CN114760208A - Wireless sensor network control method based on time interval division - Google Patents

Wireless sensor network control method based on time interval division Download PDF

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CN114760208A
CN114760208A CN202210302601.2A CN202210302601A CN114760208A CN 114760208 A CN114760208 A CN 114760208A CN 202210302601 A CN202210302601 A CN 202210302601A CN 114760208 A CN114760208 A CN 114760208A
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CN114760208B (en
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刘贵云
武夕涞
黄梓毅
梁忠伟
钟晓静
杨耀权
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    • H—ELECTRICITY
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Abstract

The invention discloses a wireless sensor network control method based on time interval division, which comprises the following steps: s1, determining the time period of the wireless sensor network; s2, constructing a state transition diagram based on the time interval of the wireless sensor network; s3, constructing a control model based on the state transition diagram; s4, constructing a cost function based on the control model; s5, constructing a Hamiltonian, and obtaining an optimal control strategy based on the cost function and the Hamiltonian. The effect of controlling the WSN is effectively improved; the invention also improves the isolation measure for inhibiting the spread of the malicious software, and adds a step of periodically injecting the node in the immune state on the basis of the isolation. Patches can be disseminated more specifically.

Description

Wireless sensor network control method based on time interval division
Technical Field
The invention relates to the field of control, in particular to a wireless sensor network control method based on time interval division.
Background
The Wireless Sensor Network (WSN) has the advantages of high coverage, low cost, flexible deployment, and the like, and is widely applied to the fields of environmental protection, national defense and military, medical health, smart power grids, and the like. The research shows that: the introduction of the WSN can effectively reduce the labor cost and effectively improve the production management level.
Taking the application of WSN in agriculture as an example: the application of the WSN in agriculture can effectively reduce the manual working time, thereby reducing the labor cost; meanwhile, the node is more sensitive to the change of temperature, humidity and air quality, and can transmit information to the management layer in time, so that the management layer can make an adjustment strategy rapidly, and the agricultural management level is improved. In addition, the detection network formed by the nodes has obvious advantages for specific environments.
Network transmission of the WSN is very energy-consuming, and early death of nodes is easily caused. The main reasons for premature node death are: the low-energy nodes are not timely replenished, so that the energy loss of the nodes is aggravated by early damage and malicious software, and the energy of the nodes is more easily exhausted.
For the energy problem, a part of the solution is to use solar energy for charging, the solar energy charging is not always continuous, and the wireless sensor network is in a non-charging state in cloudy days, at night, and the like. Therefore, a time-division-based control method is needed to control the wireless sensor network and simultaneously control the spread of the malicious software in the wireless sensor network.
Disclosure of Invention
The invention aims to disclose a wireless sensor network control method based on time interval division, and solve the problem of how to control a wireless sensor network in the time interval with solar charging and the time interval without solar charging.
In order to achieve the purpose, the invention adopts the following technical scheme:
a wireless sensor network control method based on time interval division comprises
S1, determining the time period of the wireless sensor network;
s2, constructing a state transition diagram based on the time interval of the wireless sensor network;
s3, constructing a control model based on the state transition diagram;
s4, constructing a cost function based on the control model;
s5, constructing a Hamiltonian, and obtaining an optimal control strategy based on the cost function and the Hamiltonian.
Preferably, the periods include a solar chargeable period and a non-solar chargeable period.
Preferably, the S2 includes:
the state transition diagram comprises a first state transition diagram and a second state transition diagram;
determining a state of a node, the state of the node comprising: susceptible S, infected I, immunized R, and spent D;
if the wireless sensor network is in a solar charging time period, constructing a first state transition diagram according to the transition relation of the nodes in different states;
And if the wireless sensor network is in the non-solar charging period, constructing a second state transition diagram according to the transition relation of the nodes in different states.
Preferably, the S3 includes:
the control model comprises a first control model and a second control model;
if the wireless sensor network is in the solar charging time period, constructing a first control model based on a first state transition diagram:
Figure BDA0003566111680000021
wherein S isiRepresenting susceptible nodes in the ith set, wherein i is the number of the set; t represents an independent variable, Si(nT) represents Si(t) inside of functionThe argument t of (2) is nT, nT+Is the right limit of the moment nT, nT represents the node periodic release time point, IjRepresenting an infected node representing the jth set, RiDenotes an immunized node, R, representing the ith setjDenotes the immunized node, LS, representing the j-th setiLow energy susceptible nodes representing the ith set, IiRepresents the infected node of the ith set; LI (lithium ion) powderiLow energy infected node, LR, representing the ith setiLow energy immunized node, Q, representing the ith setiAn isolation compartment representing a node in the ith set, N represents the total number of nodes,
wherein, the charging rate of the node is fitted by a quadratic function:
Figure BDA0003566111680000031
T represents a non-release time period, nT represents a regular release time point of the nodes, the nodes with the same communication connectivity can be divided into the same set, and eta sets exist in total;
βijrepresenting a malware propagation rate of a node in the jth set to a node of the ith set;
γirepresenting the low-energy node damage rate in the ith set;
μirepresenting the power outage of the nodes in the ith set;
Cirepresenting the solar charging rate of the nodes in the ith set;
αijrepresenting a patch transmission rate at a node in the jth set to the ith set;
θirepresenting the patch failure rate of the ith set;
gijrepresenting the conversion rate of the node in the jth set to the node in the ith set;
delta is a positive integer, delta T represents a period of time during which solar charging is possible
Epsilon is a positive integer, and epsilon T represents a time period of non-solar charging;
p represents the regular release rate of the immunized nodes;
qirepresents the correction coefficient, guarantees CiA value of 0 at a particular point in time;
Xirepresenting a node failure constant in the ith set;
Kirepresenting the failure constant change rate of the nodes in the ith set;
Λirepresenting the regular delivery rate of the nodes in the ith set;
eHiwhen the wireless sensor network is in the solar charging period, the isolation rate of the infection-prone nodes of the ith set in the non-putting period is represented;
Figure BDA0003566111680000032
When the wireless sensor network is in the solar charging period, the ith set is at the isolation rate of the infection-prone nodes at the regular release time point;
ΛHithe putting rate of the ith set at a regular putting time point is represented when the wireless sensor network is in a solar charging period;
ΛQHiwhen the wireless sensor network is in the solar charging period, the putting rate of the isolation compartment of the ith set at the regular putting time point is represented;
Qi(t) represents node isolation compartments in the ith set;
Ψ is a positive integer, Ψ T represents the execution time of the control strategy when the wireless sensor network is in a solar charging period, Ψ T is less than or equal to δ T;
if the wireless sensor network is in the non-solar charging period, a second control model is established based on a second state transition diagram:
Figure BDA0003566111680000041
wherein, the damage rate of the node is fitted by a linear function:
Figure BDA0003566111680000042
Kirepresenting the failure rate of change of the nodes in the ith set;
xirepresenting a node failure constant in the ith set;
eLiwhen the wireless sensor network is in the non-solar charging period, the isolation rate of the infection-prone nodes of the ith set in the non-putting period is represented;
Figure BDA0003566111680000043
representing the isolation rate of the susceptible nodes of the ith set at the regular release time point;
ΛLiThe putting rate of the ith set at the regular putting time point is represented;
ΛQLirepresenting the release rate of the isolation compartment of the ith set at the regular release time point;
phi is a positive integer, phi T represents the execution time of the control strategy when the wireless sensor network is in the non-solar charging period, and phi T is less than or equal to delta T.
Preferably, the S4 includes:
the cost function comprises a first cost function and a second cost function;
if the wireless sensor network is in the solar charging time period, constructing a first cost function based on a first control model:
Figure BDA0003566111680000051
wherein A is1iDenotes the supervision and isolation cost, A, for a susceptible WSN in a set with communication connectivity i2iRepresents the regulatory cost, A, for an infected WSN in a set with communication connectivity i3iIsolation Compartment Q in set representing connectivity to communication iiThe set-up and supervision costs of (a) are,A4irepresenting the execution cost of isolation measures taken on a set with communication connectivity i during a non-release period, A5iRepresents the implementation cost of the isolation measure adopted by the set with communication connectivity i at the time point of the periodic release, A6iRepresents the execution cost of a set of delivery nodes with communication connectivity i at regular delivery time points, A7iIsolation compartment Q representing periodic drop time point to communication connectivity i iThe execution cost of the node is released;
if the wireless sensor network is in the non-solar charging period, constructing a second cost function based on a second control model:
Figure BDA0003566111680000052
B1irepresents the supervision and isolation cost of a susceptible WSN in a set with communication connectivity i, B2iRepresents the regulatory cost of an infected WSN in a set with communication connectivity i, B3iIsolation Compartment Q in set representing connectivity to communication iiCost of setup and supervision of, B4iRepresenting the cost of implementation of isolation measures for a set of communication connectivity i during non-release periods, B5iRepresents the implementation cost of the isolation measures adopted by the set with communication connectivity i at the time point of the periodic release, B6iRepresents the execution cost of a set of delivery nodes with communication connectivity i at regular delivery time points, B7iIsolation compartment Q representing periodic drop time point to communication connectivity iiAnd releasing the execution cost of the node.
Preferably, the S5 includes:
if the wireless sensor network is in the solar chargeable period, determining an optimal control strategy in the following way:
constructing a Hamiltonian in a non-release period by the following method:
Figure BDA0003566111680000053
wherein λji(j ═ 1, 2.., 7) is a first auxiliary variable;
obtaining necessary conditions of an optimal solution of a control strategy in a non-putting time period when solar charging is available according to the Pontryagin maximum principle:
Figure BDA0003566111680000061
λji(j ═ 1, 2., 7) is a first auxiliary variable,
the optimal isolation strength of the set with communication connectivity i by adopting isolation measures in a non-release period can be obtained by utilizing an optimality condition:
Figure BDA0003566111680000062
namely:
Figure BDA0003566111680000063
represents an optimal solution that introduces optimal control;
and constructing a Hamiltonian of the replenishment time point by adopting the first auxiliary variable:
Figure BDA0003566111680000064
the necessary conditions for realizing the optimal solution of the control strategy of the periodic release time point are as follows:
Figure BDA0003566111680000065
λji(j ═ 1, 2.., 7) is a first auxiliary variable, λjiIs a function of time t, when t equals nT, expressed as λji(nT)，nT+Is the right limit of nT;
the expression for the optimal control strategy that can be obtained using the requirements of the optimal solution is as follows:
Figure BDA0003566111680000071
namely:
Figure BDA0003566111680000072
Figure BDA0003566111680000073
presentation pair
Figure BDA0003566111680000074
An optimal solution for the optimal control is introduced,
Figure BDA0003566111680000075
represents a pair Si(nT) introducing an optimal solution for optimal control,
Figure BDA0003566111680000076
pair of aHiAn optimal solution for the optimal control is introduced,
Figure BDA0003566111680000077
pair of aQHiAn optimal solution for the optimal control is introduced,
if the wireless sensor network is in the non-solar charging period, determining an optimal control strategy in the following mode:
constructing a Hamiltonian in a non-release time period:
Figure BDA0003566111680000078
wherein m isji(j ═ 1, 2.., 7) is a second auxiliary variable;
obtaining necessary conditions of an optimal solution of a control strategy in a non-putting time period when solar charging is unavailable according to the Pontryagin maximum principle:
Figure BDA0003566111680000081
The optimal isolation strength of the set with communication connectivity i in the non-release period by adopting isolation measures can be obtained by utilizing the optimality condition:
Figure BDA0003566111680000082
namely:
Figure BDA0003566111680000083
the hamiltonian of the replenishment time point constructed based on the second auxiliary variable is:
Figure BDA0003566111680000084
the necessary conditions for realizing the optimal solution of the control strategy of the periodic release time point are as follows:
Figure BDA0003566111680000085
mjiis a function of time t, when t equals nT, expressed as mji(nT)，
The expression for the optimal control strategy that can be obtained using the optimality condition is as follows:
Figure BDA0003566111680000091
namely:
Figure BDA0003566111680000092
Figure BDA0003566111680000093
respectively represent pair
Figure BDA0003566111680000094
ΛLi、ΛQLiAnd introducing an optimal solution of optimal control.
The invention improves the traditional infectious disease dynamics, provides a differential equation model with pulse birth, and uses the model to control a complex heterogeneous WSN network; from the aspect of replenishment rate, a strategy for controlling the replenishment rate is provided, a formula of optimal replenishment rate intensity is obtained based on a maximum value principle, and the effect of controlling the WSN is effectively improved; the invention also improves the isolation measure for inhibiting the spread of the malicious software, and adds a step of periodically injecting the node in the immune state on the basis of the isolation. Patches can be disseminated more specifically.
Drawings
The invention is further illustrated by means of the attached drawings, but the embodiments in the drawings do not constitute any limitation to the invention, and for a person skilled in the art, other drawings can be obtained on the basis of the following drawings without inventive effort.
Fig. 1 is a diagram of an exemplary embodiment of a wireless sensor network control method based on time division according to the present invention.
Fig. 2 shows a first state transition diagram.
Fig. 3 shows a second state transition diagram.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As shown in fig. 1, in an embodiment, the present invention provides a time-division-based wireless sensor network control method, including:
s1, determining the time period of the wireless sensor network;
s2, constructing a state transition diagram based on the time interval of the wireless sensor network;
s3, constructing a control model based on the state transition diagram;
s4, constructing a cost function based on the control model;
s5, constructing a Hamiltonian, and obtaining an optimal control strategy based on the cost function and the Hamiltonian.
One day (24 hours) is divided into two periods, which are a solar chargeable period and a non-solar chargeable period, depending on whether the light intensity can be utilized by the WSN. In the solar charging period, the change of light intensity along with time is considered, and a quadratic function is used for approximate fitting; when solar charging is unavailable, sensor nodes which do not obtain energy supply in time die prematurely, so that the death rate of the nodes is approximately fitted by a linear function in the period.
Preferably, the periods include a solar chargeable period and a non-solar chargeable period.
Preferably, the S2 includes:
the state transition diagram comprises a first state transition diagram and a second state transition diagram;
determining a state of a node, the state of the node comprising: susceptible S, infected I, immunized R, and spent D;
if the wireless sensor network is in a solar charging time period, constructing a first state transition diagram according to the transition relation of the nodes in different states;
and if the wireless sensor network is in the non-solar charging period, constructing a second state transition diagram according to the transition relation of the nodes in different states.
Preferably, the S3 includes:
the control models comprise a first control model and a second control model;
if the wireless sensor network is in the solar charging time period, constructing a first control model based on a first state transition diagram:
Figure BDA0003566111680000111
wherein S isiRepresenting susceptible nodes in the ith set, wherein i is the number of the set; t represents an independent variable, Si(nT) represents SiThe independent variable t in the (t) function takes the values nT, nT+Is the right limit of the moment nT, nT represents the node periodic release time point, IjRepresenting an infected node representing the jth set, R iDenotes an immunized node, R, representing the ith setjDenotes the immunized node, LS, representing the j-th setiLow energy susceptible nodes representing the ith set, IiRepresents the infected node of the ith set; LI (lithium ion) powderiLow energy infected node, LR, representing the ith setiLow energy immunized node, Q, representing the ith setiAn isolation compartment representing a node in the ith set, N represents the total number of nodes,
fig. 2 shows a first state transition diagram illustrating control state transition for a solar chargeable period.
Wherein, the charging rate of the node is fitted by a quadratic function:
Figure BDA0003566111680000112
t represents a non-release time period, nT represents a node release time point, nodes with the same communication connectivity can be divided into the same set, and eta sets exist in total;
βijrepresenting the malware propagation rate of the node in the jth set to the node in the ith set;
γirepresenting the low energy node damage rate in the ith set;
μirepresenting the power-down rate of the nodes in the ith set;
Cirepresenting the solar charging rate of the nodes in the ith set;
αijrepresenting the patch transmission rate of nodes at the jth set versus the ith set;
θirepresenting the patch failure rate of the ith set;
gijRepresenting the conversion rate of the node in the jth set to the node in the ith set;
delta is a positive integer, delta T represents a period of time during which solar charging is possible
Epsilon is a positive integer, and epsilon T represents a time period of non-solar charging;
p represents the regular delivery rate of the immunized nodes;
qirepresents the correction coefficient, guarantees CiA value of 0 at a particular time point;
Xirepresenting a node failure constant in the ith set;
Kirepresenting the failure constant change rate of the nodes in the ith set;
Λirepresenting the regular delivery rate of the nodes in the ith set;
eHiwhen the wireless sensor network is in the solar charging period, the isolation rate of the infection-prone nodes of the ith set in the non-putting period is represented;
Figure BDA0003566111680000121
when the wireless sensor network is in a solar charging period, the isolation rate of the infection-prone nodes of the ith set at a regular release time point is represented;
ΛHithe wireless sensor network charging method comprises the steps that when a wireless sensor network is in a solar charging period, the ith set is at the putting rate of a regular putting time point;
ΛQHithe method represents that when the wireless sensor network is in the solar charging period, the ith set is put into the isolated compartment at the regular putting time pointThe discharge rate;
Qi(t) represents node isolation bays in the ith set;
Ψ is a positive integer, Ψ T represents the execution time of the control strategy when the wireless sensor network is in a solar charging period, Ψ T is less than or equal to δ T;
If the wireless sensor network is in the non-solar charging period, constructing a second control model based on a second state transition diagram:
Figure BDA0003566111680000131
wherein, the damage rate of the node is fitted by a linear function:
Figure BDA0003566111680000132
Kirepresenting the failure rate of change of the nodes in the ith set;
xirepresenting a node failure constant in the ith set;
eLiwhen the wireless sensor network is in the non-solar charging period, the isolation rate of the infection-prone nodes of the ith set in the non-putting period is represented;
Figure BDA0003566111680000133
representing the isolation rate of the susceptible nodes of the ith set at the regular release time point;
ΛLirepresenting the delivery rate of the ith set at the regular delivery time point;
ΛQLirepresenting the release rate of the isolation compartment of the ith set at the regular release time point;
phi is a positive integer, phi T represents the execution time of the control strategy when the wireless sensor network is in the non-solar charging period, and phi T is less than or equal to delta T.
Fig. 3 is a second state transition diagram showing control state transition during a non-solar charging period.
Preferably, the S4 includes:
the cost function comprises a first cost function and a second cost function;
if the wireless sensor network is in the solar charging time period, constructing a first cost function based on a first control model:
Figure BDA0003566111680000141
Wherein, A1iRepresents the supervision and isolation cost, A, for a WSN susceptible to infection in a set with communication connectivity i2iRepresents the regulatory cost, A, for an infected WSN in a set with communication connectivity i3iRepresenting an isolation Compartment Q in a set with communication connectivity iiCost of setup and supervision, A4iRepresents the execution cost of adopting isolation measures for the set with communication connectivity i in a non-release period, A5iRepresents the implementation cost of the isolation measure adopted by the set with communication connectivity i at the time point of the periodic release, A6iRepresents the execution cost of the set delivery node with communication connectivity i at the regular delivery time point, A7iIsolation compartment Q representing periodic drop time point to communication connectivity iiThe execution cost of the node is released;
if the wireless sensor network is in the non-solar charging period, constructing a second cost function based on a second control model:
Figure BDA0003566111680000142
B1irepresents the supervision and isolation costs for a susceptible WSN in a set with communication connectivity i, B2iRepresents the regulatory cost of an infected WSN in a set with communication connectivity i, B3iIsolation Compartment Q in set representing connectivity to communication iiCost of setup and supervision of, B4iRepresenting the cost of implementation of isolation measures for a set of communication connectivity i during non-release periods, B 5iRepresents the implementation cost of the isolation measures adopted by the set with the communication connectivity i at the time point of the periodic release, B6iRepresenting the execution cost of a regularly delivered point of time to a node with communication connectivity i, B7iIsolation compartment Q for representing periodic release time point pair with communication connectivity of iiAnd releasing the execution cost of the node.
Preferably, the S5 includes:
if the wireless sensor network is in the solar charging period, determining an optimal control strategy in the following way:
constructing a Hamiltonian in a non-release period by the following method:
Figure BDA0003566111680000143
wherein λ isji(j ═ 1, 2.., 7) is a first auxiliary variable;
obtaining necessary conditions of an optimal solution of a control strategy in a non-putting time period when solar charging is available according to the Pontryagin maximum principle:
Figure BDA0003566111680000151
λji(j ═ 1, 2.., 7) is a first auxiliary variable,
the optimal isolation strength of the set with communication connectivity i in the non-release period by adopting isolation measures can be obtained by utilizing the optimality condition:
Figure BDA0003566111680000152
namely:
Figure BDA0003566111680000153
represents an optimal solution that introduces optimal control;
and constructing a Hamiltonian of the replenishment time point by adopting the first auxiliary variable:
Figure BDA0003566111680000154
the necessary conditions for realizing the optimal solution of the control strategy of the periodic release time point are as follows:
Figure BDA0003566111680000155
λji(j ═ 1, 2.., 7) is a first auxiliary variable, λ jiIs a function of time t, when t is nT, expressed as λji(nT)，nT+Is the right limit of nT;
the expression for the optimal control strategy that can be obtained using the requirements of the optimal solution is as follows:
Figure BDA0003566111680000161
namely:
Figure BDA0003566111680000162
Figure BDA0003566111680000163
presentation pair
Figure BDA0003566111680000164
An optimal solution for the optimal control is introduced,
Figure BDA0003566111680000165
represents a pair Si(nT) introducing an optimal solution for optimal control,
Figure BDA0003566111680000166
pair of aHiAn optimal solution for the optimal control is introduced,
Figure BDA0003566111680000167
pair of aQHiAn optimal solution for the optimal control is introduced,
if the wireless sensor network is in the non-solar charging period, determining an optimal control strategy in the following mode:
constructing a Hamiltonian in a non-release time period:
Figure BDA0003566111680000168
wherein m isji(j ═ 1, 2.., 7) is a second auxiliary variable;
obtaining necessary conditions of an optimal solution of a control strategy in a non-putting time period when solar charging is unavailable according to the Pontryagin maximum principle:
Figure BDA0003566111680000171
the optimal isolation strength of the set with communication connectivity i in the non-release period by adopting isolation measures can be obtained by utilizing the optimality condition:
Figure BDA0003566111680000172
namely:
Figure BDA0003566111680000173
the hamiltonian of the replenishment time point constructed based on the second auxiliary variable is:
Figure BDA0003566111680000174
the necessary conditions for realizing the optimal solution of the control strategy of the periodic release time point are as follows:
Figure BDA0003566111680000175
mjiis a function of time t, when t equals nT, expressed as mji(nT)，
The expression for the optimal control strategy that can be obtained using the optimality condition is as follows:
Figure BDA0003566111680000181
Namely:
Figure BDA0003566111680000182
Figure BDA0003566111680000183
respectively represent a pair
Figure BDA0003566111680000184
ΛLi、ΛQLiAn optimal solution for optimal control is introduced.
The invention improves the traditional infectious disease dynamics, provides a differential equation model with pulse birth, and uses the model to control a complex heterogeneous WSN network; from the aspect of replenishment rate, a strategy for controlling the replenishment rate is provided, a formula of optimal replenishment rate intensity is obtained based on a maximum value principle, and the effect of controlling the WSN is effectively improved; the invention also improves the isolation measure for inhibiting the spread of the malicious software, and adds a step of periodically injecting the node in the immune state on the basis of the isolation. Patches can be disseminated more specifically.
In infectious disease dynamics, a newly born population often joins a kinetic system in a susceptible state, and a differential equation model constructed based in part on infectious disease dynamics follows the setting, namely, a susceptible state node without a patch is added to the WSN. In the model, the nodes are not in a continuous supplementary state, and the new nodes are already in an immune state before being added into a detection system formed by the WSN, so that the addition of the new nodes can change the capability of detecting data collected and transmitted by the WSN and influence the spread of malicious software in the WSN.
Meanwhile, the invention provides an isolation-delivery strategy, namely, the immunized nodes are delivered into the isolation compartment of the infection-prone node periodically. The method is characterized in that at the regular release time point of the nodes, the immunized nodes are put into the detection system formed by the WSN, and the immunized nodes are also put into the isolation compartment formed by the susceptible nodes, so that the spread of patches is accelerated, and the susceptible nodes of the isolation compartment can obtain the patches as soon as possible.
While embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
It should be noted that, functional units/modules in the embodiments of the present invention may be integrated into one processing unit/module, or each unit/module may exist alone physically, or two or more units/modules are integrated into one unit/module. The integrated unit/module may be implemented in the form of hardware, or may also be implemented in the form of a software functional unit/module.
From the above description of the embodiments, it is clear for a person skilled in the art that the embodiments described herein can be implemented in hardware, software, firmware, middleware, code or any appropriate combination thereof. For a hardware implementation, the processor may be implemented in one or more of the following units: an Application Specific Integrated Circuit (ASIC), a Digital Signal Processor (DSP), a Digital Signal Processing Device (DSPD), a Programmable Logic Device (PLD), a Field Programmable Gate Array (FPGA), a processor, a controller, a microcontroller, a microprocessor, other electronic units designed to perform the functions described herein, or a combination thereof. For a software implementation, some or all of the flow of the embodiments may be accomplished by a computer program instructing the associated hardware.
In practice, the program may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage media may be any available media that can be accessed by a computer. Computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer.

Claims (6)

1. A wireless sensor network control method based on time interval division is characterized by comprising the following steps:
s1, determining the time period of the wireless sensor network;
s2, constructing a state transition diagram based on the time interval of the wireless sensor network;
s3, constructing a control model based on the state transition diagram;
s4, constructing a cost function based on the control model;
s5, constructing a Hamiltonian, and obtaining an optimal control strategy based on the cost function and the Hamiltonian.
2. The method as claimed in claim 1, wherein the time period includes a solar chargeable time period and a non-solar chargeable time period.
3. The time-division-based wireless sensor network control method according to claim 2, wherein the S2 includes:
the state transition diagram comprises a first state transition diagram and a second state transition diagram;
determining a state of a node, the state of the node comprising: susceptible S, infected I, immunized R, and spent D;
if the wireless sensor network is in a solar charging time period, constructing a first state transition diagram according to the transition relation of the nodes in different states;
and if the wireless sensor network is in the non-solar charging period, constructing a second state transition diagram according to the transition relation of the nodes in different states.
4. The time-division-based wireless sensor network control method according to claim 3, wherein the S3 includes:
the control model comprises a first control model and a second control model;
if the wireless sensor network is in the solar charging period, a first control model is established based on a first state transition diagram:
Figure FDA0003566111670000021
wherein S isiRepresenting susceptible nodes in the ith set, wherein i is the number of the set; t represents an independent variable, Si(nT) represents SiThe independent variable t in the (t) function takes the values nT, nT+Is the right limit of the moment nT, nT represents the node periodic release time point, IjRepresenting an infected node representing the jth set, RiDenotes an immunized node, R, representing the ith setjDenotes the immunized node, LS, representing the j-th setiLow energy susceptible nodes representing the ith set, IiRepresents the infected node of the ith set; LI (lithium ion) powderiLow energy infection representing the ith setNode, LRiLow energy immunized node, Q, representing the ith setiAn isolation compartment representing a node in the ith set, N represents the total number of nodes,
wherein, the charging rate of the node is fitted by a quadratic function:
Figure FDA0003566111670000022
t represents a non-release time period, nT represents a node release time point, nodes with the same communication connectivity can be divided into the same set, and eta sets exist in total;
βijRepresenting a malware propagation rate of a node in the jth set to a node of the ith set;
γirepresenting the low-energy node damage rate in the ith set;
μirepresenting the power outage of the nodes in the ith set;
Cirepresenting the solar charging rate of the nodes in the ith set;
αijrepresenting the patch transmission rate of nodes at the jth set versus the ith set;
θirepresenting the patch failure rate of the ith set;
gijrepresenting the conversion rate of the node in the jth set to the node in the ith set;
delta is a positive integer, delta T represents a period of time during which solar charging is possible
Epsilon is a positive integer, and epsilon T represents a time period of non-solar charging;
p represents the regular release rate of the immunized nodes;
qirepresents the correction coefficient, guarantees CiA value of 0 at a particular point in time;
Xirepresenting a node failure constant in the ith set;
Kirepresenting the failure constant change rate of the nodes in the ith set;
Λiindicates at the ithThe periodic delivery rate of the nodes of the set;
eHiwhen the wireless sensor network is in the solar charging period, the isolation rate of the infection-prone nodes of the ith set in the non-putting period is represented;
Figure FDA0003566111670000031
when the wireless sensor network is in a solar charging period, the isolation rate of the infection-prone nodes of the ith set at a regular release time point is represented;
ΛHiThe putting rate of the ith set at a regular putting time point is represented when the wireless sensor network is in a solar charging period;
ΛQHithe release rate of the isolation compartment of the ith set at the regular release time point is represented when the wireless sensor network is in the solar charging period;
Qi(t) represents node isolation compartments in the ith set;
Ψ is a positive integer, Ψ T represents the execution time of the control strategy when the wireless sensor network is in a solar charging period, Ψ T is less than or equal to δ T;
if the wireless sensor network is in the non-solar charging period, constructing a second control model based on a second state transition diagram:
Figure FDA0003566111670000041
wherein, the damage rate of the node is fitted by a linear function:
Figure FDA0003566111670000042
Kirepresenting the failure rate of change of the nodes in the ith set;
xirepresenting a node failure constant in the ith set;
eLiindicates that there is noWhen the line sensor network is in a non-solar charging period, the isolation rate of the infection-prone nodes of the ith set in a non-putting period;
Figure FDA0003566111670000043
representing the isolation rate of the susceptible nodes of the ith set at the regular release time point;
ΛLirepresenting the delivery rate of the ith set at the regular delivery time point;
ΛQLirepresenting the release rate of the isolation compartment of the ith set at the regular release time point;
Phi is a positive integer, phi T represents the execution time of the control strategy when the wireless sensor network is in the non-solar charging period, and phi T is less than or equal to delta T.
5. The time-division-based wireless sensor network control method according to claim 4, wherein the S4 includes:
the cost function comprises a first cost function and a second cost function;
if the wireless sensor network is in the solar charging time period, constructing a first cost function based on a first control model:
Figure FDA0003566111670000051
wherein, A1iDenotes the supervision and isolation cost, A, for a susceptible WSN in a set with communication connectivity i2iRepresents the regulatory cost, A, for an infected WSN in a set with communication connectivity i3iIsolation Compartment Q in set representing connectivity to communication iiCost of setup and supervision of, A4iRepresenting the execution cost of isolation measures taken on a set with communication connectivity i during a non-release period, A5iRepresents the implementation cost of the isolation measure adopted by the set with communication connectivity i at the time point of the periodic release, A6iIndicating periodic delivery time points to communication connectivity of iCost of execution of the aggregated drop nodes, A7iIsolation compartment Q representing periodic drop time point to communication connectivity iiThe execution cost of the node is released;
If the wireless sensor network is in the non-solar charging period, constructing a second cost function based on a second control model:
Figure FDA0003566111670000052
B1irepresents the supervision and isolation cost of a susceptible WSN in a set with communication connectivity i, B2iRepresents the regulatory cost of an infected WSN in a set with communication connectivity i, B3iRepresenting an isolation Compartment Q in a set with communication connectivity iiCost of setup and supervision of, B4iRepresenting the cost of implementation of isolation measures for a set of communication connectivity i during non-release periods, B5iRepresents the implementation cost of the isolation measures adopted by the set with communication connectivity i at the time point of the periodic release, B6iRepresents the execution cost of a set of delivery nodes with communication connectivity i at regular delivery time points, B7iIsolation compartment Q representing periodic drop time point to communication connectivity iiAnd releasing the execution cost of the node.
6. The time-division-based wireless sensor network control method according to claim 5, wherein the S5 includes:
if the wireless sensor network is in the solar chargeable period, determining an optimal control strategy in the following way:
constructing a Hamiltonian in a non-release period by the following method:
Figure FDA0003566111670000053
Wherein λ isji(j ═ 1,2,. 7) is a first auxiliary variable;
obtaining necessary conditions of an optimal solution of a control strategy in a non-putting time period when solar charging is available according to the Pontryagin maximum principle:
Figure FDA0003566111670000061
λji(j ═ 1, 2.., 7) is a first auxiliary variable,
the optimal isolation strength of the set with communication connectivity i in the non-release period by adopting isolation measures can be obtained by utilizing the optimality condition:
Figure FDA0003566111670000062
namely:
Figure FDA0003566111670000063
represents an optimal solution that introduces optimal control;
and constructing a Hamiltonian of the replenishment time point by adopting the first auxiliary variable:
Figure FDA0003566111670000064
the necessary conditions for realizing the optimal solution of the control strategy of the periodic release time point are as follows:
Figure FDA0003566111670000065
λji(j ═ 1, 2.., 7) is a first auxiliary variable, λjiIs a function of time t, when t equals nT, expressed as λji(nT)，nT+Is the right limit of nT;
the expression for the optimal control strategy that can be obtained using the requirements of the optimal solution is as follows:
Figure FDA0003566111670000071
namely:
Figure FDA0003566111670000072
Figure FDA0003566111670000073
presentation pair
Figure FDA0003566111670000074
An optimal solution for the optimal control is introduced,
Figure FDA0003566111670000075
represents a pair Si(nT) introducing an optimal solution for optimal control,
Figure FDA0003566111670000076
pair of aHiAn optimal solution for the optimal control is introduced,
Figure FDA0003566111670000077
pair of aQHiAn optimal solution for the optimal control is introduced,
if the wireless sensor network is in the non-solar charging period, determining an optimal control strategy in the following mode:
Constructing a Hamiltonian in a non-release time period:
Figure FDA0003566111670000078
wherein m isji(j ═ 1, 2.., 7) is a second auxiliary variable;
obtaining necessary conditions of an optimal solution of a control strategy in a non-putting time period when solar charging is unavailable according to the Pontryagin maximum principle:
Figure FDA0003566111670000081
the optimal isolation strength of the set with communication connectivity i in the non-release period by adopting isolation measures can be obtained by utilizing the optimality condition:
Figure FDA0003566111670000082
namely:
Figure FDA0003566111670000083
the hamiltonian for the replenishment time point constructed based on the second auxiliary variable is:
Figure FDA0003566111670000084
the necessary conditions for realizing the optimal solution of the control strategy of the periodic release time point are as follows:
Figure FDA0003566111670000085
mjiis a function of time t, when t equals nT, expressed as mji(nT)，
The expression for the optimal control strategy that can be obtained using the optimality condition is as follows:
Figure FDA0003566111670000091
namely:
Figure FDA0003566111670000092
Figure FDA0003566111670000093
respectively represent pair
Figure FDA0003566111670000094
ΛLi、ΛQLiAnd introducing an optimal solution of optimal control.
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