CN112469041A - 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 PDF

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CN112469041A
CN112469041A CN202011370303.4A CN202011370303A CN112469041A CN 112469041 A CN112469041 A CN 112469041A CN 202011370303 A CN202011370303 A CN 202011370303A CN 112469041 A CN112469041 A CN 112469041A
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CN112469041B (en
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刘贵云
冯凯力
钟晓静
彭智敏
李君强
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Guangzhou University
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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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • 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

Malicious program isolation and control method based on wireless sensor network
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 loss of a network of nodes, 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 cannot work normally.
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 node is isolated, so that the infected proportion of the susceptible node is 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 move in stages, and each node can only contact other nodes in a 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 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.
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 quantity ratio of each node type to the total node quantity is indicated;
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 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 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 PSR(t) the success rate of the immunization and charging operation on the susceptible node is shown;
by PIR(t) the success rate of the searching and killing and charging operations of the infected node is shown;
by POR(t) the success rate of the searching, killing and charging operations carried out on the isolated node is shown;
by PLR(t) represents the success rate of charging, immunizing, killing operations performed on low energy nodes;
by PSL(t)，PRL(t)，PIL(t) and PQL(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 PIQ(t) represents the quarantine identification rate for infected nodes;
by PLD(t) low energy node mortality;
by PSI(t) indicates infection success rate of infected nodes;
the above ratio feasible regions are all: 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 PSI(t) conversion of the ratio of S (t) I (t) to infectious node, in PSR(t) conversion of the ratio of S (t) to immunonodes, in PSL(t) converting the ratio of S (t) into low energy nodes;
infect node with PIQ(t) I (t) ratio is converted into isolated node, PIR(t) conversion of the ratio of I (t) to immunonodes, in PIL(t) ratio conversion to low energy nodes;
immunization node with PRL(t) conversion of the ratio R (t)A low energy node;
isolate node with PQR(t) conversion of Q (t) ratio to immunonodes, in PQL(t) conversion of the ratio of q (t) to low energy nodes;
low energy node with PLD(t) conversion of the ratio of L (t) to death node, in PLR(t) conversion of the ratio of L (t) to immunonodes;
death node is composed of low energy node and PLD(t) L (t) in a ratio.
Preferably, the differential equation of each node is specifically:
Figure BDA0002806451810000051
Figure BDA0002806451810000052
Figure BDA0002806451810000053
Figure BDA0002806451810000054
Figure BDA0002806451810000055
Figure BDA0002806451810000056
preferably, said mu1Cost parameters for implementing immunization and charging operations; mu.s2Cost parameters for implementing checking, killing and charging operations; mu.s3A cost parameter for implementing the isolation operation; mu.s4As a function of the cost of performing immunization, killing, and charging operations; t is tfOptimally controlling the research end time for the method; i (t)f) Is the end time tfThe number proportion of infected nodes;
according to the number ratio I (t) of infected nodesf) Inter-node conversion ratio PSR(t)S(t)、PIR(t)/(t)、PQR(t)Q(t)、PIQ(t) I (t) and PLR(t) L (t), constructing a cost objective function J to obtain the minimum cost for isolating and controlling the malicious program, wherein the construction cost objective function is specifically as follows:
Figure BDA0002806451810000057
preferably, a Hamiltonian is constructed according to a PonderRiagin maximum principle and a differential equation set and a cost target function;
delta. the1、δ2、δ3And delta4Respectively representing covariates delta1(t)、δ2(t)、δ3(t) and δ4(t), both defined identically;
the construction of the Hamiltonian H specifically comprises the following steps:
Figure BDA0002806451810000061
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 specifically comprises:
Figure BDA0002806451810000062
Figure BDA0002806451810000063
Figure BDA0002806451810000064
Figure BDA0002806451810000065
in particular, at the end time tfThe cross-section condition of the covariate is specifically as follows:
δ1(tf)＝δ3(tf)＝δ4(tf)＝0
δ2(tf)＝1
the solving optimization conditions are specifically as follows:
the optimization condition is obtained by the maximum value principle of Ponderland gold:
Figure BDA0002806451810000066
Figure BDA0002806451810000067
Figure BDA0002806451810000068
Figure BDA0002806451810000069
Figure BDA0002806451810000071
solving the above equation yields:
Figure BDA0002806451810000072
Figure BDA0002806451810000073
Figure BDA0002806451810000074
Figure BDA0002806451810000075
Figure BDA0002806451810000076
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:
Figure BDA0002806451810000077
Figure BDA0002806451810000078
Figure BDA0002806451810000079
Figure BDA00028064518100000710
Figure BDA00028064518100000711
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 sensing 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 the reduction factors.
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 method for malware isolation and control based on a wireless sensor network;
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 according to the conversion 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 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 movement model of the 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, classifying nodes, including susceptible node S (t), infected node I (t), immune node R (t), isolation node Q (t), low energy node L (t) and death node 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 the 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 PSIAnd 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 immune to malicious programs, eliminates the malicious programs and cannot be attacked by infected nodes, and the node has a common energy loss speed.
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 region, and the nodes move in stages, defining a stage as: the node moves from an initial point to an end point at a constant speed V, and the moving time is TmoveAnd stays at the end point for a period of time TstopFor a moving time TmoveAnd a stop time TstopBoth are random variables;
s14, at unit time TunitAn infected node i (t) has a transmission radius r within which the number of susceptible nodes that can be contacted is:
Figure BDA0002806451810000101
at a unit time TunitSusceptible node of internal, successful infectionNumber of points NSI(t) is
Figure BDA0002806451810000102
Wherein, the infection success rate of the infection node I (t) susceptible node is omega.
S15, at time t:
by PSRThe success rate of implementing immunization and charging operations on the susceptible node is shown;
by PIRThe success rate of searching and killing and charging operations on the infected node is shown;
by PQRThe success rate of searching, killing and charging operations on the isolated nodes is shown;
by PLRThe success rate of charging, immunizing, searching and killing operations of the low-energy nodes is shown;
by PSL，PRL，PIL，PQLRespectively representing the proportion of the susceptible node, the immune node, the infected node and the isolated node converted into the low-energy node;
by PIQRepresenting the quarantine identification rate of infected nodes;
by PLDIndicating low energy node mortality;
by PSIIndicating the infection success rate of the infected node;
for PSRAccording to the time per unit TunitThe number of susceptible nodes which are successfully infected is NSI(t), the following may be allowed:
Figure BDA0002806451810000111
namely NSI(t)＝PSRS(t)。
S2, constructing a node state transition diagram according to the state transition relation of the nodes, and listing differential equations of each node according to the transition diagram, wherein the differential equations specifically comprise:
s21, the state conversion relation of the nodes is specifically as follows:
susceptible node with PSIS (t) I (t) ratio is converted into infection node, and P is usedSRS (t) ratio is converted into an immune node as PSLS (t) converting the proportion into low-energy nodes;
infect node with PIQI (t) ratio is converted into isolated node, PIRI (t) ratio conversion to immunonodes, with PILI (t) proportional conversion to low energy nodes;
immunization node with PRLR (t) ratio is converted into low energy nodes;
isolate node with PQRQ (t) ratio to immunonodes, in PQLQ (t) ratio conversion to low energy nodes;
low energy node with PLDL (t) ratio to death node, PLRL (t) proportional conversion to an immunonode;
death node is composed of low energy node and PLDL (t) is converted in proportion;
the mutual transformation proportion of the nodes is as follows: u ═ 0, 1.
S22, as shown in fig. 2, according to the node state transition diagram, the following node differential equation set is obtained:
Figure BDA0002806451810000112
Figure BDA0002806451810000121
Figure BDA0002806451810000122
Figure BDA0002806451810000123
Figure BDA0002806451810000124
Figure BDA0002806451810000125
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, wherein the cost objective function specifically comprises the following steps:
according to the number of infected nodes I (t), PSI、PIR、PQR、PIQAnd PLRAnd solving the minimum cost of isolation and control of the malicious program, and constructing a cost objective function:
Figure BDA0002806451810000126
wherein, mu1Cost parameters for implementing immunization and charging operations; mu.s2Cost parameters for implementing checking, killing and charging operations; mu.s3A cost parameter for implementing the isolation operation; mu.s4As 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:
Figure BDA0002806451810000127
wherein, delta1、δ2、δ3And delta4Respectively representing covariates delta1(t)、δ2(t)、δ3(t) and δ4(t)。
S5, solving the covariate differential equation set, the cross-section condition and the optimization condition according to the Hamiltonian, and obtaining the 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 gold maximum principle:
Figure BDA0002806451810000131
Figure BDA0002806451810000132
Figure BDA0002806451810000133
Figure BDA0002806451810000134
s52, at terminal time tfThe optimization target of the objective function is only I (t)f) And S (t)f)、Q(tf)、L(tf) Not shown, therefore the cross-sectional conditions were:
δ1(tf)＝δ3(tf)＝δ4(tf)＝0
δ2(tf)＝1
s53, obtaining an optimized condition according to the maximum value principle of Ponderland Richmus:
Figure BDA0002806451810000135
Figure BDA0002806451810000136
Figure BDA0002806451810000137
Figure BDA0002806451810000138
Figure BDA0002806451810000139
solving the above equation yields:
Figure BDA00028064518100001310
Figure BDA0002806451810000141
Figure BDA0002806451810000142
Figure BDA0002806451810000143
Figure BDA0002806451810000144
s54, obtaining an optimization control pair according to the optimization conditions:
Figure BDA0002806451810000145
Figure BDA0002806451810000146
Figure BDA0002806451810000147
Figure BDA0002806451810000148
Figure BDA0002806451810000149
the condition for obtaining the minimum value of the objective function J in step S3 is the optimal 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 an … …" does not exclude the presence of other identical elements 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 (9)

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 move in stages, and each node can only contact other nodes in a 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 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 according to claim 1, wherein the building of the node movement model of the wireless sensor network specifically comprises:
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 quantity ratio of each node type to the total node quantity is indicated;
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。
3. the method for isolating and controlling the malicious program based on the wireless sensor network as claimed in claim 2, wherein 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 malicious node, 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 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 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.
4. The method for isolating and controlling the malicious programs based on the wireless sensor network as claimed in claim 3, wherein at time t:
by PSR(t) the success rate of the immunization and charging operation on the susceptible node is shown;
by PIR(t) the success rate of the searching and killing and charging operations of the infected node is shown;
by POR(t) the success rate of the searching, killing and charging operations carried out on the isolated node is shown;
by PLR(t) represents the success rate of charging, immunizing, killing operations performed on low energy nodes;
by PSL(t)，PRL(t)，PIL(t) and POL(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 PIQ(t) represents the quarantine identification rate for infected nodes;
by PLD(t) low energy node mortality;
by PSI(t) indicates infection success rate of infected nodes;
the above ratio feasible regions are all: u ═ 0, 1.
5. The method as claimed in claim 4, wherein the step of constructing the node state transition graph is specifically that the node state transition graph is constructed according to the following transition relations:
susceptible node with PSI(t) conversion of the ratio of S (t) I (t) to infectious node, in PSR(t) conversion of the ratio of S (t) to immunonodes, in PSL(t) converting the ratio of S (t) into low energy nodes;
infect node with PIQ(t) I (t) ratio is converted into isolated node, PIR(t) conversion of the ratio of I (t) to immunonodes, in PIL(t) ratio conversion to low energy nodes;
immunization node with PRL(t) the ratio of R (t) is converted into a low energy node;
isolate node with PQR(t) conversion of Q (t) ratio to immunonodes, in PQL(t) conversion of the ratio of Q (t) to Low energyA volume node;
low energy node with PLD(t) conversion of the ratio of L (t) to death node, in PLR(t) conversion of the ratio of L (t) to immunonodes;
death node is composed of low energy node and PLD(t) L (t) in a ratio.
6. The method according to claim 5, wherein the differential equation of each node is specifically as follows:
Figure FDA0002806451800000031
Figure FDA0002806451800000032
Figure FDA0002806451800000033
Figure FDA0002806451800000034
Figure FDA0002806451800000035
Figure FDA0002806451800000036
7. the method as claimed in claim 6, wherein μ ™ is selected from a group consisting of mu, u, and k1Cost parameters for implementing immunization and charging operations; mu.s2Cost parameters for implementing checking, killing and charging operations; mu.s3A cost parameter for implementing the isolation operation; mu.s4As a function of the cost of performing immunization, killing, and charging operations; t is tfOptimally controlling the research end time for the method; i (t)f) Is the end time tfThe number proportion of infected nodes;
according to the number ratio I (t) of infected nodesf) Inter-node conversion ratio PSR(t)S(t)、PIR(t)I(t)、PQR(t)Q(t)、PIQ(t) I (t) and PLR(t) L (t), constructing a cost objective function J to obtain the minimum cost for isolating and controlling the malicious program, wherein the construction cost objective function is specifically as follows:
Figure FDA0002806451800000041
8. the method for isolating and controlling the malicious programs based on the wireless sensor network as claimed in claim 7, wherein a Hamiltonian is constructed according to a differential equation set and a cost objective function by the Ponderrichardian maximum principle;
delta. the1、δ2、δ3And delta4Respectively representing covariates delta1(t)、δ2(t)、δ3(t) and δ4(t), both defined identically;
the construction of the Hamiltonian H specifically comprises the following steps:
Figure FDA0002806451800000042
9. the method as claimed in claim 8, 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 principles of pointryagin maxima;
the system of the covariate differential equations specifically comprises:
Figure FDA0002806451800000043
Figure FDA0002806451800000051
Figure FDA0002806451800000052
Figure FDA0002806451800000053
in particular, at the end time tfThe cross-section condition of the covariate is specifically as follows:
δ1(tf)＝δ3(tf)＝δ4(tf)＝0
δ2(tf)＝1
the solving optimization conditions are specifically as follows:
the optimization condition is obtained by the maximum value principle of Ponderland gold:
Figure FDA0002806451800000054
Figure FDA0002806451800000055
Figure FDA0002806451800000056
Figure FDA0002806451800000057
Figure FDA0002806451800000058
solving the above equation yields:
Figure FDA0002806451800000059
Figure FDA00028064518000000510
Figure FDA00028064518000000511
Figure FDA00028064518000000512
Figure FDA00028064518000000513
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:
Figure FDA00028064518000000514
Figure FDA00028064518000000515
Figure FDA0002806451800000061
Figure FDA0002806451800000062
Figure FDA0002806451800000063
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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