CN112469041B - Malicious program isolation and control method based on wireless sensor network - Google Patents
Malicious program isolation and control method based on wireless sensor network Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
- H04W12/009—Security arrangements; Authentication; Protecting privacy or anonymity specially adapted for networks, e.g. wireless sensor networks, ad-hoc networks, RFID networks or cloud networks
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- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Abstract
The invention discloses a malicious program isolation and control method based on a wireless sensor network, which comprises the following steps: constructing a node moving model of the wireless sensor network; constructing a node state transition diagram, and listing differential equations of all nodes according to the transition diagram; constructing a cost objective function according to the immunity proportion, the killing proportion, the charging proportion, the isolation proportion and the number proportion of infected nodes of the nodes; constructing a Hamiltonian by using a cost target function and differential equations of all nodes according to a Ponderland gold maximum principle; and obtaining a covariance variable differential equation set according to the Hamiltonian, solving a transverse condition and an optimization condition, and finally obtaining an optimal control pair according to the optimization condition. The method starts from a traditional wireless sensor network model, further considers the influence of node isolation and node charge and discharge on the system model, thereby being more suitable for the actual situation and having certain guiding significance for restraining the spread of malicious programs.
Description
Technical Field
The invention belongs to the technical field of chargeable directionless sensor networks, and particularly relates to a malicious program isolation and control method based on a wireless sensor network.
Background
A Wireless Sensor Network (WSN) is a distributed Sensor network whose distal end is a Sensor that can sense and examine the outside world. The sensors in the WSN communicate in a wireless mode, so that the network is flexibly set, the position of the equipment can be changed at any time, and the equipment can also interact with the Internet.
The malicious program is a special program, and because the structural characteristics of the basic wireless sensor network are relatively simple, the malicious program can cause certain loss to the malicious program. There are various ways in which malicious programs cause node network loss, such as: attacking a certain part of the node to make the node continuously emit heat, thereby causing paralysis; and the information receiving function of the node can be attacked, so that the node cannot receive data and normally work.
The infectious disease model is used for researching the spreading speed, the space range and other problems of the infectious disease and guiding the effective prevention and treatment work of the infectious disease. Common models of infectious diseases are classified as SI, SIR, SIRQ, SIRQD, etc. In the field of wireless sensor networks, an infectious disease model can be combined to guide the killing and immunization work of malicious programs to a certain extent. In a traditional malicious program propagation model, the relationship among susceptible nodes, infected nodes and immune nodes is mainly considered, and the influence caused by node charging and discharging and node isolation is not considered. In practical situations, the malicious program can attack the charging and discharging functions of the node, so that the node cannot be normally charged and finally dies due to energy exhaustion; meanwhile, the nodes are isolated, so that the infected proportion of the susceptible nodes can be effectively reduced. Therefore, the traditional malicious program propagation model is not suitable for the current wireless sensor network.
Disclosure of Invention
The invention mainly aims to overcome the defects and shortcomings in the prior art and provides a malicious program isolation and control method based on a wireless sensor network.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a malicious program isolation and control method based on a wireless sensor network, which comprises the following steps:
constructing a node moving model of the wireless sensor network, assuming that a plurality of nodes are divided into a plurality of node types, all the nodes exist in a two-dimensional area, the nodes are uniformly distributed in the two-dimensional area, and simultaneously, the nodes move in stages, and each node can only contact with other nodes in the transmission range of the node;
constructing a node state transition diagram according to the state transition relation of the nodes, and listing differential equations of all the nodes according to the node state transition diagram;
constructing a cost objective function according to the immunity proportion, the killing proportion, the charging proportion, the isolation proportion and the number of infected nodes of the nodes;
constructing a Hamiltonian according to the obtained cost target function and the differential equation of each node;
and obtaining a set of covariance variable differential equations by a Ponderland Ridgkin maximum principle according to a Hamiltonian, solving a cross section condition and an optimization condition, and finally obtaining an optimal control pair according to the optimization condition.
Preferably, the building of the node movement model of the wireless sensor network specifically includes:
assuming that all nodes exist in a two-dimensional area with the area of A, the total number of the nodes is N, the number of the nodes is not supplemented along with the change of time, the radius of information transmission of each node is r, and each node can only contact with other nodes in the transmission radius r;
the node types comprise susceptible nodes S (t), infected nodes I (t), immune nodes R (t), isolated nodes Q (t), low-energy nodes L (t) and dead nodes D (t);
for S (t), I (t), R (t), Q (t), L (t) and D (t), the number proportion of each node type relative to the total number of nodes is defined;
all types of nodes meet the following proportional relation at any time t:
S(t)+I(t)+R(t)+Q(t)+L(t)+D(t)＝1。
preferably, the immunization refers to that a patch of a malicious node is installed inside the node, and when the malicious node attacks, the node is not affected by the patch, so that an immune function is generated on the malicious node;
the charging means that after the nodes of the wireless sensor network enter a low-energy state, the unmanned aerial vehicle is manually controlled to charge the nodes, and the energy is recovered to the highest state;
the searching and killing refers to that a computer system is manually operated to search and kill viruses on the nodes;
the isolation refers to that the node identification system closes the information transmission function of the node;
the susceptible node does not immunize a malicious program, and is attacked by the infected node and then converted into an infected node;
the infected node is attacked by a malicious program, and at the moment, the node is not judged as an isolated node by an internal identification system and can attack a sensitive node contacted in a transmission radius r;
the immune node is used for immunizing the malicious program, eliminating the malicious program and preventing the malicious program from being attacked by the infected node;
the isolation node is attacked by the malicious program, but the node is judged to be stored with the malicious program by the internal identification system and is converted into the isolation node, and the information transmission function of the node is closed by the identification system, so that the isolation node cannot attack the susceptible node;
the low-energy nodes are classified into high-energy consumption nodes and ordinary-energy consumption nodes; when the node is lower than the threshold value, the node is automatically identified as a low-energy node, meanwhile, because the node is in a low-energy state, the energy level of the node cannot support the information sending function, and the internal identification system closes the information transmission function; the node can simultaneously perform three functions of immunization, searching and killing and charging, and finally the low-energy node is converted into an immunization node; the energy consumption high nodes are converted by infection nodes and isolation nodes, and the energy consumption common nodes are converted by susceptible nodes and immune nodes;
the dead node cannot normally move, cannot be charged and discharged and cannot transmit information, and meanwhile cannot attack other nodes.
Preferably, at time t:
by P SR (t) the success rate of the immunization and charging operation on the susceptible node is shown;
by P IR (t) the success rate of the searching and killing and charging operations of the infected node is shown;
by P OR (t) the success rate of the searching, killing and charging operations carried out on the isolated node is shown;
by P LR (t) success rate of charging, immunizing, killing operations on low energy nodes；
By P SL (t)，P RL (t)，P IL (t) and P QL (t) respectively representing the conversion rate of the susceptible node, the immune node, the infected node and the isolated node into the low-energy node;
by P IQ (t) represents the quarantine identification rate for infected nodes;
by P LD (t) low energy node mortality;
by P SI (t) indicates infection success rate of the infected node;
the above ratio domains are: u = [0,1].
Preferably, the constructing of the node state transition diagram specifically includes constructing the node state transition diagram according to the following transition relationships:
susceptible node with P SI (t) S (t) I (t) ratio to infectious node, in P SR (t) S (t) ratio conversion to immunonodes, in P SL (t) converting the S (t) ratio into a low energy node;
infect node with P IQ (t) I (t) ratio to isolated node, with P IR (t) I (t) ratio conversion to immunonodes, in P IL (t) converting the I (t) ratio into a low energy node;
immunization node with P RL (t) converting the ratio of R (t) into low energy nodes;
isolating node with P QR (t) Q (t) ratio to immunonodes, in P QL (t) converting the Q (t) ratio into a low energy node;
low energy node with P LD (t) conversion of the L (t) ratio into death node, in P LR (t) converting the ratio L (t) into an immunonode;
death node is composed of low energy node and P LD (t) L (t) ratio.
Preferably, the differential equation of each node is specifically:
preferably, said mu 1 Cost parameters for implementing immunization and charging operations; mu.s 2 Cost parameters for implementing checking, killing and charging operations; mu.s 3 A cost parameter for implementing the isolation operation; mu.s 4 As a function of the cost of performing immunization, killing, and charging operations; t is t f Optimally controlling the research end time for the method; i (t) f ) Is the end time t f The number proportion of infected nodes;
according to the number ratio I (t) of infected nodes f ) Inter-node conversion ratio P SR (t)S(t)、P IR (t)/(t)、P QR (t)Q(t)、P IQ (t) I (t) and P LR (t) L (t), constructing a cost objective function J to obtain a minimum cost for isolation and control of the malicious program, wherein the construction cost objective function is specifically:
preferably, a Hamiltonian is constructed according to a PonderRiagin maximum principle and a differential equation set and a cost target function;
delta. The 1 、δ 2 、δ 3 And delta 4 Respectively representing covariates delta 1 (t)、δ 2 (t)、δ 3 (t) and δ 4 (t), both defined identically;
the construction of the Hamiltonian H specifically comprises the following steps:
preferably, based on the maximum value principle of the pointryagin, the covariate differential equation is the negative of the partial derivative of the proportion of the number of the corresponding nodes in the Hamiltonian;
the system of the covariate differential equations is specifically as follows:
in particular, at the end time t f The cross-section condition of the covariate is specifically as follows:
δ 1 (t f )＝δ 3 (t f )＝δ 4 (t f )＝0
δ 2 (t f )＝1
the solving optimization conditions are specifically as follows:
the optimization condition is obtained according to the maximum value principle of Ponderland gold:
solving the above equation yields:
the optimal control pair obtained according to the optimization conditions is the minimum cost for isolating and controlling the malicious program;
solving the solution of the obtained optimization condition to obtain the optimal control pair, which is specifically as follows:
where min refers to the minimum value, max refers to the maximum value, and a certain ratio with a sign indicates the value of the ratio under optimal control.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the method starts from a traditional malicious program propagation model, adds factors of node charging and discharging and node isolation, establishes a novel wireless sensor network model, and performs optimal control analysis on the model to obtain an optimal control pair which can minimize the number of infected nodes and implement immune operation, charging operation and searching and killing operation cost under the control of a reduction factor.
2. The invention starts from the traditional wireless sensor network model, further considers the influence of node isolation and node charge and discharge on the system model, and is more suitable for the actual situation.
Drawings
FIG. 1 is a flow chart of a wireless sensor network based malware isolation and control method;
fig. 2 is a node state transition diagram of the method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
The method constructs a node moving model of the wireless sensor network; constructing a state relation conversion diagram among the nodes according to the model of the infectious diseases; and writing differential equation sets in columns according to the conversion chart; constructing a cost objective function according to the immunity proportion, the killing proportion, the charging proportion, the isolation proportion and the number of infected nodes of the nodes; constructing a Hamiltonian according to the differential equation set and the target function; and (3) obtaining an optimal control pair which has the minimum number of infected nodes, immunization, malicious program removal, isolation and charging cost under optimal control by utilizing a Pompe-Richardson maximum principle. The invention starts from the traditional wireless sensor network model, further considers the influence of node isolation and node charge and discharge on the system model, and is more suitable for the actual situation.
As shown in fig. 1, a malicious program isolation and control method based on a wireless sensor network according to the present invention includes the following steps:
s1, constructing a node moving model of a wireless sensor network, specifically:
s11, assuming that all nodes exist in a two-dimensional area with the area of A, the total number of the nodes is N, the number of the nodes is not supplemented along with the change of time, the radius of information transmission of each node is r, and each node is intelligently contacted with other nodes in the transmission radius r;
s12, carrying out type division on nodes, wherein the nodes comprise susceptible nodes S (t), infected nodes I (t), immune nodes R (t), isolated nodes Q (t), low-energy nodes L (t) and dead nodes D (t);
in this embodiment, all nodes satisfy the following relationship at any time t:
S(t)+I(t)+R(t)+Q(t)+L(t)+D(t)＝1
the immunization refers to that a patch of a malicious node is installed in the node, and when the malicious node attacks, the node is not influenced by the patch, so that an immune function is generated on the malicious node;
the charging means that after the nodes of the wireless sensor network enter a low-energy state, the unmanned aerial vehicle is manually controlled to charge the nodes, and the energy is recovered to the highest state;
the searching and killing refers to that a computer system is manually operated to search and kill viruses on nodes;
the isolation refers to that the node identification system closes the information transmission function of the node;
the susceptible node does not generate immunity to malicious programs, can be attacked by the infected node, and further has P SI And the proportion of susceptible nodes is converted into infected nodes, and the energy loss speed of the susceptible nodes is ordinary.
The infected node is attacked by a malicious program, and the node is not judged as an isolated node by an internal identification system at the moment, so that the node can attack a sensitive node contacted in a transmission radius r; meanwhile, internal elements of the node may be continuously heated due to attack, and cannot normally work, so that energy is consumed at a high speed, and the energy loss speed of the node is high.
The immune node is used for immunizing a malicious program, eliminating the malicious program and preventing the malicious program from being attacked by the infected node, and the energy loss speed of the node is ordinary.
The isolation node is attacked by the malicious program, but the node is judged to be stored with the malicious program by the internal identification system, so that the PIQ ratio is converted into the isolation node, the information transmission function of the node is closed by the identification system, and the isolation node cannot attack the susceptible node. But the internal components of the isolated node continue to heat up, which is a high rate of energy loss at the node.
The low-energy nodes are divided into two types, namely high-energy-consumption nodes (converted by infected nodes and isolated nodes) and common-energy-consumption nodes (converted by susceptible nodes and immune nodes); when the node is lower than the threshold value sigma, the node is automatically identified as a low-energy node, meanwhile, because the node is in a low-energy state, the energy level of the node cannot support the information sending function, and the internal identification system closes the information transmission function; the node can simultaneously perform three functions of immunization, searching and killing and charging according to a certain proportion, and finally the low-energy node is converted into the immune node.
The dead node cannot normally move, cannot perform activities such as charging and discharging, information transmission and the like, and cannot attack other nodes.
S13, the nodes present uniform spatial distribution in the two-dimensional area, and simultaneously the nodes move in stages, wherein one stage is defined as: the node moves from an initial point to an end point at a constant speed V, and the moving time is T move And stays at the end point for a period of time T stop For a moving time T move And a stop time T stop Both are random variables;
s14, in unit time T unit Within the transmission radius r of an infected node I (t), the number of susceptible nodes that can be contacted is:
at a unit time T unit The number of susceptible nodes which are successfully infected is N SI (t) is
Wherein the infection success rate of the susceptible node of the infected node I (t) is omega.
S15, at time t:
by P SR The success rate of immunization and charging operation on the susceptible node is shown;
with P IR The success rate of searching and killing and charging operations on the infected node is shown;
with P QR The success rate of searching, killing and charging operations on the isolated nodes is shown;
by P LR Representation to low energy nodeThe success rate of charging, immunization, searching and killing operations is implemented;
with P SL ，P RL ，P IL ，P QL Respectively representing the proportion of the susceptible node, the immune node, the infected node and the isolated node converted into the low-energy node;
by P IQ Representing the quarantine identification rate of infected nodes;
by P LD Indicating low energy node mortality;
with P SI Indicating the infection success rate of the infected node;
for P SR According to the time per unit T unit The number of susceptible nodes which are successfully infected is N SI (t), the following may be allowed:
namely N SI (t)＝P SR S(t)。
S2, constructing a node state transition diagram according to the state transition relation of the nodes, and listing differential equations of all the nodes according to the transition diagram, wherein the differential equations specifically comprise the following steps:
s21, the state conversion relation of the nodes is specifically as follows:
susceptible node with P SI S (t) I (t) ratio is converted into infection node as P SR S (t) ratio is converted into an immunonode, denoted P SL Converting the S (t) proportion into low-energy nodes;
infect node with P IQ I (t) ratio is converted into isolated node, P IR I (t) ratio conversion to immunonodes, with P IL I (t) is converted into a low-energy node in proportion;
immunization node with P RL Converting the proportion of R (t) into low-energy nodes;
isolate node with P QR Conversion of the Q (t) ratio to an immunonode, denoted P QL Converting the Q (t) ratio into a low-energy node;
low energy node with P LD The ratio of L (t) is converted into death node as P LR Conversion of L (t) ratio to immunonodes；
Death node is composed of low energy node and P LD L (t) is converted in proportion;
the mutual transformation proportion of the nodes is as follows: u = [0,1].
S22, as shown in fig. 2, obtaining the following node differential equation set according to the node state transition diagram:
s3, constructing a cost objective function according to the immunity proportion, the killing proportion, the charging proportion, the isolation proportion and the number of infected nodes of the nodes, and specifically:
according to the number of infected nodes I (t), P SI 、P IR 、P QR 、P IQ And P LR And solving the minimum cost of the isolation and control of the malicious program, and constructing a cost objective function:
wherein, mu 1 Cost parameters for implementing immunization and charging operations; mu.s 2 Cost parameters for implementing checking, killing and charging operations; mu.s 3 A cost parameter for implementing the isolation operation; mu.s 4 As a function of the cost of implementing immunization, killing, and charging.
S4, constructing a Hamiltonian, specifically:
according to the cost objective function and the differential equation of each node, a Hamiltonian is constructed:
wherein, delta 1 、δ 2 、δ 3 And delta 4 Respectively representing covariates delta 1 (t)、δ 2 (t)、δ 3 (t) and δ 4 (t)。
S5, solving a covariate differential equation set, a cross section condition and an optimization condition according to the Hamiltonian, and obtaining an optimal control pair according to the optimization condition, wherein the optimal control pair specifically comprises the following steps:
s51, obtaining a covariate differential equation set according to the Hamiltonian and the Ponderland Kingson maximum principle:
s52, at terminal time t f The optimization target of the objective function is only I (t) f ) And S (t) f )、Q(t f )、L(t f ) Not shown, therefore the cross-sectional conditions are:
δ 1 (t f )＝δ 3 (t f )＝δ 4 (t f )＝0
δ 2 (t f )＝1
s53, obtaining an optimized condition according to the maximum value principle of Ponderland Richmin:
solving the above equation yields:
s54, obtaining an optimization control pair according to the optimization conditions:
the condition for obtaining the minimum value for the objective function J in step S3 is the optimization control pair obtained in step S54.
It should also be noted that in this specification, terms such as "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising a … …" does not exclude the presence of another identical element in a process, method, article, or apparatus that comprises the element.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (5)
1. A malicious program isolation and control method based on a wireless sensor network is characterized by comprising the following steps:
constructing a node moving model of the wireless sensor network, assuming that a plurality of nodes are divided into a plurality of node types, all the nodes exist in a two-dimensional area, the nodes are uniformly distributed in the two-dimensional area, and simultaneously, the nodes move in stages, and each node can only contact with other nodes in the transmission range of the node;
the method for constructing the node movement model of the wireless sensor network specifically comprises the following steps:
assuming that all nodes exist in a two-dimensional area with the area of A, the total number of the nodes is N, the number of the nodes is not supplemented along with the change of time, the radius of information transmission of each node is r, and each node can only contact with other nodes in the transmission radius r;
the node types comprise susceptible nodes S (t), infected nodes I (t), immune nodes R (t), isolated nodes Q (t), low-energy nodes L (t) and dead nodes D (t);
for S (t), I (t), R (t), Q (t), L (t) and D (t), the number proportion of each node type relative to the total number of nodes is defined;
all types of nodes meet the following proportional relation at any time t:
S(t)+I(t)+R(t)+Q(t)+L(t)+D(t)＝1；
the susceptible node does not immunize a malicious program, and is attacked by the infected node and then converted into an infected node;
the infected node is attacked by a malicious program, and the node is not judged as an isolated node by an internal identification system at the moment and attacks a sensitive node contacted in a transmission radius r;
the immune node is used for immunizing the malicious program, eliminating the malicious program and preventing the malicious program from being attacked by the infected node;
the isolation node is attacked by the malicious program, but the node is judged to be stored with the malicious program by the internal identification system and is converted into the isolation node, and the information transmission function of the node is closed by the identification system, so that the isolation node cannot attack the susceptible node;
the low-energy nodes are divided into high-energy consumption nodes and common-energy consumption nodes; when the node is lower than the threshold value, the node is automatically identified as a low-energy node, meanwhile, because the node is in a low-energy state, the energy level of the node cannot support the information sending function, and the internal identification system closes the information transmission function; the node can simultaneously perform three functions of immunization, searching and killing and charging, and finally the low-energy node is converted into an immunization node; the energy consumption high nodes are converted by infection nodes and isolation nodes, and the energy consumption common nodes are converted by susceptible nodes and immune nodes;
the dead node cannot normally move, cannot carry out charging and discharging and information transmission, and cannot attack other nodes;
at time t:
with P SR (t) the success rate of the immunization and charging operation on the susceptible node is shown;
with P IR (t) the success rate of the searching and killing and charging operations of the infected node is shown;
by P QR (t) the success rate of the searching, killing and charging operations carried out on the isolated node is shown;
with P LR (t) success rate of charging, immunization, killing operations performed on low-energy nodes；
The immunization refers to that a patch of a malicious node is installed in the node, and when the malicious node attacks, the node is not influenced by the patch, so that an immune function is generated on the malicious node;
the charging means that after the nodes of the wireless sensor network enter a low-energy state, the unmanned aerial vehicle is manually controlled to charge the nodes, and the energy is recovered to the highest state;
the searching and killing refers to that a computer system is manually operated to search and kill viruses on the nodes;
the isolation refers to that the node identification system closes the information transmission function of the node;
by P SL (t)，P RL (t)，P IL (t) and P QL (t) respectively representing the conversion rate of the susceptible node, the immune node, the infected node and the isolated node into the low-energy node;
by P IQ (t) represents the quarantine identification rate for infected nodes;
by P LD (t) low energy node mortality;
with P SI (t) indicates infection success rate of infected nodes;
the above ratio feasible regions are all: u = [0,1];
constructing a node state transition diagram according to the state transition relation of the nodes, and listing differential equations of all the nodes according to the node state transition diagram;
the method for constructing the node state transition graph specifically comprises the following steps of constructing the node state transition graph according to the following transition relations:
susceptible node with P SI (t) S (t) I (t) ratio to infectious node, in P SR (t) S (t) ratio conversion to immunonodes, in P SL (t) converting the S (t) ratio into a low energy node;
infect node with P IQ (t) I (t) ratio to isolated node, with P IR (t) I (t) ratio conversion to immunonodes, in P IL (t) converting the I (t) ratio into a low energy node;
immunization node with P RL (t) converting the R (t) ratio into low energy nodes;
isolate node with P QR (t) Q (t) ratio to immunonode, P QL (t) converting the Q (t) ratio into a low energy node;
low energy node with P LD (t) conversion of the L (t) ratio into death node, in P LR (t) converting the ratio L (t) into an immunonode;
death node is composed of low energy node and P LD (t) converting the ratio L (t);
constructing a cost objective function according to the immunity proportion, the killing proportion, the charging proportion, the isolation proportion and the number of infected nodes of the nodes;
constructing a Hamiltonian according to the obtained cost target function and the differential equation of each node;
and obtaining a covariate differential equation set by a Ponderland Riagingt maximum principle according to a Hamiltonian, solving a cross section condition and an optimization condition, and finally obtaining an optimal control pair according to the optimization condition.
2. The method for isolating and controlling the malicious program based on the wireless sensor network according to claim 1, wherein the differential equation of each node is specifically:
3. the method according to claim 2, wherein a cost objective function is constructed according to the immune proportion, the killing proportion, the charging proportion, the isolation proportion and the number of infected nodes of the nodes, and specifically comprises:
according to the number of infected nodes I (t), P SI 、P IR 、P QR 、P IQ And P LR And solving the minimum cost of isolation and control of the malicious program, and constructing a cost objective function:
wherein, mu 1 Cost parameters for implementing immunization and charging operations; mu.s 2 Cost parameters for implementing checking, killing and charging operations; mu.s 3 A cost parameter for implementing the isolation operation; mu.s 4 As a function of the cost of implementing immunization, killing, and charging.
4. The method for isolating and controlling the malicious program based on the wireless sensor network according to claim 3, wherein the constructing of the hamiltonian specifically comprises:
according to the cost objective function and the differential equation of each node, a Hamiltonian is constructed:
wherein, delta 1 、δ 2 、δ 3 And delta 4 Respectively representing covariates delta 1 (t)、δ 2 (t)、δ 3 (t) and δ 4 (t), both are defined identically.
5. The method as claimed in claim 4, wherein the covariance variable differential equation is a negative of a partial derivative of a proportion of the number of corresponding nodes to a Hamiltonian function, based on the Ponderland maximum principle;
the system of the covariate differential equations specifically comprises:
in particular, at the end time t f The cross-section condition of the covariate is specifically as follows:
δ 1 (t f )＝δ 3 (t f )＝δ 4 (t f )＝0
δ 2 (t f )＝1
the optimization conditions are specifically as follows:
the optimization condition is obtained by the maximum value principle of Ponderland gold:
solving the above equation yields:
the optimal control pair obtained according to the optimization conditions is the minimum cost for isolating and controlling the malicious program;
solving the solution of the obtained optimization condition to obtain the optimal control pair, which is specifically as follows:
where min refers to the minimum value, max refers to the maximum value, and a certain ratio with a sign indicates the value of the ratio under optimal control.
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