CN115643579A - Method for controlling malicious programs of information physical system of power distribution network based on PC-PLC - Google Patents

Abstract

The invention discloses a power distribution network information physical system malicious program control method based on a PC-PLC, which comprises the following steps: s1: PL and PLC network nodes are divided based on real problem analysis; s2: constructing a network node state transition diagram; s3: constructing a differential equation set of a malicious program propagation model; s4: a control strategy is proposed; s5: constructing a cost function; s6: constructing a Lagrange function, and introducing a Lagrange multiplier; s7: constructing a Hamiltonian; s8: constructing a covariate equation set and a cross-section condition; s9: and solving the optimal control pair. According to the method, the cost function for controlling the malicious program is constructed, the Hamilton equation is constructed according to the differential equation of the model and the cost function, the collaborative equation set and the optimal control pair are solved, and the purpose that a better control effect is achieved with the minimum cost is achieved.

Description

A malicious program control method based on PC-PLC distribution network cyber-physical system

technical field

The present invention relates to the technical field of wireless rechargeable sensor networks, in particular to a method for controlling malicious programs in a cyber-physical system of a PC-PLC power distribution network for modeling and optimal control of malicious program propagation in a wireless charging sensor network of a power system.

Background technique

In recent years, with the rapid development of wireless rechargeable sensor network technology, its application is becoming more and more common, and it can be seen in military, agriculture, industry, transportation, information equipment and other fields. As the foundation of national economic development, the power industry, in order to quickly respond to social electricity demand, achieve real-time safe and flexible information exchange, and realize reasonable optimization and effective scheduling of resources. The traditional power grid can no longer meet the needs of power development. The modern power system It has developed into a power cyber-physical system with deep integration of power grid and information network.

The modern power cyber-physical system, on the basis of the physical layer of the traditional power network, couples the information layer, and communicates with each other through a large number of sensor connections to achieve real-time perception, detection, and processing of information in its target area. However, while the power grid enjoys the benefits brought by the power cyber-physical system—making the operation of the modern power grid more cost-effective and efficient—it also needs to bear the potential security risks brought by intelligent interconnection to the power system operation. As far as the modern power cyber-physical system is concerned, all aspects of power generation, power transmission, power distribution, and power consumption may be attacked by malicious programs, and the availability, integrity, and confidentiality of the system will be damaged to varying degrees. Severe cases may even cause the entire power grid to be paralyzed. Therefore, the security issues of modern power networks cannot be ignored.

Based on the potential information security threats of modern power grids, fully considering the spread and infection mechanism of malicious programs, establishing a realistic network model to analyze and research the optimal control strategy to suppress the spread of malicious programs and ensure the security of network information is an important task today. topic.

Contents of the invention

In order to prevent and deal with the adverse effects of malicious programs on the information of electric power cyber-physical systems, the present invention provides a PC-PLC power distribution network cyber-physical system malicious program propagation model based on nonlinear time-delay heterogeneous model to solve the above problems.

The present invention provides following technical scheme:

A malicious program control method based on a PC-PLC power distribution network cyber-physical system, comprising the following steps:

S1: Divide PL and PLC network nodes based on analysis of real problems;

S2: Build a network node state transition diagram;

S3: Differential equations for building a malicious program propagation model;

S4: propose control strategy;

S5: Build a cost function;

S6: Construct a Lagrangian function and introduce a Lagrangian multiplier;

S7: Construct a Hamiltonian function;

S8: Construct costate variable equations and transversal conditions;

S9: Solve the optimal control pair.

Preferably, in the step S1, the computer PC network and the programmable controller PLC network are recorded as the A network and the B network respectively, and each device of the A network and the B network corresponds to a node, and according to the degree of infection of the node , classifying them as infected nodes, susceptible nodes, immune nodes and isolated nodes. Preferably, in said S2, from all texts x in T, including adversarial samples and clean samples, select the most important k words, and sort them, denoted as C(x).

Preferably, in the step S3, the system of differential equations is constructed based on the network node state transition diagram, specifically as follows:

In the formula, θ _xy (t) is defined as the probability that a susceptible node has an adjacent infected node, x=1,2; y=1,2, where "1" represents the PC network, and "2" represents the PLC network, namely :

θ ₁₁ (t) represents the probability that a PC-susceptible node is adjacent to a PC-infected node, θ ₁₂ (t) represents the probability that a PC-susceptible node is adjacent to a PLC-infected node, and θ ₂₁ (t) represents the probability that a PLC-susceptible node is adjacent to a PC The probability that the infected node is adjacent, θ ₂₂ (t) represents the probability that the PLC susceptible node is adjacent to the PLC infected node, as follows:

分别是在t时刻PC网络度为(i,j)的易感节点(S)、感染节点(I)、隔离节点(Q)、免疫节点(R)的数量，

分别是在t时刻PLC网络度为(k,l)的易感节点、感染节点、免疫节点的数量,

为PC网络度为(i,j)的各节点总数，

为PLC网络度为(k,l)的各节点总数；一 个PC节点的度，用(i,j)表示，即表示为PC网络的某个节点与i个其他PC节点 及j个PLC节点相连接；一个PLC节点的度，用(k,l)表示，即意为PLC网络的 某个节点与k个其他PLC节点及,l个PC节点相连接；同时，任意时刻满足以 下关系：

are the number of susceptible nodes (S), infected nodes (I), isolated nodes (Q) and immune nodes (R) with PC network degree (i, j) at time t,

are the number of susceptible nodes, infected nodes and immune nodes with PLC network degree (k,l) at time t, respectively,

is the total number of nodes with PC network degree (i, j),

is the total number of nodes in the PLC network whose degree is (k, l); the degree of a PC node is expressed by (i, j), which means that a node in the PC network is related to i other PC nodes and j PLC nodes Connection; the degree of a PLC node is represented by (k,l), which means that a node in the PLC network is connected to k other PLC nodes and l PC nodes; at the same time, the following relationship is satisfied at any time:

γ ₁ and γ ₂ are the virus detection and killing rates of PC and PLC network infection nodes respectively; μ ₁ is the birth rate and death rate of PC network nodes, and μ ₂ is the birth rate and death rate of PLC network nodes; b is the proportion of births of PC network immune nodes; 1-b is the birth ratio of PC network susceptible nodes; θ ₁ is the infection rate of PC network susceptible nodes caused by PLC network; θ ₂ is the infection rate of PLC network susceptible nodes caused by PC network; δ ₁ is the infection rate of PC network Infection node isolation rate; ω ₁ is PC network isolation node recovery rate; η ₁ , η ₂ is PC, PLC network immune node loss rate; τ ₁ is the delay of PC network immune node losing immunity, τ ₂ is PLC network Delay of immune node losing immunity; β ₁ , β ₂ , β ₃ , β ₄ , c, d, g, h are all normal numbers.

More preferably, in the step S4, the control strategy includes killing infected nodes and injecting immune patches, increasing the removal and isolation of infected nodes, killing isolated nodes and injecting immune patches, and increasing the number of newly launched nodes The proportion of immune nodes in the middle;

Select γ ₁ , γ ₂ , b, δ ₁ , and ω ₁ as optimal control variables, and the feasible region of optimal control variables is U={u=(γ ₁ ,γ ₂ ,b,δ ₁ ,ω ₁ )|,0≤ γ ₁ ≤1,0≤γ ₂ ≤1,0≤b≤1,0≤δ ₁ ≤1,0≤ ω ₁ ≤1,t∈[0,t _f ]}, t _f represents the optimal control terminal moment.

More preferably, in the step S5, the cost function is represented by J(γ ₁ ,γ ₂ ,b,δ ₁ ,ω ₁ ), and is determined by the following formula:

where u ₁ (t)=γ ₁ , u ₂ (t)=γ ₂ , u ₃ (t)=b, u ₄ (t)=δ ₁ , u ₅ (t)=ω ₁ .

More preferably, in said S6, the constructed Lagrangian function is as follows:

More preferably, in said S7, the constructed Hamiltonian function is as follows:

Among them, λ _i (t), (i=1, 2, 3, 4, 5, 6, 7) is the optimally controlled co-state variable.

More preferably, in said step S8, the transversal conditions of construction are as follows:

λ _i (t _f )=0, i=1,2,3,4,5,6,7.

More optimally, in said S8, the co-state equation is:

七个变量。Among them, x ₁ , x ₂ , x ₃ , x ₄ , x ₅ , x ₄ , x ₇ correspond in turn

seven variables.

More optimally, in said S9, the final optimal control pair of the system is:

The beneficial effects of the present invention are:

The present invention fully considers the current reality and is used to simulate the propagation of malicious programs in the wireless rechargeable sensor network of the PC-PLC distribution network information physical system in reality: considering the nonlinear infection rate, the rate of malicious programs infecting sensor nodes The capacity is not fixed. The bilinear incidence rate and the standard incidence rate assumed in the early research are extreme ideals; considering heterogeneity, the rechargeable sensors used in the current power grid often have heterogeneity, and heterogeneity can be recharged. Sensors have been widely used in complex scenarios due to their good network stability, reliability, and survivability; considering the time lag, in reality, malicious programs infecting sensor immune nodes cannot make them lose immunity all at once, and often have a certain Delay, and the delay is different for different networks. For the control of the established PC-PLC distribution network cyber-physical system malicious program propagation model, an optimal control scheme is provided: construct a cost function for controlling malicious programs, construct the Hamiltonian equation according to the differential equation and cost function of the model, and solve Co-state equations and optimal control pairs achieve better control effects at the lowest cost.

Description of drawings

The present invention is further described by using the accompanying drawings, but the embodiments in the accompanying drawings do not constitute any limitation to the present invention. For those of ordinary skill in the art, without paying creative work, other embodiments can also be obtained according to the following accompanying drawings Attached picture.

Fig. 1 is the flow chart of the malicious program control method based on PC-PLC distribution network information physical system of the present invention;

Fig. 2 is a state transition diagram of the PC and PLC wireless rechargeable sensor network of the present invention.

Detailed ways

Below in conjunction with specific embodiment the malicious program control method based on PC-PLC power distribution network information physics system is described in further detail, and these embodiments are only used for the purpose of comparison and explanation, and the present invention is not limited in these embodiments.

Example

In order to prevent and deal with the adverse effects of malicious programs on the information of electric power cyber-physical systems, the embodiment of the present invention provides a PC-PLC power distribution network cyber-physical system malicious program propagation model based on nonlinear time-delay heterogeneous model, and provides corresponding optimal control method.

As shown in Figure 1, the malicious program control method based on the PC-PLC power distribution network cyber-physical system includes the following steps:

S1: Divide PL and PLC network nodes based on analysis of real problems;

Build a PC-PLC power distribution network cyber-physical system malicious program propagation model modeling, record the computer network (PC network) and programmable controller network (PLC network) as A network and B network, each of A network and B network Each device corresponds to a node, and according to the degree of infection of the node, it is classified into infected nodes, susceptible nodes, immune nodes and isolated nodes.

S2: Build a network node state transition diagram;

Construct the state transition diagram of PC and PLC wireless rechargeable sensor network as shown in Figure 2, assuming that the PC network (A) includes susceptible state nodes (S), infected state nodes (I), isolated state nodes (Q) and immune State node (R), PLC network (B) includes susceptibility state node (S), infection state node (I), immune state node (R), and the total number of network nodes is N. Assuming that the birth rate of state nodes in PC network is μ ₁ , newly born state nodes include susceptible state nodes and immune state nodes, among which, the proportion of susceptible state nodes is 1-b, and the proportion of immune state nodes is b; the proportion of newly born state nodes in PLC network is The state node birth rate is μ ₂ , and the newly born nodes are all susceptible state nodes.

Definition γ ₁ and γ ₂ are the virus killing rate of PC and PLC network infection status nodes respectively; μ ₁ is the birth rate and death rate of PC network status nodes, μ ₂ is the birth rate and death rate of PLC network status nodes; b is the immune status of PC network The birth ratio of nodes; 1-b is the birth ratio of nodes in the susceptible state of the PC network; θ ₁ is the infection rate of nodes in the susceptible state of the PC network caused by the PLC network; θ ₂ is the infection rate of nodes in the susceptible state of the PLC network caused by the PC network Infection rate; δ ₁ is the PC network infection state node isolation rate; ω ₁ is the PC network isolation state node recovery rate; η ₁ , η ₂ is the PC, PLC network immune state node loss rate; τ ₁ is the PC network immune state node Delay of losing immunity, τ ₂ is the delay of losing immunity of PLC network immune status nodes; β ₁ , β ₂ , β ₃ , β ₄ , c, d, g, h are all normal numbers.

For PC network susceptible nodes, if there are new nodes invested, some of them may be infected by infected nodes of PC network and become infected nodes, and may also be infected by infected nodes of PLC network and become infected nodes, and some may Will be removed on death. For PC network infection state nodes, some will be isolated, some will be turned into immune state nodes through measures such as virus inspection, killing and patching, and some may be removed due to death. For PC network isolation nodes, some will be recovered by treatment and become immune state nodes, and some will be removed due to death. For the PC network immune state nodes, there are new nodes input, some may lose immunity and become susceptible state nodes, and some may be removed due to death.

For PLC network susceptible nodes, if there are new nodes invested, some of them may be infected by the infection state nodes of the PLC network and become infected state nodes, or may be infected by the infection state nodes of the PC network and become infected state nodes, and some may Will be removed on death. For PLC network infection nodes, some will be turned into immune state nodes through measures such as virus inspection, killing and patching, and some may be removed due to death. For PLC network immune state nodes, some may lose immunity and become susceptible state nodes, and some may be removed due to death.

Define θ _xy (t) as the probability that a susceptible node has an adjacent infected node, x=1,2; y=1,2, where "1" represents the PC network, and "2" represents the PLC network, namely:

θ ₁₁ (t) represents the probability that a PC susceptible state node is adjacent to a PC infected state node, θ ₁₂ (t) represents the probability that a PC susceptible state node is adjacent to a PLC infected state node, and θ ₂₁ (t) represents the probability that a PLC susceptible state node The probability that the susceptible state node is adjacent to the PC infected state node, θ ₂₂ (t) represents the probability that the PLC susceptible state node is adjacent to the PLC infected state node, as follows:

Define the degree of a state node of a PC network, represented by (i, j), that is, a certain state node of the PC network is connected with i state nodes of other PC networks and j state nodes of the PLC network; a PLC The degree of the state node of the network is represented by (k,l), which means that a certain state node of the PLC network is connected with k state nodes of other PLC networks and l state nodes of the PC network; at the same time, at any time Satisfy the following relationship:

S3: Differential equations for building a malicious program propagation model;

The PC-PLC network node state transition differential equation is as follows:

分别是在t时刻PC网络度为(i,j)的易感节点(S)、感染节点(I)、隔离节点(Q)、免疫节点(R)的数量，

分别是在t时刻PLC网络度为(k,l)的易感节点、感染节点、免疫节点的数量,

为PC网络度为(i,j)的各节点总数，

为PLC网络度为(k,l)的各节点总数。

are the number of susceptible nodes (S), infected nodes (I), isolated nodes (Q) and immune nodes (R) with PC network degree (i, j) at time t,

are the number of susceptible nodes, infected nodes and immune nodes with PLC network degree (k,l) at time t, respectively,

is the total number of nodes with PC network degree (i, j),

is the total number of nodes with PLC network degree (k,l).

S4: propose control strategy;

In order to effectively resist the attack of malicious programs, it adopts the method of killing infected nodes and injecting immune patches, increasing the removal and isolation of infected nodes, killing isolated nodes and injecting immune patches, and increasing the number of immune nodes among newly launched nodes. The proportion of several measures.

In order to achieve the optimization goal, γ ₁ , γ ₂ , b, δ ₁ , ω ₁ are selected as optimization control variables by using the Pontryagin maximum principle, and the feasible region of the optimization control variables is U={u=(γ ₁ ,γ ₂ ,b,δ ₁ ,ω ₁ )|,0≤ γ ₁ ≤1,0≤γ ₂ ≤1,0≤b≤1,0≤δ ₁ ≤1,0≤ω ₁ ≤1,t∈ [0,t _f ]}, t _f represents the terminal moment of this optimal control.

S5: Build a cost function;

The cost function is denoted by J(γ ₁ ,γ ₂ ,b,δ ₁ ,ω ₁ ), and is determined by the following formula:

where u ₁ (t)=γ ₁ , u ₂ (t)=γ ₂ , u ₃ (t)=b, u ₄ (t)=δ ₁ , u ₅ (t)=ω ₁ .

S6: Construct a Lagrangian function and introduce a Lagrangian multiplier;

The constructed Lagrange function is as follows:

S7: Construct a Hamiltonian function;

The constructed Hamiltonian function is as follows:

Among them, λ _i (t), (i=1, 2, 3, 4, 5, 6, 7) is the optimally controlled co-state variable.

S8: Construct costate variable equations and transversal conditions;

The costate equation is:

七个变量。In the above formula, x ₁ , x ₂ , x ₃ , x ₄ , x ₅ , x ₄ , x ₇ correspond to

seven variables.

The transversal conditions for the construction are as follows:

λ _i (t _f )=0, i=1,2,3,4,5,6,7.

Among them, the optimized conditions are:

Right now:

S9: Solve the optimal control pair;

Solve the solution to get the final optimal control pair of the system as:

The above embodiments of the present invention focus on establishing a malicious program propagation model of the PC-PLC distribution network information physical system, which is used to simulate the wireless communication of the PC-PLC distribution network information physical system after fully considering the current reality The situation of malicious program propagation in charging sensor network. The model takes into account factors such as nonlinear infection rate, heterogeneity, and time lag. The present invention controls the malicious program propagation model of the established PC-PLC distribution network information physical system, and provides an optimal control scheme; constructs a cost function for controlling malicious programs, and constructs the Hamiltonian equation according to the differential equation and the cost function of the model , to solve the co-state equations and the optimal control pair to achieve a better control effect at the minimum cost.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting the protection scope of the present invention, although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand , the technical solution of the present invention may be modified or equivalently replaced without departing from the spirit and scope of the technical solution of the present invention.

Claims (10)

1. A malicious program control method based on PC-PLC power distribution network information physical system, it is characterized in that, comprising the following steps: S1: Divide PL and PLC network nodes based on analysis of real problems; S2: Build a network node state transition diagram; S3: Differential equations for building a malicious program propagation model; S4: propose control strategies; S5: Build a cost function; S6: Construct a Lagrangian function and introduce a Lagrangian multiplier; S7: Construct a Hamiltonian function; S8: Construct costate variable equations and transversal conditions; S9: Solve the optimal control pair. 2. The malicious program control method based on PC-PLC power distribution network cyber-physical system according to claim 1, characterized in that, in the step S1, the computer PC network and the programmable controller PLC network are respectively marked as A network And B network, each device of A network and B network corresponds to a node, and according to the degree of infection of the node, it is classified into infected node, susceptible node, immune node and isolated node. 3. the malicious program control method based on the PC-PLC power distribution network information physical system according to claim 1, is characterized in that, in the described step S3, builds differential equations based on the network node state transition graph, specifically as follows:

In the formula, θ _xy (t) is defined as the probability that a susceptible node has an adjacent infected node, x=1,2; y=1,2, where "1" represents the PC network, and "2" represents the PLC network, namely : θ ₁₁ (t) represents the probability that a PC-susceptible node is adjacent to a PC-infected node, θ ₁₂ (t) represents the probability that a PC-susceptible node is adjacent to a PLC-infected node, and θ ₂₁ (t) represents the probability that a PLC-susceptible node is adjacent to a PC The probability that the infected node is adjacent, θ ₂₂ (t) represents the probability that the PLC susceptible node is adjacent to the PLC infected node, as follows:

are the number of susceptible nodes (S), infected nodes (I), isolated nodes (Q) and immune nodes (R) with PC network degree (i, j) at time t,

are the number of susceptible nodes, infected nodes and immune nodes with PLC network degree (k,l) at time t, respectively,

is the total number of nodes with PC network degree (i, j),

is the total number of nodes in the PLC network whose degree is (k, l); the degree of a PC node is expressed by (i, j), which means that a node in the PC network is related to i other PC nodes and j PLC nodes Connection; the degree of a PLC node is represented by (k,l), which means that a node in the PLC network is connected to k other PLC nodes and l PC nodes; at the same time, the following relationship is satisfied at any time:

γ ₁ and γ ₂ are the virus detection and killing rates of PC and PLC network infection nodes respectively; μ ₁ is the birth rate and death rate of PC network nodes, and μ ₂ is the birth rate and death rate of PLC network nodes; b is the proportion of births of PC network immune nodes; 1-b is the birth ratio of PC network susceptible nodes; θ ₁ is the infection rate of PC network susceptible nodes caused by PLC network; θ ₂ is the infection rate of PLC network susceptible nodes caused by PC network; δ ₁ is the infection rate of PC network Infection node isolation rate; ω ₁ is PC network isolation node recovery rate; η ₁ , η ₂ is PC, PLC network immune node loss rate; τ ₁ is the delay of PC network immune node losing immunity, τ ₂ is PLC network Delay of immune node losing immunity; β ₁ , β ₂ , β ₃ , β ₄ , c, d, g, h are all normal numbers. 4. The malicious program control method based on PC-PLC power distribution network cyber-physical system according to claim 3, characterized in that, in the step S4, the control strategy includes checking and killing infected nodes and injecting immune patches, increasing Remove and isolate infected nodes, check and kill isolated nodes and inject immune patches, and increase the proportion of immune nodes among newly launched nodes; Select γ ₁ , γ ₂ , b, δ ₁ , and ω ₁ as optimal control variables, and the feasible region of optimal control variables is U={u=(γ ₁ ,γ ₂ ,b,δ ₁ ,ω ₁ )|,0≤ γ ₁ ≤1,0≤γ ₂ ≤1,0≤b≤1,0≤δ ₁ ≤1,0≤ω ₁ ≤1,t∈[0,t _f ]}, t _f represents the optimal control terminal moment. 5. The malicious program control method based on PC-PLC distribution network cyber-physical system according to claim 3, characterized in that, in the step S5, the cost function is J(γ ₁ , γ ₂ , b, δ ₁ ,ω ₁ ), which is determined by the following formula:

where u ₁ (t)=γ ₁ , u ₂ (t)=γ ₂ , u ₃ (t)=b, u ₄ (t)=δ ₁ , u ₅ (t)=ω ₁ . 6. the malicious program control method based on PC-PLC power distribution network information physical system according to claim 5, is characterized in that, in the described S6, the Lagrangian function of construction is as follows:

7. the malicious program control method based on PC-PLC power distribution network information physics system according to claim 5, is characterized in that, in described step S7, the Hamiltonian function of construction is as follows:

Wherein, λ _i (t), (i=1, 2, 3, 4, 5, 6, 7) is a co-state variable of optimal control. 8. The malicious program control method based on the PC-PLC power distribution network cyber-physical system according to claim 4, wherein, in the step S8, the transversal conditions of construction are as follows: λ _i (t _f )=0, i=1, 2, 3, 4, 5, 6, 7. 9. The malicious program control method based on PC-PLC power distribution network cyber-physical system according to claim 8, characterized in that, in the step S8, the co-state equation is:

Among them, x ₁ , x ₂ , x ₃ , x ₄ , x ₅ , x ₄ , x ₇ correspond in turn

seven variables. 10. The malicious program control method based on the PC-PLC power distribution network cyber-physical system according to claim 7, wherein in the S9, the final optimal control pair of the system is:

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