CN115643579A - Method for controlling malicious programs of information physical system of power distribution network based on PC-PLC - Google Patents
Method for controlling malicious programs of information physical system of power distribution network based on PC-PLC Download PDFInfo
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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
Technical Field
The invention relates to the technical field of wireless chargeable sensor networks, in particular to a method for controlling malicious programs of a PC-PLC-based power distribution network information physical system, which is used for carrying out propagation modeling and optimal control on malicious programs of a wireless chargeable sensor network of a power system.
Background
In recent years, with the rapid development of wireless chargeable sensor network technology, the application of the wireless chargeable sensor network technology is increasingly common, and the shadow can be seen in the fields of military affairs, agriculture, industry, traffic, information equipment and the like. The power industry is used as the basis of national economic development, the power industry rapidly responds to social power consumption requirements, meanwhile, real-time, safe and flexible information traffic is achieved, reasonable optimization and effective scheduling of resources are achieved, a traditional power grid cannot meet the requirements of power development, and a modern power system is developed into a power information physical system with deep integration of the power grid and the information grid.
A modern electric power information physical system is coupled with an information layer on the basis of a traditional electric power network physical layer, and mutual communication is carried out through a large number of sensor connections so as to realize real-time sensing, detection and processing of information in a target area. However, the power grid enjoys the benefits of the physical system of power information, which makes modern power grids more economical and efficient to operate, and also bears the potential risks of safety aspects caused by intelligent interconnection to the operation of the power system. In terms of modern power information physical systems, network attacks of malicious programs can be possibly suffered in each link of power generation, power transmission, power distribution and power utilization, the usability, integrity, confidentiality and the like of the system are damaged in different degrees, and even the whole power grid is broken down seriously. Therefore, the security issues of modern power networks cannot be ignored.
The method is an important topic at present, based on potential information security threats of modern power networks, fully considering malicious program propagation and infection mechanisms, and establishing a practical network model to analyze and research an optimal control strategy to inhibit malicious program propagation and guarantee network information security.
Disclosure of Invention
In order to prevent and deal with adverse effects of malicious programs on information of the power information physical system, the invention provides a PC-PLC power distribution network information physical system malicious program transmission model based on a nonlinear time-lag heterogeneous model, so as to solve the problems.
The invention provides the following technical scheme:
a power distribution network information physical system malicious program control method based on a PC-PLC comprises the following steps:
s1: PL and PLC network nodes are divided based on the analysis of the real problems;
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 Lagrangian function, and introducing a Lagrangian multiplier;
s7: constructing a Hamiltonian;
s8: constructing a covariate equation set and a cross-section condition;
s9: and solving the optimal control pair.
Preferably, in step S1, the PC network and the PLC network are respectively denoted as a network a and a network B, each device of the network a and the network B corresponds to a node, and the nodes are classified into an infected node, a susceptible node, an immune node, and an isolated node according to the degree of infection of the node. Preferably, in S2, the most important k words are selected from all the texts x in T, including the confrontation sample and the clean sample, and are sorted, and are denoted as C (x).
Preferably, in step S3, a system of differential equations is constructed based on the state transition diagram of the network node, specifically as follows:
in the formula, theta xy (t) is defined as the probability that a susceptible node has a neighboring infected node, x =1,2; y =1,2, wherein "1" represents a PC network and "2" represents a PLC network, i.e.:
θ 11 (t) represents the probability that a PC susceptible node is adjacent to a PC infected node, θ 12 (t) represents the probability of a PC susceptible node being adjacent to a PLC infected node, θ 21 (t) represents the probability that a PLC-susceptible node is adjacent to a PC-infected node, θ 22 (t) represents the probability that the PLC susceptible node is adjacent to the PLC infected node, and the probability is as follows:
γ 1 、γ 2 are respectively provided withVirus killing rate of infected nodes of PC and PLC networks; mu.s 1 Is the birth rate and death rate of PC network nodes, mu 2 The birth rate and the death rate of the PLC network nodes; b is the birth ratio of the immune nodes of the PC network; 1-b is the birth proportion of susceptible nodes of the PC network; theta.theta. 1 Infection rate caused by a PLC network for the PC network susceptible nodes; theta.theta. 2 The infection rate of the susceptible nodes of the PLC network caused by the PC network; delta. For the preparation of a coating 1 Infecting the node isolation rate for the PC network; omega 1 Isolating the node recovery rate for the PC network; eta 1 、η 2 The node failure immunity rate of the PC and PLC network; tau. 1 Time delay, tau, for loss of immunity of PC network immune node 2 Delaying the immunity losing capability of the PLC network immunity node; beta is a beta 1 、β 2 、β 3 、β 4 C, d, g and h are normal numbers.
Preferably, in the step S4, the control strategy includes searching and killing the infected node and injecting an immune patch, increasing the removal of isolation of the infected node, searching and killing the isolated node and injecting an immune patch, and increasing the proportion of immune nodes in newly released nodes;
selecting gamma 1 、γ 2 、b、δ 1 、ω 1 As the optimization control variable, the feasible domain of the optimization control variable 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 And the terminal time of the optimal control is shown.
Preferably, in the step S5, the cost function is J (γ) 1 ,γ 2 ,b,δ 1 ,ω 1 ) Expressed, determined by the following equation:
wherein u 1 (t)＝γ 1 ,u 2 (t)＝γ 2 ,u 3 (t)＝b,u 4 (t)＝δ 1 ,u 5 (t)＝ω 1 。
Preferably, in S6, the lagrangian function is constructed as follows:
preferably, in S7, the hamiltonian is constructed as follows:
wherein λ is i (t), (i =1,2,3,4,5,6, 7) are covariates for optimal control.
Preferably, in step S8, the cross-section conditions are as follows:
λ i (t f ）＝0,i＝1,2,3,4,5,6,7。
preferably, in S8, the collaborative equation is:
wherein x is 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 4 ,x 7 Correspond to each other in sequence
Seven variables.
Preferably, in S9, the final optimal control pair of the system is:
the invention has the beneficial effects that:
the invention fully considers the situation of malicious program propagation in a wireless chargeable sensor network used for simulating a PC-PLC power distribution network information physical system in reality after the current practical situation: the nonlinear infection rate is considered, the capability of a malicious program for infecting the sensor node is not fixed, and the bilinear occurrence rate and the standard occurrence rate which are supposed in early research are extreme ideal conditions; in consideration of isomerism, rechargeable sensors used in the existing power grid are often heterogeneous, and the heterogeneous rechargeable sensors are widely applied to complex scenes due to good network stability, reliability and survivability; considering time lag, the sensor immune node cannot be lost at once due to infection of a malicious program in reality, and the time delay is different for different networks. The method is characterized in that control is performed aiming at the established PC-PLC distribution network information physical system malicious program propagation model, and an optimal control scheme is provided: and a cost function for controlling the malicious program is constructed, a Hamilton equation is constructed according to a differential equation of the model and the cost function, a collaborative equation set and a best control pair are solved, and a good control effect is achieved with the minimum cost.
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The invention is further described with the aid of the accompanying drawings, in which the embodiments do not constitute any limitation of the invention, and for a person skilled in the art, without inventive effort, further drawings may be derived from the following figures.
FIG. 1 is a flow chart of a method for controlling malicious programs of a PC-PLC-based power distribution network information physical system;
FIG. 2 is a state transition diagram of a PC/PLC wireless chargeable sensor network according to the present invention.
Detailed Description
The method for controlling malicious programs based on the cyber-PLC power distribution cyber-physical system is further described in detail with reference to specific embodiments, which are only used for comparison and explanation purposes, and the present invention is not limited to these embodiments.
Examples
In order to prevent and deal with adverse effects of malicious programs on information of the power information physical system, the PC-PLC power distribution network information physical system malicious program propagation model based on the nonlinear time lag heterogeneous model and the corresponding optimal control method are provided.
As shown in fig. 1, the method for controlling the malicious program of the PC-PLC-based power distribution network cyber-physical system includes the following steps:
s1: PL and PLC network nodes are divided based on the analysis of the real problems;
a PC-PLC power distribution network information physical system malicious program propagation model is established, a computer network (PC network) and a programmable controller network (PLC network) are recorded as an A network and a B network, each device of the A network and the B network corresponds to a node, and the nodes are classified into infected nodes, susceptible nodes, immune nodes and isolated nodes according to the degree of infection of the nodes.
S2: constructing a network node state transition diagram;
a state transition diagram of the PC and PLC wireless chargeable sensor network shown in fig. 2 is constructed, and it is assumed that the PC network (a) includes a susceptible state node (S), an infected state node (I), an isolated state node (Q), and an immune state node (R), and the PLC network (B) includes a susceptible state node (S), an infected state node (I), and an immune state node (R), and the total number of network nodes is N. Suppose the status node occurrence rate of the PC network is mu 1 The new born state nodes comprise susceptible state nodes and immune state nodes, wherein the susceptible state node proportion is 1-b, and the immune state node proportion is b; the state node birth rate of the PLC network is mu 2 And all the new born nodes are susceptible state nodes.
Definition of gamma 1 、γ 2 Respectively the virus killing rates of the nodes in the PC and PLC network infection states; mu.s 1 Is the node birth rate and death rate of the PC network state, mu 2 The birth rate and the death rate of the nodes in the PLC network state are calculated; b is the birth proportion of the immune state node of the PC network; 1-b is the birth proportion of the nodes in the PC network susceptibility state; theta.theta. 1 Infection rate caused by a PLC network for a PC network susceptible state node; theta 2 For PLC networksThe node is susceptible to infection caused by the PC network; delta. For the preparation of a coating 1 The node isolation rate is the PC network infection state; omega 1 Isolating the state node recovery rate for the PC network; eta 1 、η 2 The node immunization failure rate of the PC and PLC network; tau is 1 Time delay of losing immunity ability for PC network immunity state node 2 The time delay of losing the immunity capability of the node in the immunity state of the PLC network is delayed; beta is a 1 、β 2 、β 3 、β 4 C, d, g and h are normal numbers.
For the susceptible nodes of the PC network, new nodes are invested, part of the susceptible nodes of the PC network can be infected by the infected nodes of the PC network to become infected nodes, part of the susceptible nodes of the PLC network can be infected by the infected nodes of the PC network to become infected nodes, and part of the susceptible nodes of the PLC network can be removed due to death. For the PC network infected state node, a part may be isolated, a part may be changed into an immune state node by virus killing, patching and other measures, and a part may be removed due to death. For the PC network quarantine node, part of the node is recovered by treatment to become an immune state node, and part of the node is removed by death. For the PC network immune state node, a new node is introduced, part of the node may lose the immune ability and become susceptible state nodes, and part of the node may be removed due to death.
For the susceptible nodes of the PLC network, new nodes are input, part of the susceptible nodes of the PLC network can be infected by the infected nodes of the PLC network to become infected nodes, part of the susceptible nodes of the PC network can be infected by the infected nodes of the PC network to become infected nodes, and part of the susceptible nodes of the PC network can be removed due to death. For a PLC network infected node, part of the node can be changed into an immune state node through virus killing, patching and other measures, and part of the node can be removed due to death. For PLC network immune status nodes, part of the immune status nodes may become immune-competent status nodes, and part may be removed by death.
Definition of theta xy (t) is the probability of a susceptible node having a neighboring infection status node, x =1,2; y =1,2, wherein "1" represents a PC network and "2" represents a PLC network, i.e.:
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 the PC susceptibility state node is adjacent to the PLC infection state node, θ 21 (t) represents the probability that a PLC susceptibility status node is adjacent to a PC infection status node, θ 22 (t) represents the probability that the PLC susceptible state node is adjacent to the PLC infected state node, and the probability is as follows:
defining the degree of the state nodes of one PC network, and expressing the degree by (i, j), namely, expressing that a certain state node of the PC network is connected with the state nodes of i other PC networks and the state nodes of j PLC networks; the degree of the state nodes of one PLC network is expressed by (k, l), namely that a certain state node of the PLC network is connected with the state nodes of k other PLC networks and the state nodes of l PC networks; meanwhile, the following relationship is satisfied at any time:
s3: constructing a differential equation set of a malicious program propagation model;
the state conversion differential equation of the PC-PLC network node is as follows:
S4: a control strategy is proposed;
in order to effectively resist the attack of malicious programs, the method adopts several measures of killing infected nodes and injecting immune patches, increasing the removal of isolation of the infected nodes, killing isolated nodes and injecting immune patches and increasing the proportion of immune nodes in newly released nodes.
In order to realize the optimization target, the maximum value principle of Pontryagin is utilized to select gamma 1 、γ 2 、b、δ 1 、ω 1 As the optimization control variable, the feasible domain of the optimization control variable 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 And the terminal time of the optimal control is shown.
S5: constructing a cost function;
cost function is represented by J (gamma) 1 ,γ 2 ,b,δ 1 ,ω 1 ) Expressed, determined by the following equation:
wherein 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: constructing a Lagrange function, and introducing a Lagrange multiplier;
the lagrangian function is constructed as follows:
s7: constructing a Hamiltonian;
the hamiltonian is constructed as follows:
wherein λ is i (t), (i =1,2,3,4,5,6, 7) are covariates for optimal control.
S8: constructing a covariate equation set and a cross-section condition;
the cooperative equation is:
in the above formula, x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 4 ,x 7 Correspond to each other in sequence
Seven variables.
The cross-sectional conditions were constructed as follows:
λ i (t f ）＝0,i＝1,2,3,4,5,6,7。
wherein, the obtained optimized conditions are as follows:
namely:
s9: solving an optimal control pair;
the solution is solved to obtain the final optimal control pair of the system as follows:
the embodiment of the invention is mainly used for establishing a malicious program propagation model of the PC-PLC power distribution network information physical system, and the model fully considers the current practical situation and is used for simulating the propagation condition of the malicious program in the wireless chargeable sensor network of the PC-PLC power distribution network information physical system. The model considers factors such as nonlinear infection rate, isomerism, time lag and the like. The method is used for controlling the established PC-PLC power distribution network information physical system malicious program propagation model, and an optimal control scheme is provided; and a cost function aiming at a control malicious program is constructed, a Hamiltonian equation is constructed according to a differential equation of the model and the cost function, a collaborative equation set and an optimal control pair are solved, and a better control effect is achieved with the minimum cost.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the protection scope of the present invention, although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.
Claims (10)
1. A method for controlling malicious programs of a power distribution network information physical system based on a PC-PLC is characterized by comprising the following steps:
s1: PL and PLC network nodes are divided based on the analysis of the real problems;
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 Lagrangian function, and introducing a Lagrangian multiplier;
s7: constructing a Hamiltonian;
s8: constructing a covariate equation set and a cross-section condition;
s9: and solving the optimal control pair.
2. The method for controlling the malicious programs of the PC-PLC-based power distribution network information physical system according to claim 1, wherein in the step S1, the computer PC network and the PLC network are recorded as an A network and a B network respectively, each device of the A network and the B network corresponds to a node, and the nodes are classified into an infected node, a susceptible node, an immune node and an isolated node according to the degree of infection of the nodes.
3. The PC-PLC-based power distribution network cyber-physical system malicious program control method according to claim 1, wherein in the step S3, a system of differential equations is constructed based on a network node state transition diagram, specifically as follows:
in the formula, theta xy (t) is defined as the probability that a susceptible node has a neighboring infected node, x =1,2; y =1,2, where "1" represents a PC network and "2" represents a PLC network, i.e.:
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, θ 21 (t) represents the probability that a PLC-susceptible node is adjacent to a PC-infected node, θ 22 (t) represents the probability of the PLC susceptible node being adjacent to the PLC infected node, and the probability is as follows:
γ 1 、γ 2 respectively the virus killing rates of the PC network infection node and the PLC network infection node; mu.s 1 Is the birth rate and death rate of PC network nodes, mu 2 Birth rate and death rate of PLC network nodes; b is the birth proportion of the immune nodes of the PC network; 1-b is the birth proportion of susceptible nodes of the PC network; theta 1 Infection rate caused by a PLC network for the PC network susceptible nodes; theta 2 The infection rate of the susceptible nodes of the PLC network caused by the PC network; delta 1 Infecting the node isolation rate for the PC network; omega 1 Isolating the node recovery rate for the PC network; eta 1 、η 2 The immunization node immunization rate of the PC and PLC networks is obtained; tau is 1 Time delay, tau, for loss of immunity of PC network immune node 2 The time delay of losing the immunity of the immunity node of the PLC network is delayed;β 1 、β 2 、β 3 、β 4 all of c, d, g and h are normal numbers.
4. The PC-PLC-based power distribution network cyber-physical system malicious program control method according to claim 3, wherein in the step S4, the control strategy includes killing infected nodes and injecting immune patches, increasing removal of isolation of infected nodes, killing isolated nodes and injecting immune patches, and increasing the proportion of immune nodes in newly released nodes;
selecting gamma 1 、γ 2 、b、δ 1 、ω 1 As the optimization control variable, the feasible domain of the optimization control variable 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 And the terminal time of the optimal control is shown.
5. The method for controlling the cyber physical system malicious programs on the power distribution network according to the PC-PLC of claim 3, wherein the cost function is J (gamma) in the step S5 1 ,γ 2 ,b,δ 1 ,ω 1 ) Expressed, determined by the following formula:
wherein u is 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 PC-PLC-based power distribution network cyber-physical system malicious program control method according to claim 5, wherein in S6, a Lagrangian function is constructed as follows:
7. the method for controlling the malicious programs of the cyber physical system of the power distribution network according to claim 5, wherein in the step S7, a Hamiltonian is constructed as follows:
wherein λ is i (t), (i =1,2,3,4,5,6,7) is a covariate variable for optimal control.
8. The PC-PLC-based power distribution network cyber-physical system malicious program control method according to claim 4, wherein in the step S8, cross-section conditions are constructed as follows:
λ i (t f )＝0,i＝1,2,3,4,5,6,7。
9. the PC-PLC-based power distribution network cyber-physical system malicious program control method according to claim 8, wherein in the step S8, a collaborative equation is:
wherein x is 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 4 ,x 7 Correspond to each other in sequence
Seven variables.
10. The PC-PLC-based power distribution network cyber-physical system malicious program control method according to claim 7, wherein in S9, a final optimal control pair of the system is as follows:
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