrid network attack;
s4: based on Lyapunov stability theory and Kronecker method, adopting a traction control strategy to obtain a sufficient condition for stabilizing a synchronous error system by utilizing partial nodes;
s5: solving the inequality of the linear matrix, and obtaining the gain of the controller and the triggering parameters of the dynamic event;
in the step S1, a system state model of N nodes is established in consideration of the situations of multiple nodes and complex connection between nodes in the complex network system:
wherein the method comprises the steps ofIs the state vector of node i, +.>E and M are parameter matrices of appropriate dimensions as a continuous nonlinear function, u i (t) is a control input vector of a node i, c > 0 is coupling strength, Γ represents a network internal coupling matrix, and a= [ a ] ij ] N×N Representing the topology of the network for the outcoupling matrix and satisfying +.>
A synchronization error model is derived and a synchronization error model is derived,for a solution of an isolated node in a complex network, the following is satisfied:
select delta i (t)＝x i And (t) -pi (t) is a synchronous error, and the synchronous error dynamic system is as follows:
wherein g (x) i (t),π(t))＝g(x i (t))-g(π(t))；
In the step S2, a dynamic event triggering mechanism is introduced, wherein the dynamic event triggering mechanism consists of a zero-order retainer, a comparator and a register, and the dynamic event triggering condition is determined by the following inequality:
wherein the method comprises the steps of And->Represents the last transmitted data and the current sampled data, respectively, ">Represents the last trigger time, k is a non-negative integer,
λ i (t) satisfies the following relationship:
wherein 0 < lambda i (t)＜1,σ i ＞0,ξ i > 0, is a known constant for adjusting dynamic event triggering parameters,
the next release instant is determined by the following equation:
in S3, the control input is affected by the FDI attack, and the input signal will become:
wherein alpha is i (t) is the attack probability of FDI attack on the ith node, θ (u) i (t)) is the attack function of the ith node,
further consider the impact of DOS attacks on the system:
the hybrid network attack model is expressed as:
in the step S4, the specific steps of using the sufficient conditions for stabilizing the synchronization error system by using part of the nodes include:
the above hybrid network model was converted to the following form using the Kronecker product method:
namely:
wherein,
α(t)＝diag N {α i (t)},θ(u(t))＝col N {θ(u i (t))},
wherein, l is the l nodes of traction control,
the Lyapunov function is constructed as follows
Wherein,
the Lee function is derived along the closed loop system, and the derivative is negatively determined to obtain a sufficient condition for stabilizing the synchronous error system by utilizing partial nodes, thereby ensuring the asymptotically stable synchronous error system, namely realizing the synchronous control of the controlled complex dynamic network to the isolated nodes,
given a scalar k 1 ,k 2 ，α 1 ,τ M The matrices E, M, A, Γ, when there is a symmetric positive definite matrix X > 0, Y > 0,so that the following inequality is established, the synchronization error system is stabilized:
wherein,
the controller gain and dynamic event triggering conditions are as follows:
the invention has the following beneficial effects:
(1) The complex network dynamic event triggering traction control method under hybrid attack provided by the invention considers the simultaneous existence of FDI attack and DOS attack in a transmission channel, and establishes a new system model. Meanwhile, a dynamic event trigger mechanism is introduced, so that the event trigger threshold can be dynamically adjusted, the data transmission efficiency is improved, and the bandwidth load is reduced.
(2) The invention adopts a traction control strategy, only controls part of nodes in the complex network, indirectly transmits the control action through the coupling between the nodes, reduces the number of controlled nodes in the network, reduces the total number of controllers, and saves the control cost and calculation consumption. And simultaneously, based on the method, a sufficient condition for stabilizing the synchronous error model is given by utilizing a linear matrix inequality and a Lyapunov theory.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a scaleless network diagram of 9 nodes in a simulation case;
FIG. 3a is a first component of the synchronization error for each node of a complex network in a simulation case;
FIG. 3b is a second component of the synchronization error for each node of the complex network in the simulation case;
FIG. 4 is a graph comparing control input signals of nodes not interfered by the hybrid attack and the nodes interfered by the hybrid attack in a simulation case;
FIG. 5 is a graph of dynamic event trigger mechanism release and interval time in a simulation case;
fig. 6 is a graph of an attack signal in a simulated case.
Detailed Description
The following cases are merely illustrative, and are intended to more clearly describe the technical solutions of the present invention, and are not intended to limit the scope of application of the present invention. Unless otherwise indicated, terms of art or academic expressions used herein are intended to be in the ordinary meaning as is accorded to the technical field of this invention.
Fig. 1 is a schematic structural diagram of a hybrid-attacked complex network dynamic event-triggered traction control method, comprising the steps of:
s1: establishing a complex network synchronization error model with N nodes;
s2: introducing a dynamic event triggering mechanism into the synchronous error model, and designing dynamic event triggering conditions;
s3: considering the influence of FDI attack and DOS attack on system input at the same time, and establishing a complex network synchronization error model with N nodes under the hybrid network attack;
s4: based on Lyapunov stability theory and Kronecker method, adopting a traction control strategy to obtain a sufficient condition for stabilizing a synchronous error system by utilizing partial nodes;
s5: solving the inequality of the linear matrix, and obtaining the gain of the controller and the triggering parameters of the dynamic event;
in the step S1, a system state model of N nodes is established in consideration of the situations of multiple nodes and complex connection between nodes in the complex network system:
wherein the method comprises the steps ofIs the state vector of node i, +.>E and M are parameter matrices of appropriate dimensions as a continuous nonlinear function, u i (t) is a control input vector of a node i, c > 0 is coupling strength, Γ represents a network internal coupling matrix, and a= [ a ] ij ] N×N Representing the topology of the network for the outcoupling matrix and satisfying +.>
A synchronization error model is derived and a synchronization error model is derived,for a solution of an isolated node in a complex network, the following is satisfied:
select delta i (t)＝x i And (t) -pi (t) is a synchronous error, and the synchronous error dynamic system is as follows:
wherein g (x) i (t),π(t))＝g(x i (t))-g(π(t))；
In the step S2, a dynamic event triggering mechanism is introduced, and the dynamic event triggering mechanism consists of a zero-order retainer, a comparator and a register. The dynamic event trigger condition is determined by the following inequality:
wherein the method comprises the steps ofRepresents the last transmitted data and the current sampled data, respectively, ">K is a non-negative integer representing the last trigger time.
λ i (t) satisfies the following relationship:
wherein 0 < lambda i (t)＜1,σ i ＞0,ξ i > 0, is a known constant for adjusting dynamic event triggering parameters.
The next release instant is determined by the following equation:
when transmitting signals in a network channel, communication delay is unavoidable, and the delay is usedRepresenting andthe time of transmitting data to the controller can be expressed as +.>
Definition of the definitionThe actual synchronization error can be written as:
the actual control input can then be described as:
in the step S3, the control input is affected by the FDI attack, and the trigger error is considered, and the input signal may be expressed as:
the control input under the influence of an FDI attack while taking into account the trigger error can be expressed as:
wherein alpha is i (t) is the attack probability of FDI attack on the ith node, θ (u) i (t)) is the ithAttack function of the node.
Consider the impact of DOS attacks on the system:
the hybrid network attack model is:
in the step S4, based on Lyapunov stability theory and Kronecker method, a traction control strategy is adopted to obtain sufficient conditions for stabilizing a synchronous error system by using partial nodes:
the above hybrid network model is transformed into the following form using the Kronecker product method:
namely:
wherein,
α(t)＝diag N {α i (t)},θ(u(t))＝col N {θ(u i (t))},
where l is the l nodes of traction control.
The Lyapunov function is constructed as follows
Wherein,
v (t) derives t and finds its expectation, it can be obtained:
when t is E D 1k In the time-course of which the first and second contact surfaces,
thus, the first and second light sources are connected,
further, the processing unit is used for processing the data,
from the triggering conditions
For the nonlinear function G (t), the following is satisfied:
zeta taking 1 (t)＝col{Δ(t)Δ(t-τ(t))Δ(t-τ M ) G (t) ε (t) θ (u (t)) } is obtained
Wherein,
wherein,
when phi is 1 When the number of the groups is less than 0,for any t E D 1k There is->
When t is E D 2k In the time-course of which the first and second contact surfaces,
wherein ζ 2 (t)＝col{Δ(t)Δ(t-τ(t))Δ(t-τ M )G(t)}
Wherein,
given a scalar k 1 ,k 2 ，α 1 ,τ M The matrices E, M, A, Γ, when there is a symmetric positive definite matrix X > 0, Y > 0,so that the following inequality is established, the synchronization error system is stabilized:
wherein:
the controller gain and dynamic event triggering conditions are as follows:
the simulation analysis is carried out by an example, the inequality of the linear matrix is solved by writing a MATLAB program, the gain of the controller and the triggering parameters of the dynamic event are obtained, a simulation curve is drawn, and the effectiveness of the design method is proved by the simulation example.
Considering a complex network system with 9 nodes as shown in fig. 2, the system parameters are set as follows:
the initial state of the system is as follows:
x 1 (0)＝[0.55 -2.34] T ，x 2 (0)＝[2.12 -0.57] T ，x 3 (0)＝[2.74 -1.22] T ，
x 4 (0)＝[-3.1 -4.1] T ，x 5 (0)＝[-7 -2] T ，x 6 (0)＝[2 1] T ，
x 7 (0)＝[-3.8 -3] T ，x 8 (0)＝[-1.65 -4.2] T ，x 9 (0)＝[-1 -2.2] T ，
nonlinear functionThe sampling period is set to 0.1s,
setting FDI attack probability α=0.5, attack function θ (u i (t)) is:
θ(u i (t))＝0.1u i (t)+tanh(0.1u i (t))
setting DOS attack time as follows:
t∈(0，0.47)∪(5.52，6.70)∪(8.04，9.25)∪(10.40，10.80)
the nodes with the numbers of 1, 2, 3 and 7 are selected as traction points of traction control,
let sigma 1 ＝σ 2 ＝σ 3 ＝σ 4 ＝σ 5 ＝σ 6 ＝σ 7 ＝σ 8 ＝σ 9 ＝0.3，
ξ 1 ＝ξ 2 ＝ξ 3 ＝ξ 4 ＝ξ 5 ＝ξ 6 ＝ξ 7 ＝ξ 8 ＝ξ 9 ＝42，k 1 ＝k 2 ＝1。
Solving the linear matrix inequality by using an LMI toolbox of MATLAB to obtain the following formula:
K 1 ＝[-0.8807 -0.7289],K 2 ＝[-0.8381 -0.6884],K 3 ＝[-0.8353 -0.6971],
K 7 ＝[-0.8430 -0.6909],K 4 ＝K 5 ＝K 6 ＝K 8 ＝K 9 ＝0,
in the present simulation example, the synchronization error of the system is shown in fig. 3, and it can be seen that under the dual attack of FDI and DOS, the system realizes synchronization, and the control effect of the controller is good. Fig. 4 shows a control input signal comparison diagram of each node not interfered by the hybrid attack and the hybrid attack, so that the interference condition of the FDI attack on the control signal can be intuitively seen, and under the traction control strategy, no control action is exerted on the nodes with numbers 4, 5, 6, 8 and 9. Fig. 5 shows a dynamic event trigger mechanism release and interval time diagram, and it can be seen that under the traction control strategy there is no trigger action on nodes numbered 4, 5, 6, 8, 9. Fig. 6 shows a graph of an FDI attack signal.
Claims (1)
1. The complex network dynamic event triggering traction control method under hybrid attack is characterized by comprising the following steps:
s1: establishing a complex network synchronization error model with N nodes;
s2: introducing a dynamic event triggering mechanism into the synchronous error model, and designing dynamic event triggering conditions;
s3: considering the influence of FDI attack and DOS attack on system input at the same time, and establishing a complex network synchronization error model with N nodes under the hybrid network attack;
s4: based on Lyapunov stability theory and Kronecker method, adopting a traction control strategy to obtain a sufficient condition for stabilizing a synchronous error system by utilizing partial nodes;
s5: solving the inequality of the linear matrix, and obtaining the gain of the controller and the triggering parameters of the dynamic event;
in the step S1, a system state model of N nodes is established in consideration of the situations of multiple nodes and complex connection between nodes in the complex network system:
wherein the method comprises the steps ofIs the state vector of node i, g:>e and M are parameter matrices of appropriate dimensions as a continuous nonlinear function, u i (t) is a control input vector of a node i, c > 0 is coupling strength, Γ represents a network internal coupling matrix, and a= [ a ] ij ] N×N Representing the topology of the network for the outcoupling matrix and satisfying +.>
A synchronization error model is derived and a synchronization error model is derived,for a solution of an isolated node in a complex network, the following is satisfied:
select delta i (t)＝x i And (t) -pi (t) is a synchronous error, and the synchronous error dynamic system is as follows:
wherein g (x) i (t),π(t))＝g(x i (t))-g(π(t))；
In the step S2, a dynamic event triggering mechanism is introduced, wherein the dynamic event triggering mechanism consists of a zero-order retainer, a comparator and a register, and the dynamic event triggering condition is determined by the following inequality:
wherein the method comprises the steps ofAnd->Represents the last transmitted data and the current sampled data, respectively, ">Represents the last trigger time, k is a non-negative integer,
λ i (t) satisfies the following relationship:
wherein 0 < lambda i (t)＜1,σ i ＞0,ξ i > 0, is a known constant for adjusting dynamic event triggering parameters,
the next release instant is determined by the following equation:
in S3, the control input is affected by the FDI attack, and the input signal will become:
wherein alpha is i (t) is the attack probability of FDI attack on the ith node, θ (u) i (t)) is the attack function of the ith node,
further consider the impact of DOS attacks on the system:
the hybrid network attack model is expressed as:
in the step S4, the specific steps of using the sufficient conditions for stabilizing the synchronization error system by using part of the nodes include:
the above hybrid network model is transformed into the following form using the Kronecker product method:
wherein Δ (t) =col N {δ i (t)},G(t)＝col N {g(x i (t),π(t))},
Δ(t-τ(t))＝col N {δ i (t-τ i (t))},ε(t)＝col N {ε i (t)},
α(t)＝diag N {α i (t)},θ(u(t))＝col N {θ(u i (t))},
l is the l nodes of the traction control,
the Lyapunov function is constructed as follows
Wherein,
the Lee function is derived along the closed loop system, and the derivative is negatively determined to obtain a sufficient condition for stabilizing the synchronous error system by utilizing partial nodes, thereby ensuring the asymptotically stable synchronous error system, namely realizing the synchronous control of the controlled complex dynamic network to the isolated nodes,
given a scalar k 1 ,k 2 ，α 1 ,τ M The matrices E, M, A, Γ, when there is a symmetric positive definite matrix X > 0, Y > 0,so that the following inequality is established, the synchronization error system is stabilized:
wherein,
the controller gain and dynamic event triggering conditions are as follows:
K＝XY -1 ,
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