CN114760208B - Wireless sensor network control method based on time division - Google Patents
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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 a time period of a wireless sensor network; s2, constructing a state transition diagram based on a time period 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 acquiring 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 steps on the basis of isolation, namely periodically injecting the nodes in the immunized state. Patches may be propagated more targeted.
Description
Technical Field
The invention relates to the field of control, in particular to a wireless sensor network control method based on time division.
Background
The wireless sensor network (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 sanitation, smart grid and the like. Studies have shown that: the introduction of WSN can effectively reduce labor cost and effectively improve production management level.
Taking the application of WSN in agriculture as an example: the WSN can effectively reduce the manual work time by being applied to agriculture, so that the labor cost is reduced; meanwhile, the nodes are more sensitive to the changes of temperature, humidity and air quality, and can timely transmit information to a management layer, so that the management layer can quickly make adjustment strategies, and the agricultural management level is improved. Furthermore, a detection network consisting of nodes has significant advantages for certain circumstances.
The network transmission of the WSN is very energy-consuming, and the node is easy to prematurely die. The main reason for premature node extinction is: failure of low energy nodes to get replenishment in time to damage in advance and malware can exacerbate the energy loss of the node, making the node more energy-efficient.
For the energy problem, a part of solution thinking is to charge by using solar energy, the solar energy charging is not always continuous, and the wireless sensor network is in a non-charging state in cloudy days or at night and other times. Therefore, a control method based on time division is needed to control the wireless sensor network, and meanwhile, control the propagation of malicious software in the wireless sensor network.
Disclosure of Invention
The invention aims to disclose a wireless sensor network control method based on time division, which solves the problem of how to control a wireless sensor network in a solar charging time period and a non-solar charging time period.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a wireless sensor network control method based on time division comprises the following steps
S1, determining a time period of a wireless sensor network;
s2, constructing a state transition diagram based on a time period 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 acquiring an optimal control strategy based on the cost function and the Hamiltonian.
Preferably, the period includes 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 disabled D;
if the wireless sensor network is in a solar charging period, a first state transition diagram is constructed according to the transition relation of the nodes in different states;
if the wireless sensor network is in the solar charging impossible period, a second state transition diagram is constructed 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 a solar charging period, a first control model is built based on a first state transition diagram:
wherein S is i Representing the susceptible nodes in the ith set, wherein i is the number of the set; t represents an independent variable, S i (nT) represents S i The independent variable t in the (t) function takes the value nT, nT + Is the right limit of nT at this moment, nT represents the periodic node delivery time point, I j Representing an infected node representing the jth set, R i Representing immunized nodes representing the ith collection, R j Representing immunized nodes representing a j-th set, LS i Representing low energy susceptible nodes of the ith collection, I i An infected node representing the ith set; LI (LI) i Low energy infected node representing the ith set, LR i Representing the low energy immunized node of the ith set, Q i Represents the isolation compartment of nodes in the ith set, N represents the total number of nodes,
the charging rate of the node is fitted by a quadratic function:
t represents a non-throwing period, nT represents a periodic throwing time point of nodes, the nodes with the same communication connectivity are divided into the same set, and a total of eta sets exist;
β ij representing malware propagation rates of nodes in the jth set to nodes of the ith set;
γ i representing a low energy node failure rate at the ith set;
μ i representing the power down rate of nodes in the ith set;
C i representing the node solar charge rate at the ith set;
α ij representing patch transmission rates for nodes in the jth set to the ith set;
θ i representing the failure rate of the patch of the ith set;
g ij representing the conversion rate of the nodes in the j-th set to the nodes in the i-th set;
delta is a positive integer, δT represents the period of time during which solar charging is possible
Epsilon is a positive integer, epsilon T represents a period of non-solar charging;
p represents the periodic administration rate of immunized nodes;
q i representing correction coefficients, ensure C i A value of 0 at a particular point in time;
X i representing node failure constants at the ith set;
K i representing the node failure constant change rate at the ith set;
Λ i representing the periodic delivery rate of nodes in the ith set;
e Hi indicating the susceptibility of the ith set in a non-throwing period when the wireless sensor network is in a solar charging periodThe isolation rate of the dyeing nodes;
when the wireless sensor network is in a solar charging period, the i-th set is at the isolation rate of the easily-infected nodes at the periodic release time point;
Λ Hi representing the release rate of the ith set at a periodic release time point when the wireless sensor network is in a solar charging period;
Λ QHi representing the release rate of the isolation compartment of the ith set at a periodic release time point when the wireless sensor network is in a solar charging period;
Q i (t) represents a node isolation compartment in the ith set;
the method comprises the steps that ψT is a positive integer, and when the wireless sensor network is in a solar charging period, execution time of a control strategy is controlled, wherein ψT is less than or equal to δT;
if the wireless sensor network is in the solar charging impossible period, a second control model is built based on a second state transition diagram:
the damage rate of the nodes is fitted by a linear function:
K i representing failure constant rate of change for nodes in the ith set;
x i representing node failure constants at the ith set;
e Li when the wireless sensor network is in a non-solar charging period, the i-th set is in the isolation rate of the easily-infected nodes in the non-throwing period;
the isolation rate of the susceptible nodes of the ith set at the periodic release time point is represented;
Λ Li representing the delivery rate of the ith set at a periodic delivery time point;
Λ QLi representing the compartment release rate of the ith set at the periodic 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 a non-solar charging period, and phi T is less than or equal to delta T.
Preferably, the S4 includes:
the cost function includes a first cost function and a second cost function;
if the wireless sensor network is in a solar chargeable period, a first cost function is built based on a first control model:
wherein A is 1i Represents the supervision and isolation cost of the WSN which is easy to be infected in the collection with the communication connectivity of i, A 2i Representing the regulatory cost of an infected WSN in a collection with communication connectivity i, A 3i Representing isolated compartment Q in a set having i connectivity to communications i Set up and administration costs of A 4i Representing the execution cost of adopting isolation measures for a set with communication connectivity i in a non-put period, A 5i Representing the execution cost of adopting isolation measures for a set with communication connectivity i at regular release time points, A 6i Representing the execution cost of a periodic delivery time point to a collective delivery node with the communication connectivity of i, A 7i Isolated compartment Q representing periodic drop time point to communication connectivity i i The execution cost of the node is put in;
if the wireless sensor network is in the solar charging impossible period, constructing a second cost function based on a second control model:
B 1i representing the supervision and isolation cost of WSNs susceptible to infection in a collection with communication connectivity i, B 2i Representing the supervision cost of the infected WSNs in the collection with communication connectivity i, B 3i Representing isolated compartment Q in a set having i connectivity to communications i Set up and administration costs of B 4i Representing the execution cost of adopting isolation measures for a set with communication connectivity i in a non-put period, B 5i Representing the execution cost of adopting isolation measures for a set with communication connectivity i at regular release time points, B 6i Representing the execution cost of the periodic delivery time point to the collective delivery node with the communication connectivity of i, B 7i Isolated compartment Q representing periodic drop time point to communication connectivity i i And putting the execution cost of the node.
Preferably, the S5 includes:
if the wireless sensor network is in a solar charging period, determining an optimal control strategy by the following method:
the Hamiltonian in the non-delivery period is constructed by:
wherein lambda is ji (j=1, 2,., 7) is a first auxiliary variable;
obtaining a necessary condition of an optimal solution of a control strategy in a non-throwing period when solar charging is possible according to the Pontrian maximum principle:
λ ji (j=1, 2,., 7) is a first auxiliary variable,
the optimal isolation strength of adopting isolation measures for the set with the communication connectivity of i in the non-throwing period can be obtained by utilizing the optimality condition:
namely:
* Representing an optimal solution that introduces optimal control;
constructing a Hamiltonian of the replenishment time point by adopting a first auxiliary variable:
the necessary conditions for realizing the optimal solution of the periodic release time point control strategy are as follows:
λ ji (j=1, 2,.,. 7) is a first auxiliary variable, λ ji Is a function of time t, expressed as λ when t=nt ji (nT)，nT + Is the right limit of nT;
the expression of the optimal control strategy can be obtained by using the requirement of the optimal solution as follows:
namely:
representation pair->An optimal solution for optimal control is introduced,
representation pair S i (nT) introducing an optimal solution for optimal control,
representation pair lambda Hi An optimal solution for optimal control is introduced,
representation pair lambda QHi An optimal solution for optimal control is introduced,
if the wireless sensor network is in a solar charging impossible period, determining an optimal control strategy by the following method:
constructing a Hamiltonian in a non-throwing period:
wherein m is ji (j=1, 2,.,. 7) is a second auxiliary variable;
obtaining a necessary condition of an optimal solution of a control strategy in a non-throwing period when solar charging is impossible according to the Pontrian maximum principle:
the optimal isolation strength of adopting isolation measures for the set with the communication connectivity of i in the non-throwing period can be obtained by utilizing the optimality condition:
namely:
the hamiltonian at the replenishment time point constructed based on the second auxiliary variable is:
the necessary conditions for realizing the optimal solution of the periodic release time point control strategy are as follows:
m ji as a function of time t, when t=nt, denoted as m ji (nT)，
The expression for the optimal control strategy can be obtained using the optimality conditions as follows:
namely:
respectively represent pair->Λ Li 、Λ QLi And 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 angle of the replenishment rate, a strategy for controlling the replenishment rate is provided, and a formula of the optimal replenishment rate strength is obtained based on a maximum principle, so that 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 steps on the basis of isolation, namely periodically injecting the nodes in the immunized state. Patches may be propagated more targeted.
Drawings
The invention will be further described with reference to the accompanying drawings, in which embodiments do not constitute any limitation of the invention, and other drawings can be obtained by one of ordinary skill in the art without inventive effort from the following drawings.
Fig. 1 is a diagram illustrating 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
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
As shown in an embodiment of fig. 1, the present invention provides a wireless sensor network control method based on time division, including:
s1, determining a time period of a wireless sensor network;
s2, constructing a state transition diagram based on a time period 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 acquiring an optimal control strategy based on the cost function and the Hamiltonian.
Based on whether the light intensity can be utilized by the WSN, one day (24 hours) is divided into two periods, namely a solar chargeable period and a solar non-chargeable period. In the solar charging period, the change of light intensity along with time is considered, and the light intensity is approximately fitted by a quadratic function; sensor nodes that do not get energy refueled in time will decay prematurely when they are not solar charged, so the mortality of the nodes is approximately fitted by a linear function during this period.
Preferably, the period includes 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 disabled D;
if the wireless sensor network is in a solar charging period, a first state transition diagram is constructed according to the transition relation of the nodes in different states;
if the wireless sensor network is in the solar charging impossible period, a second state transition diagram is constructed 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 a solar charging period, a first control model is built based on a first state transition diagram:
wherein S is i Representing the susceptible nodes in the ith set, wherein i is the number of the set; t represents an independent variable, S i (nT) represents S i The independent variable t in the (t) function takes the value nT, nT + Is the right pole of the instant nTLimit, nT, represents the periodic node release time point, I j Representing an infected node representing the jth set, R i Representing immunized nodes representing the ith collection, R j Representing immunized nodes representing a j-th set, LS i Representing low energy susceptible nodes of the ith collection, I i An infected node representing the ith set; LI (LI) i Low energy infected node representing the ith set, LR i Representing the low energy immunized node of the ith set, Q i Represents the isolation compartment of nodes in the ith set, N represents the total number of nodes,
fig. 2 shows a first state transition diagram showing a control state transition for a solar chargeable period.
The charging rate of the node is fitted by a quadratic function:
t represents a non-throwing period, nT represents a periodic throwing time point of nodes, the nodes with the same communication connectivity are divided into the same set, and a total of eta sets exist;
β ij representing malware propagation rates of nodes in the jth set to nodes of the ith set;
γ i representing a low energy node failure rate at the ith set;
μ i representing the power down rate of nodes in the ith set;
C i representing the node solar charge rate at the ith set;
α ij representing patch transmission rates for nodes in the jth set to the ith set;
θ i representing the failure rate of the patch of the ith set;
g ij representing the conversion rate of the nodes in the j-th set to the nodes in the i-th set;
delta is a positive integer, δT represents the period of time during which solar charging is possible
Epsilon is a positive integer, epsilon T represents a period of non-solar charging;
p represents the periodic administration rate of immunized nodes;
q i representing correction coefficients, ensure C i A value of 0 at a particular point in time;
X i representing node failure constants at the ith set;
K i representing the node failure constant change rate at the ith set;
Λ i representing the periodic delivery rate of nodes in the ith set;
e Hi when the wireless sensor network is in a solar charging period, the isolation rate of the susceptible nodes of the ith set in a non-throwing period is shown;
when the wireless sensor network is in a solar charging period, the i-th set is at the isolation rate of the easily-infected nodes at the periodic release time point;
Λ Hi representing the release rate of the ith set at a periodic release time point when the wireless sensor network is in a solar charging period;
Λ QHi representing the release rate of the isolation compartment of the ith set at a periodic release time point when the wireless sensor network is in a solar charging period;
Q i (t) represents a node isolation compartment in the ith set;
the method comprises the steps that ψT is a positive integer, and when the wireless sensor network is in a solar charging period, execution time of a control strategy is controlled, wherein ψT is less than or equal to δT;
if the wireless sensor network is in the solar charging impossible period, a second control model is built based on a second state transition diagram:
the damage rate of the nodes is fitted by a linear function:
K i representing failure constant rate of change for nodes in the ith set;
x i representing node failure constants at the ith set;
e Li when the wireless sensor network is in a non-solar charging period, the i-th set is in the isolation rate of the easily-infected nodes in the non-throwing period;
the isolation rate of the susceptible nodes of the ith set at the periodic release time point is represented;
Λ Li representing the delivery rate of the ith set at a periodic delivery time point;
Λ QLi representing the compartment release rate of the ith set at the periodic 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 a 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 transitions in the solar charging impossible period.
Preferably, the S4 includes:
the cost function includes a first cost function and a second cost function;
if the wireless sensor network is in a solar chargeable period, a first cost function is built based on a first control model:
wherein A is 1i Represents the supervision and isolation cost of the WSN which is easy to be infected in the collection with the communication connectivity of i, A 2i Representing the regulatory cost of an infected WSN in a collection with communication connectivity i, A 3i Representing isolated compartment Q in a set having i connectivity to communications i Set up and administration costs of A 4i Representing the execution cost of adopting isolation measures for a set with communication connectivity i in a non-put period, A 5i Representing the execution cost of adopting isolation measures for a set with communication connectivity i at regular release time points, A 6i Representing the execution cost of a periodic delivery time point to a collective delivery node with the communication connectivity of i, A 7i Isolated compartment Q representing periodic drop time point to communication connectivity i i The execution cost of the node is put in;
if the wireless sensor network is in the solar charging impossible period, constructing a second cost function based on a second control model:
B 1i representing the supervision and isolation cost of WSNs susceptible to infection in a collection with communication connectivity i, B 2i Representing the supervision cost of the infected WSNs in the collection with communication connectivity i, B 3i Representing isolated compartment Q in a set having i connectivity to communications i Set up and administration costs of B 4i Representing the execution cost of adopting isolation measures for a set with communication connectivity i in a non-put period, B 5i Representing the execution cost of adopting isolation measures for a set with communication connectivity i at regular release time points, B 6i Representing the execution cost of the periodic delivery time point to the collective delivery node with the communication connectivity of i, B 7i Isolated compartment Q representing periodic drop time point to communication connectivity i i And putting the execution cost of the node.
Preferably, the S5 includes:
if the wireless sensor network is in a solar charging period, determining an optimal control strategy by the following method:
the Hamiltonian in the non-delivery period is constructed by:
wherein lambda is ji (j=1, 2,., 7) is a first auxiliary variable;
obtaining a necessary condition of an optimal solution of a control strategy in a non-throwing period when solar charging is possible according to the Pontrian maximum principle:
λ ji (j=1, 2,., 7) is a first auxiliary variable,
the optimal isolation strength of adopting isolation measures for the set with the communication connectivity of i in the non-throwing period can be obtained by utilizing the optimality condition:
namely:
* Representing an optimal solution that introduces optimal control;
constructing a Hamiltonian of the replenishment time point by adopting a first auxiliary variable:
the necessary conditions for realizing the optimal solution of the periodic release time point control strategy are as follows:
λ ji (j=1, 2,.,. 7) is a first auxiliary variable, λ ji Is a function of time t, expressed as λ when t=nt ji (nT)，nT + Is the right limit of nT;
the expression of the optimal control strategy can be obtained by using the requirement of the optimal solution as follows:
namely:
representation pair->An optimal solution for optimal control is introduced,
representation pair S i (nT) introducing an optimal solution for optimal control,
representation pair lambda Hi An optimal solution for optimal control is introduced,
representation pair lambda QHi Introducing an optimal solution of optimal control->
If the wireless sensor network is in a solar charging impossible period, determining an optimal control strategy by the following method:
constructing a Hamiltonian in a non-throwing period:
wherein m is ji (j=1, 2,.,. 7) is a second auxiliary variable;
obtaining a necessary condition of an optimal solution of a control strategy in a non-throwing period when solar charging is impossible according to the Pontrian maximum principle:
the optimal isolation strength of adopting isolation measures for the set with the communication connectivity of i in the non-throwing period can be obtained by utilizing the optimality condition:
namely:
the hamiltonian at the replenishment time point constructed based on the second auxiliary variable is:
the necessary conditions for realizing the optimal solution of the periodic release time point control strategy are as follows:
m ji as a function of time t, when t=nt, denoted as m ji (nT)，
The expression for the optimal control strategy can be obtained using the optimality conditions as follows:
namely:
respectively represent pair->Λ Li 、Λ QLi And 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 angle of the replenishment rate, a strategy for controlling the replenishment rate is provided, and a formula of the optimal replenishment rate strength is obtained based on a maximum principle, so that 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 steps on the basis of isolation, namely periodically injecting the nodes in the immunized state. Patches may be propagated more targeted.
In infectious disease dynamics, the new born population often adds a dynamics system in an easily infected state, and a differential equation model constructed based in part on infectious disease dynamics takes over this setup, namely adding easily infected nodes without patches to the WSN. In the model, the nodes are not in a continuously-supplemented state, and the new nodes are in an immunized 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 the acquisition and transmission data of the WSN and influence the transmission of malicious software in the WSN, and therefore, the invention adopts a control strategy for the periodic delivery of the nodes, and is particularly characterized in that the optimal delivery rate is obtained by fixing the delivery time.
Meanwhile, the invention provides an isolation-release strategy, namely, periodically releasing immunized nodes into an isolation compartment of the susceptible node. The method is characterized in that at the regular release time points of the nodes, immunized nodes are put into a detection system formed by WSNs, and immunized nodes are put into an isolation compartment formed by easily infected nodes, so that the spreading of patches is quickened, and the easily infected nodes of the isolation compartment can acquire patches as soon as possible.
While embodiments of the invention have been shown and described, it will be understood by those skilled in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
It should be noted that, in each embodiment of the present invention, each functional unit/module may be integrated in one processing unit/module, or each unit/module may exist alone physically, or two or more units/modules may be integrated in one unit/module. The integrated units/modules described above may be implemented either in hardware or in software functional units/modules.
From the description of the embodiments above, it will be apparent to those skilled in the art that the embodiments described herein may be implemented in hardware, software, firmware, middleware, code, or any suitable 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 an embodiment may be accomplished by a computer program to instruct the associated hardware.
When implemented, the above-described programs may be stored in or transmitted 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. The computer readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage media 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 (3)
1. The wireless sensor network control method based on time interval division is characterized by comprising the following steps of:
s1, determining a time period of a wireless sensor network;
s2, constructing a state transition diagram based on a time period 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 acquiring an optimal control strategy based on a cost function and the Hamiltonian, wherein the time period comprises a solar charging time period and a non-solar charging time period, and the S2 comprises:
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 disabled D; if the wireless sensor network is in a solar charging period, a first state transition diagram is constructed according to the transition relation of the nodes in different states;
if the wireless sensor network is in the solar charging disabled period, a second state transition diagram is constructed according to the transition relation of the nodes in different states, and the step S3 includes:
the control model comprises a first control model and a second control model;
if the wireless sensor network is in a solar charging period, a first control model is built based on a first state transition diagram:
wherein S is i Representing the susceptible nodes in the ith set, wherein i is the number of the set; t represents an independent variable, S i (nT) represents S i The independent variable t in the (t) function takes the value nT, nT + Is the right limit of nT at this moment, nT represents the periodic node delivery time point, I j An infected node representing the j-th set, R i Represents the immunized node of the ith collection, R j The immunized node, LS, representing the j-th set i Representing low energy susceptible nodes of the ith collection, I i An infected node representing the ith set; LI (LI) i Low energy infected node representing the ith set, LR i Representing the low energy immunized node of the ith set, Q i Representing the isolated compartment of nodes in the ith set, N representing the total number of nodes, wherein the charge rates of the nodes are fitted with a quadratic function:
t represents a non-throwing period, nT represents a periodic throwing time point of nodes, the nodes with the same communication connectivity are divided into the same set, and a total of eta sets exist; beta ij Representing malware propagation rates of nodes in the jth set to nodes of the ith set; gamma ray i Representing a low energy node failure rate at the ith set; mu (mu) i Representing the power down rate of nodes in the ith set; c (C) i Representing the node solar charge rate at the ith set; alpha ij Representing patch transmission rates for nodes in the jth set to the ith set; θ i Representing the failure rate of the patch of the ith set; g ij Representing the conversion rate of the nodes in the j-th set to the nodes in the i-th set; delta is a positive integer, and δT represents a period of time during which solar energy can be charged; epsilon is a positive integer, epsilon T represents a period of non-solar charging; p represents the periodic administration rate of immunized nodes; q i Representing correction coefficients, ensure C i A value of 0 at a particular point in time; x is x i Representing node failure constants at the ith set; k (K) i Representing the node failure constant change rate at the ith set; Λ type i Representing the periodic delivery rate of nodes in the ith set; e, e Hi When the wireless sensor network is in a solar charging period, the isolation rate of the susceptible nodes of the ith set in a non-throwing period is shown;when the wireless sensor network is in a solar charging period, the i-th set is at the isolation rate of the easily-infected nodes at the periodic release time point; Λ type Hi Representing the release rate of the ith set at a periodic release time point when the wireless sensor network is in a solar charging period; Λ type QHi Representing the release rate of the isolation compartment of the ith set at a periodic release time point when the wireless sensor network is in a solar charging period; q (Q) i (t) represents a node isolation compartment in the ith set; if the wireless sensor network is in the solar charging impossible period, a second control model is built based on a second state transition diagram:
the damage rate of the nodes is fitted by a linear function:
K i representing failure constant rate of change for nodes in the ith set; x is x i Representing node failure constants at the ith set; e, e Li When the wireless sensor network is in a non-solar charging period, the i-th set is in the isolation rate of the easily-infected nodes in the non-throwing period;the isolation rate of the susceptible nodes of the ith set at the periodic release time point is represented; Λ type Li Representing the delivery rate of the ith set at a periodic delivery time point; Λ type QLi Representing the isolated bay loading rate for the ith collection at the periodic loading time point.
2. The wireless sensor network control method based on time division according to claim 1, wherein the step S4 comprises:
the cost function includes a first cost function and a second cost function;
if the wireless sensor network is in a solar chargeable period, a first cost function is built based on a first control model:
wherein A is 1i Represents the supervision and isolation cost of the WSN which is easy to be infected in the collection with the communication connectivity of i, A 2i Representing the regulatory cost of an infected WSN in a collection with communication connectivity i, A 3i Representing isolated compartment Q in a set having i connectivity to communications i Set up and administration costs of A 4i Representing the execution cost of adopting isolation measures for a set with communication connectivity i in a non-put period, A 5i Representing the execution cost of adopting isolation measures for a set with communication connectivity i at regular release time points, A 6i Representing the execution cost of a periodic delivery time point to a collective delivery node with the communication connectivity of i, A 7i Isolated compartment Q representing periodic drop time point to communication connectivity i i The execution cost of the node is put in; the method comprises the steps that ψT is a positive integer, and when the wireless sensor network is in a solar charging period, execution time of a control strategy is controlled, wherein ψT is less than or equal to δT;
if the wireless sensor network is in the solar charging impossible period, constructing a second cost function based on a second control model:
B 1i representing the supervision and isolation cost of WSNs susceptible to infection in a collection with communication connectivity i, B 2i Representing the supervision cost of the infected WSNs in the collection with communication connectivity i, B 3i Representing isolated compartment Q in a set having i connectivity to communications i Set up and administration costs of B 4i Representing the execution cost of adopting isolation measures for a set with communication connectivity i in a non-put period, B 5i Representing the execution cost of adopting isolation measures for a set with communication connectivity i at regular release time points, B 6i Representing the execution cost of the periodic delivery time point to the collective delivery node with the communication connectivity of i, B 7i Isolated compartment Q representing periodic drop time point to communication connectivity i i The execution cost of the node is put in,is a positive integer>Indicating the execution time of the control strategy when the wireless sensor network is in the solar charging impossible period,/->
3. The wireless sensor network control method based on time division according to claim 2, wherein the step S5 comprises:
if the wireless sensor network is in a solar charging period, determining an optimal control strategy by the following method: the Hamiltonian in the non-delivery period is constructed by:
wherein lambda is ji (j=1, 2,., 7) is a first auxiliary variable;
obtaining a necessary condition of an optimal solution of a control strategy in a non-throwing period when solar charging is possible according to the Pontrian maximum principle:
λ ji (j=1, 2,., 7) is a first auxiliary variable,
the optimal isolation strength of adopting isolation measures for the set with the communication connectivity of i in the non-throwing period can be obtained by utilizing the optimality condition:
namely:
* Representing an optimal solution that introduces optimal control;
constructing a Hamiltonian of the replenishment time point by adopting a first auxiliary variable:
the necessary conditions for realizing the optimal solution of the periodic release time point control strategy are as follows:
λ ji (j=1, 2,.,. 7) is a first auxiliary variable, λ ji Is a function of time t, expressed as λ when t=nt ji (nT)，nT + Is the right limit of nT;
the expression of the optimal control strategy can be obtained by using the requirement of the optimal solution as follows:
namely:
representation pair->Introducing an optimal solution of optimal control->Representation pair S i (nT) introducing an optimal solution for optimal control,representation pair lambda Hi Introducing an optimal solution of optimal control->Representation pair lambda QHi Introducing an optimal solution of optimal control, and if the wireless sensor network is in a non-solar charging period, determining an optimal control strategy by the following method:
constructing a Hamiltonian in a non-throwing period:
wherein m is ji (j=1, 2,.,. 7) is a second auxiliary variable;
obtaining a necessary condition of an optimal solution of a control strategy in a non-throwing period when solar charging is impossible according to the Pontrian maximum principle:
the optimal isolation strength of adopting isolation measures for the set with the communication connectivity of i in the non-throwing period can be obtained by utilizing the optimality condition:
namely:
the hamiltonian at the replenishment time point constructed based on the second auxiliary variable is:
the necessary conditions for realizing the optimal solution of the periodic release time point control strategy are as follows:
m ji as a function of time t, when t=nt, denoted as m ji (nT), the expression that can obtain the optimal control strategy using the optimality condition is as follows:
namely:
respectively represent pair->Λ Li 、Λ QLi And introducing an optimal solution of optimal control.
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