A wireless charger switch scheduling method for optimizing long-term charging utility

Abstract

The application discloses a wireless charger switch scheduling method for optimizing long-term charging efficiency, which comprises the following steps: defining a chargeable sensor set, a wireless charger set and a charging power of the chargeable sensor, and obtaining a chargeable sensor battery level and a charging efficiency in each time slot by using a time discretization method; formalizing a time-average charging efficiency optimization scheduling problem; converting the time-average charging efficiency optimization scheduling problem into a real-time wireless charger switch scheduling problem in each time slot; and calling a time-average charging efficiency optimization scheduling algorithm to calculate a wireless charger start strategy of each time slot. The wireless chargeable sensor network can cope with the change of sensor energy consumption rate caused by random events in long-term operation, and improve the charging efficiency of single scheduling from a long-term perspective under the conditions of meeting the time-average cost budget and the time-average response rate expectation.

Description

Technical Field

[0001] This invention relates to the field of wireless rechargeable sensor network charging scheduling technology, specifically a wireless charger switching scheduling method for optimizing long-term charging efficiency. Background Technology

[0002] Wireless rechargeable sensor networks are widely used in industrial and commercial applications due to their significant advantages. Sensors, as a crucial component of wireless sensor networks, are typically charged via physical connections. However, physical connections are susceptible to problems such as leakage due to aging wires, leading to safety issues within the sensor network. Wireless chargers, on the other hand, transmit power to the sensor via electromagnetic waves, thus charging it. Currently, sensors primarily receive energy by installing antennas.

[0003] Numerous studies have been conducted on charging scheduling for wireless chargers. However, previous work has largely focused on deterministic charging scheduling, such as minimizing charging latency, maximizing energy harvesting, optimizing event capture, and maximizing charging utility under constant environmental conditions. In reality, wireless sensor networks are typically deployed for long-term operation, such as temperature detection and environmental monitoring. Therefore, charging scheduling should be continuous over a long period to meet the long-term energy replenishment needs of sensor nodes. In other words, the charging scheduling problem in long-term operating scenarios is a long-term stochastic optimization problem.

[0004] In this long-term charging scheduling, the charging system is more concerned with long-term constraints (time-average constraints) than with short-term constraints in each round of scheduling. For example, although a wireless rechargeable sensor network has a long-term energy replenishment budget, it is not concerned with the charging cost in a specific round of scheduling; long-term constraints will significantly influence the charging scheduling. This is because the objective can be further optimized, as time-average constraints do not need to be strictly enforced in each round of scheduling.

[0005] Furthermore, wireless rechargeable sensor networks often face the occurrence of random events, which are unpredictable and can significantly impact the energy consumption of sensor nodes. For example, if an abnormal intrusion occurs, the sensor network will continuously detect it, greatly increasing the energy consumption rate of the sensor nodes. In dealing with real-world random events, long-term random charging scheduling is more reasonable than short-term deterministic charging scheduling. Therefore, research on wireless charger switching scheduling methods for long-term sensor charging efficiency is a practically significant and urgently needed problem to solve. Summary of the Invention

[0006] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0007] In view of the above-mentioned problems, the present invention is proposed.

[0008] Therefore, the technical problem solved by this invention is: for long-term operating wireless rechargeable sensor networks, considering that the energy consumption rate of rechargeable sensors is time-varying due to unpredictable random events such as environmental anomalies and drastic changes in temperature and humidity, a wireless charger activation strategy is formulated in real time under long-term cost budget constraints and response rate expectation constraints.

[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a wireless charger switch scheduling method for optimizing long-term charging efficiency, comprising:

[0010] The rechargeable sensor battery level and charging efficiency within each time slot are obtained using a time discretization method.

[0011] Formalizing the time-averaged charging utility optimization scheduling problem;

[0012] The time-average charging efficiency optimization scheduling problem is transformed into a real-time wireless charger switching scheduling problem within each time slot.

[0013] The time-average charging efficiency optimization scheduling algorithm is invoked to calculate the wireless charger activation strategy for each time slot.

[0014] As a preferred embodiment of the wireless charger switch scheduling method for long-term charging efficiency described in this invention, the method further includes, before obtaining the rechargeable sensor battery level and charging efficiency in each time slot using a time discretization method, the following steps are taken:

[0015] Define a collection of rechargeable sensors and wireless chargers;

[0016] Define the charging power of the rechargeable sensor;

[0017] The set of rechargeable sensors is: N = {o1, o2, ..., o} n The set of wireless chargers is: M = {s1, s2, ..., s} m}

[0018] In a preferred embodiment of the wireless charger switch scheduling method for long-term charging effectiveness described in this invention, the charging power of the rechargeable sensor includes:

[0019] Rechargeable sensor oj From wireless chargers i The obtained charging power is expressed as:

[0020]

[0021] Where α and β are two constants determined by the magnetic field environment and hardware parameters of the wireless charger and rechargeable sensor, and D is the maximum charging distance of the wireless charger, d(s) i ,o j (This is a rechargeable sensor) j With wireless chargers i The distance between them. When d(s) i ,o j If )≤D, the rechargeable sensor always receives positive power;

[0022] As a preferred embodiment of the wireless charger switch scheduling method for long-term charging efficiency described in this invention, the step of obtaining the rechargeable sensor battery level and charging efficiency in each time slot using a time discretization method includes:

[0023] Discretize a continuous period of time into time slices. in Let T be the set of time slots, and τ be the length of each time slot. The activation strategy of the wireless charger set in time slot t is X(t) = (x1(t), x2(t), ..., x m x1(t) = 1 indicates that wireless charger s1 is turned on in time slot t, and x1(t) = 0 indicates that wireless charger s1 is not turned on in time slot t. The activation cost of each wireless charger is c. i In time slot t, the rechargeable sensor will only issue a request when the charge level is less than a threshold δ. j The charging amount when the wireless charger's activation strategy is X(t) is:

[0024]

[0025] Where R(t) is the set of rechargeable sensors that make a request in time slot t, and the wireless charger only charges the rechargeable sensors that made the request, while E MAX For the battery capacity of the rechargeable sensor, B j (t) represents the rechargeable sensor at the start of time slot t. j Battery level, E MAX -B j (t) represents the rechargeable sensor o in time slot t. j The maximum acceptable charging amount. Based on the decision of the current time slot, the next time slot for rechargeable sensors... j The battery level can be expressed as:

[0026]

[0027] Where w j (t) represents the rechargeable sensor in time slot t. j The power consumption rate is random in each time slot due to environmental influences. The energy consumption rate of the sensor in each time slot is assumed to be the value at the beginning of the time slot.

[0028] The total charging efficiency of a wireless rechargeable sensor network in time slot t is defined as:

[0029]

[0030] Where λ j For rechargeable sensors o j The unit perception utility generated for different perception tasks and perception capabilities.

[0031] As a preferred embodiment of the wireless charger switch scheduling method for long-term charging efficiency described in this invention, the formalized time-averaged charging efficiency optimization scheduling problem includes:

[0032] Establish long-term charging budget constraints;

[0033] Establish long-term response rate expectation constraints;

[0034] With maximizing the average charging efficiency as the optimization objective, a formalized scheduling problem for optimizing the average charging efficiency is obtained.

[0035] As a preferred embodiment of the wireless charger switch scheduling method for long-term charging efficiency described in this invention, the establishment of long-term charging budget constraints includes:

[0036]

[0037] Ensure that the average time-to-use charger startup cost is less than the average time-to-use charging cost budget C. avg ,in Indicates the activation cost of the wireless charger in time slot t;

[0038] As a preferred embodiment of the wireless charger switch scheduling method for long-term charging efficiency described in this invention, the step of establishing long-term response rate expectation constraints includes:

[0039]

[0040] Guarantee the average response rate is greater than the expected average response rate ζ. avg The set of rechargeable sensors for each time slot response can be represented as:

[0041]

[0042] As a preferred embodiment of the wireless charger switch scheduling method for maximizing long-term charging efficiency described in this invention, the formalized scheduling problem for maximizing average charging efficiency includes:

[0043] P1:

[0044] st(5),(6)

[0045] x i (t)∈{0,1} (9)

[0046] Where the expectation is taken This is because problem P1 aims to maximize the long-term average charging utility, while the charging utility of each time slot is based on random events.

[0047] As a preferred embodiment of the wireless charger switching scheduling method for long-term charging efficiency described in this invention, the method for transforming the time-averaged charging efficiency optimization scheduling problem into a real-time wireless charger switching scheduling problem within each time slot includes:

[0048] The long-run stochastic optimization problem P1 is transformed into a short-run optimization problem for each time slot using the Lyapunov method.

[0049] Before using the Lyapunov method, the P1 problem is first transformed into a standard stochastic optimization problem:

[0050] P1′:

[0051] st(5),(9)

[0052]

[0053] Where η avg =1-ζ avg Let U'(X(t)) be the expected average non-response rate, and let U'(X(t)) = -U(X(t)). Problems P1 and P1' are completely equivalent.

[0054] Define a virtual queue for the activation cost of wireless chargers:

[0055] Q(t+1)=max{Q(t)+C(t)-C avg ,0} (12)

[0056] To describe the cost exceeding the average hourly budget C for each time slot avg The cost backlog is initialized to Q(0) = 0;

[0057] Define a virtual queue for enabling the wireless charger's response rate:

[0058]

[0059] To describe the expected average non-response rate η for each time slot exceeding the specified time. avg The backlog of non-response rate, where ψ(t) is the set of rechargeable sensors whose charging requests are responded to in time slot t, that is, the set of rechargeable sensors that are charged by the wireless charger after issuing a charging request, and initialize Z(0) = 0.

[0060] When the virtual queues (12) and (13) are stable, that is:

[0061]

[0062]

[0063] This satisfies the long-term constraints (5)(11) of the transformed problem P1', because we can obtain from the definition (12) of the virtual queue:

[0064] C(t)≤Q(t+1)-Q(t+C avg (16)

[0065] By taking the expected value of both sides of inequality (16) over all time slots, summing them up, dividing by the number of time slots T, and finally taking the limit over T, we can obtain the following:

[0066]

[0067] Since Q(0) = 0, as long as equation (14) holds, the long-term constraint (5) of problem P1' can be satisfied. Similarly, when equation (15) holds, the long-term constraint (11) of problem P1' can be satisfied.

[0068] Therefore, in order to optimize dynamic wireless rechargeable sensor networks over the long term and ensure the stability of virtual queues, a Lyapunov function L(Θ(t)) and a drift function Δ(Θ(t)) are introduced:

[0069]

[0070]

[0071] The standardized stochastic optimization problem P1' can then be transformed into a real-time optimization problem P2 that combines charging cost, response rate, and charging utility. The goal of this problem is to minimize the drift penalty function in each time slot.

[0072] P2:min X(t) Δ(Θ(t))+VU′(X(t)) (20)

[0073] Where V is a non-negative controllable parameter used to balance charging utility and virtual queue;

[0074] Considering the dynamic nature of the system, the drift function of each time slot is unpredictable, so it can be obtained through the queue definitions (12)(13):

[0075]

[0076]

[0077] The definition of the junction and drift function (19) further transforms the objective:

[0078]

[0079] The second inequality is due to the fundamental inequality, and It is a constant, C max It is the maximum charging cost that a time slot can generate;

[0080] Since the right-hand side of inequality (23) is the upper bound of the optimization objective of P2, and A is a constant, solving problem P2 can be transformed into solving problem P3:

[0081] P3:

[0082] Since in each time slot Q(t), Z(t), η avg C avg Since all are known constants, the optimization objective for P3, after simplification and negation, can be equivalently transformed into solving problem P4.

[0083] P4:

[0084] For ease of description, let the objective function of P4 be F(S(X(t))). Where S(X(t))={s i |x i Given that (t)=1}, assume there are two wireless charger activation sets H and K, satisfying And s i ∈M\K, we get:

[0085] F(H∪{s i})-F(H)=G(H∪{s i})-G(H)-c i Q(t) (26)

[0086] F(K∪{s i})-F(K)=G(K∪{s i})-G(K)-c i Q(t) (27)

[0087] Since G(S(X(t))) is a weighted sum of charging efficiency and response rate, it is clearly a sub-mode, therefore:

[0088] G(H∪{s i})-G(H)≥G(K∪{s i})-G(K) (28)

[0089] Therefore, combining equations (26), (27), and (28), we can obtain:

[0090] F(H∪{s i})-F(H)≥F(K∪{s i})-F(K) (29)

[0091] Since the objective function of problem P4 is submodular, a greedy scheduling algorithm based on the average charging efficiency was designed.

[0092] As a preferred embodiment of the wireless charger switching scheduling method for long-term charging efficiency described in this invention, the step of calling the time-averaged charging efficiency optimization scheduling algorithm to calculate the wireless charger activation strategy for each time slot includes:

[0093] A1: Input parameters: controllable parameter V, average hourly charging cost budget C avg Expected average non-response rate η avg Each rechargeable sensor j Perceived utility λ per unit j and initial charge B j (0)=E MAX And each wireless charger i Startup cost c i ;

[0094] A2: Initialize the virtual queues Q(0) = 0, Z(0) = 0, and set the request queues for all time slots to an empty set.

[0095] A3: The decision to initialize the current time slot at the beginning of each time slot is to turn off all wireless chargers X(t) = 0, and observe the w of the current time slot. j (t), R(t), Q(t), Z(t) and B j (t);

[0096] A4: Let the objective function of problem P4 be F(S(X(t))). It is to select the wireless charger that brings the maximum marginal value from the set of all unactivated wireless chargers in the current time slot. Its corresponding activation strategy The default value is 0. The wireless charger will be turned on as long as its marginal value is greater than zero.

[0097] A5: Repeat step A4 until the marginal value of turning on the selected wireless charger is less than or equal to zero, and obtain the wireless charger activation strategy X for the current time slot. * (t);

[0098] A6: According to formula (7) Wireless charger activation strategy X for the current time slot * (t) Obtain the set of rechargeable sensors that responded, then calculate the number of unresponded requests |R(t)|-|ψ(t)| and the wireless charger activation cost. And update the virtual queue Q(t+1)=max{Q(t)+C(t)-C} for the next time slot according to the queue definitions (11)(12). avg ,0} and

[0099] A7: Calculate the power level of all rechargeable sensors in the wireless rechargeable sensor network in the next time slot according to formulas (2) and (3). j (t+1), if B j If (t+1) < δ, then add it to the request queue R(t+1) of the next time slot;

[0100] A8: Starting from time slot 0, repeat A3 to A7 for each time slot t until the last time slot ends;

[0101] A9: Return the wireless charger activation policy X for each time slot t * (t).

[0102] The beneficial effects of the present invention are as follows: The present invention provides a wireless charger switching scheduling method to optimize long-term charging efficiency. It can cope with the changes in the energy consumption rate of rechargeable sensors caused by random events in long-term operating wireless rechargeable sensor networks. At the same time, under the condition of meeting the time-average cost budget and time-average response rate expectations, the method improves the charging efficiency of a single scheduling by centrally scheduling wireless chargers in the long term. Attached Figure Description

[0103] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0104] Figure 1 The flowchart illustrates a wireless charger switch scheduling method for long-term charging effectiveness provided in the first embodiment of the present invention.

[0105] Figure 2 The flowchart of the time-averaged charging efficiency optimization scheduling algorithm in the wireless charger switch scheduling method for optimizing long-term charging efficiency provided in the first embodiment of the present invention is shown.

[0106] Figure 3 The network topology diagram is provided for a wireless charger switch scheduling method for optimizing long-term charging efficiency according to the second embodiment of the present invention.

[0107] Figure 4 This is a comparison diagram of the charger activation strategies output by a wireless charger switch scheduling method for optimizing long-term charging efficiency, provided in the second embodiment of the present invention.

[0108] Figure 5 This is a comparison diagram of sensor performance in a physical experiment of a wireless charger switch scheduling method for optimizing long-term charging efficiency, provided in the second embodiment of the present invention.

[0109] Figure 6 A comparison chart of the average response rate of a wireless charger switch scheduling method for optimizing long-term charging efficiency provided in the third embodiment of the present invention.

[0110] Figure 7 The diagram shows a comparison of the effects of a wireless charger switch scheduling method for optimizing long-term charging efficiency, as provided in the third embodiment of the present invention.

[0111] Figure 8 The third embodiment of the present invention provides a comparison of the time-averaged charging efficiency of a wireless charger switch scheduling method for optimizing long-term charging efficiency under different control parameters V.

[0112] Figure 9 The third embodiment of the present invention provides a comparison of the time-averaged queue lengths of a wireless charger switch scheduling method for optimizing long-term charging efficiency under different control parameters V. Detailed Implementation

[0113] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0114] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0115] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0116] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0117] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0118] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0119] Example 1

[0120] Reference Figure 1 , Figure 2 As an embodiment of the present invention, a wireless charger switch scheduling method for optimizing long-term charging efficiency is provided, comprising:

[0121] S1: Define the set of rechargeable sensors and the set of wireless chargers. It should be noted that:

[0122] Specifically, the set of rechargeable sensors is: N = {o1, o2, ..., o nThe set of wireless chargers is: M = {s1, s2, ..., s} m The wireless charger and rechargeable sensors are both distributed on a two-dimensional plane.

[0123] S2: Defines the charging power of the rechargeable sensor. It should be noted that:

[0124] Rechargeable sensor o j From directed wireless chargers i The obtained charging power is:

[0125]

[0126] Where α and β are two constants determined by the magnetic field environment and hardware parameters of the wireless charger and rechargeable sensor, and D is the maximum charging distance of the wireless charger, d(s) i ,o j (This is a rechargeable sensor) j With wireless chargers i The distance between them.

[0127] When d(s) i ,o j If )≤D, the rechargeable sensor always acquires positive power.

[0128] S3: The rechargeable sensor battery level and charging efficiency within each time slot are obtained using a time discretization method. It should be noted that:

[0129] Furthermore, a continuous period of time is discretized into time slices. in Let T be the set of time slots, and τ be the length of each time slot. The activation strategy of the wireless charger set in time slot t is X(t) = (x1(t), x2(t), ..., x m x1(t) = 1 indicates that wireless charger s1 is turned on in time slot t, and x1(t) = 0 indicates that wireless charger s1 is not turned on in time slot t. The activation cost of each wireless charger is c. i In time slot t, the rechargeable sensor will only issue a request when the charge level is less than a threshold δ. j The charging amount when the wireless charger's activation strategy is X(t) is:

[0130]

[0131] Where R(t) is the set of rechargeable sensors that make a request in time slot t, and the wireless charger only charges the rechargeable sensors that made the request, while E MAX For the battery capacity of the rechargeable sensor, B j(t) represents the rechargeable sensor at the start of time slot t. j Battery level, E MAX -B j (t) represents the rechargeable sensor o in time slot t. j The maximum acceptable charging amount.

[0132] Based on the decision made in the current time slot, the next time slot will be a rechargeable sensor. j The battery level can be expressed as:

[0133]

[0134] Where w j (t) represents the rechargeable sensor in time slot t. j The power consumption rate is a random value in each time slot due to environmental influences. The energy consumption rate of the sensor in each time slot is assumed to be the value at the beginning of the time slot.

[0135] The total charging efficiency of a wireless rechargeable sensor network in time slot t is defined as:

[0136]

[0137] Where λ j For rechargeable sensors o j The unit perception utility generated for different perception tasks and perception capabilities.

[0138] S4: The problem of wireless charger switch scheduling for formalizing long-term charging utility. It should be noted that:

[0139] Establish long-term charging budget constraints:

[0140]

[0141] Ensure that the average time-to-use charger startup cost is less than the average time-to-use charging cost budget C. avg ,in This represents the charger activation cost for time slot t.

[0142] Establish long-term response rate expectation constraints:

[0143]

[0144] Guarantee the average response rate is greater than the expected average response rate ζ. avg The set of sensors for each time slot response can be represented as:

[0145]

[0146] With maximizing average charging efficiency as the optimization objective, a unified formalized scheduling problem for optimizing average charging efficiency is obtained:

[0147] P1:

[0148] st(5),(6)

[0149] x i (t)∈{0,1} (9)

[0150] S5: The time-averaged charging efficiency optimization scheduling problem is transformed into a real-time wireless charger switching scheduling problem within each time slot. It should be noted that:

[0151] Before using the Lyapunov method, the P1 problem is first transformed into a standard stochastic optimization problem:

[0152] P1′:

[0153] st(5),(9)

[0154]

[0155] Where η avg =1-ζ avg Let U′(X(t)) = -U(X(t)), and let P1 and P1' be completely equivalent; define a virtual queue for the wireless charger's activation cost:

[0156] Q(t+1)=max{Q(t)+C(t)-C avg ,0} (12)

[0157] To describe the cost exceeding the average hourly budget C for each time slot avg The cost backlog is initialized to Q(0) = 0;

[0158] Define a virtual queue for enabling the wireless charger's response rate:

[0159]

[0160] To describe the expected average non-response rate η for each time slot exceeding the specified time. avg The backlog of non-response rate is denoted as Z(0), where ψ(t) is the set of rechargeable sensors whose charging requests are responded to in time slot t, i.e., the set of rechargeable sensors that are charged by the wireless charger after issuing a charging request, and Z(0) is initialized to 0.

[0161] When the virtual queues (12) and (13) are stable, the long-term constraints (5) and (11) of the transformed problem P1' can be satisfied. Therefore, in order to optimize the dynamic wireless rechargeable sensor network in the long term and ensure the stability of the queue, the Lyapunov function L(Θ(t)) and the drift function Δ(Θ(t)) are introduced:

[0162]

[0163]

[0164] The standardized stochastic optimization problem P1' can then be transformed into a real-time optimization problem P2 that combines charging cost, response rate, and charging utility. The goal of this problem is to minimize the drift penalty function in each time slot.

[0165] P2:min X(t) Δ(Θ(t))+VU′(X(t)) (16)

[0166] Here, V is a non-negative controllable parameter used to balance charging utility and virtual queues.

[0167] Considering the dynamic nature of the system, the drift function of each time slot is unpredictable. Therefore, the target is further transformed through the queue definition (12)(13) and the drift function (15):

[0168]

[0169] in, It is a constant, C max It is the maximum charging cost that a time slot can generate.

[0170] Since the expression on the right side of inequality (17) is the upper bound of the optimization objective of P2, and A is a constant, solving the P2 problem can be transformed into solving the following formula 18, and this formula is denoted as problem P3:

[0171] P3:

[0172] Since in each time slot Q(t), Z(t), η avg C avg Since all are known constants, the optimization objective for P3, after simplification and negation, can be equivalently obtained by solving the following formula 19, and denoted as problem P4:

[0173] P4:

[0174] S6: Call the time-averaged charging efficiency optimization scheduling algorithm to calculate the wireless charger activation strategy for each time slot.

[0175] It should be noted that:

[0176] Furthermore, the time-average charging efficiency optimization scheduling algorithm includes:

[0177] A1: Input parameters:

[0178] Controllable parameter V, average hourly charging cost budget C avg Expected average non-response rate η avg Each rechargeable sensor j Perceived utility λ per unit j and initial charge B j (0)=E MAX And each wireless charger i Startup cost c i .

[0179] A2: Initialize the virtual queues Q(0) = 0, Z(0) = 0, and set the request queues for all time slots to an empty set.

[0180] A3: The decision to initialize the current time slot at the beginning of each time slot is to turn off all wireless chargers X(t) = 0, and observe the w of the current time slot. j (t), R(t), Q(t), Z(t) and B j (t);

[0181] A4: Let the objective function of problem P4 be F(S(X(t))). It is to select the wireless charger that brings the maximum marginal value from the set of all unactivated wireless chargers in the current time slot. Its corresponding activation strategy The default value is 0. The wireless charger will be turned on as long as its marginal value is greater than zero.

[0182] A5: Repeat step A4 until the marginal value of turning on the selected wireless charger is less than or equal to zero, and obtain the wireless charger activation strategy X for the current time slot. * (t).

[0183] A6: According to formula (7) Wireless charger activation strategy X for the current time slot * (t) Obtain the set of rechargeable sensors that responded, then calculate the number of unresponded requests |R(t)|-|ψ(t)| and the wireless charger activation cost. And update the virtual queue Q(t+1)=max{Q(t)+C(t)-C} for the next time slot according to the queue definitions (11)(12). avg ,0} and

[0184] A7: Calculate the power level of all rechargeable sensors in the wireless rechargeable sensor network in the next time slot according to formulas (2) and (3). j (t+1), if B j If (t+1) < δ, then add it to the request queue R(t+1) of the next time slot.

[0185] A8: Starting from time slot 0, repeat A3 to A7 for each time slot t until the last time slot ends.

[0186] A9: Return the wireless charger activation policy X for each time slot t * (t).

[0187] The above algorithms also possess theoretically guaranteed properties:

[0188] (1) The time-averaged charging utility optimization scheduling algorithm is a polynomial-time algorithm; the output of the wireless charger result that iteratively finds the maximum utility in step A4 requires O(m 2 The time complexity is 0, and in addition, F(S(X) needs to be calculated in each iteration. * The value of (t) needs to be O(n), so the time complexity of the time-averaged charging utility optimization scheduling algorithm is O(nm). 2 The Real-Time Equalization Utility Scheduling Algorithm is a polynomial-time algorithm. This polynomial-time algorithm can guarantee accurate results while saving a significant amount of computation time.

[0189] (2) The output of the time-averaged charging efficiency optimization scheduling algorithm in each time slot is denoted as X. * (t), the degree value of problem P4 obtained from the output is denoted as CP4. * The optimal solution and optimal value of P4 are denoted as X. OPT (t) and CP4 OPT And N OPT This represents the number of chargers that are activated in the optimal solution. as well as Based on the greedy selectivity s in step A4 of the time-averaged charging efficiency optimization scheduling algorithm. * It must be the first wireless charger selected by the time-average charging efficiency optimization scheduling algorithm, so F(s) * )≥F(s o ), by analyzing F(s) * ) and F(s o Scaling can yield CP4. * ≥F(s * )and Furthermore, due to N OPT ≤m, we can get

[0190] (3) For any positive number V, the difference between the solution obtained by the time-averaged charging utility optimization scheduling algorithm in all time slots and the optimal solution of the original problem is finite. First, define the optimal w-only strategy, denoted as X. # (t), the strategy satisfies:

[0191]

[0192] C(X # (t))≤C avg (31)

[0193]

[0194] The optimal solution to the original problem is OPT. Since the original problem P1 is negative, OPT = -OPT'. Therefore, we can obtain:

[0195]

[0196]

[0197] The first inequality is due to inequality (23); the second inequality is due to... The third inequality is because for problem P4, the value of the optimal solution to P4 is better than the value of the optimal w-only strategy; the last inequality is based on equations (31) and (32).

[0198] Taking the expectation of both sides of inequality (33) and summing them over each time slot, we can then obtain a term related to the virtual queue on the right side of the inequality. The startup cost and average time budget of the wireless charger in the problem can be scaled up proportionally without changing the nature of the problem or affecting the response rate. This ensures that the term on the right side of the inequality regarding the virtual queue is less than zero and can be directly removed from the inequality. Finally, based on equation (30), inequality (33) can be simplified to:

[0199]

[0200] Simplifying (34) yields:

[0201]

[0202] Because U′(X * (t))=-U(X * Given (t)) and OPT=-OPT′, we finally obtain the difference between the optimal value of the time-averaged charging utility optimization scheduling algorithm and the optimal value of the original problem:

[0203]

[0204] (4) The solution of the time-averaged charging utility optimization scheduling algorithm is a feasible solution to the original problem P1, that is, it can stabilize the queue, because there exists a w-only policy X in any time slot. ★ (t) does not depend on the state of the virtual queue and satisfy:

[0205]

[0206] Similar to inequality (33), we can obtain:

[0207]

[0208] Combining (37) and (38), we can further obtain:

[0209]

[0210] Take the maximum value U′ of U′(X(t)). max and minimum value U′ min Then, by scaling inequality (40), we can obtain:

[0211]

[0212] Taking the expectation of both sides of inequality (41), and then summing them up in each time slot and simplifying, we can obtain:

[0213]

[0214] Based on the fundamental inequality (42), it can be expressed as:

[0215]

[0216] Then, take the square root of inequality (43) and divide both sides by T. As T approaches infinity, we get:

[0217]

[0218] Since both the virtual queues Q(T) and Z(T) are non-negative, the stability condition of the queue can be obtained:

[0219]

[0220] This demonstrates that the solution obtained by the time-averaged charging utility optimization scheduling algorithm is a feasible solution to the original problem.

[0221] Furthermore, equation (42) can be obtained by scaling:

[0222]

[0223] Simplifying inequality (46) and dividing both sides by T, we can see that the length of the time-averaged queue is bounded as T approaches infinity:

[0224]

[0225] Only V is a controllable parameter, which means that the upper bound of the time-averaged queue length is proportional to the size of the chosen controllable parameter V.

[0226] Example 2

[0227] Reference Figures 1-5 As an embodiment of the present invention, the charger and sensor are placed as follows: Figure 3 As shown, with the goal of maximizing the average charging efficiency, the charging activation strategy within each time slot is solved.

[0228] Depend on Figure 1 As shown in the flowchart, the wireless charger switch scheduling method for long-term charging efficiency described in this invention includes the following steps:

[0229] In this embodiment S1, the set of rechargeable sensors is N = {o1, o2, o3, o4, o5, o6, o7, o8}, and the set of wireless chargers is M = {s1, s2, s3, s4, s5}. Both the wireless chargers and the rechargeable sensors are distributed on a 3m * 3m two-dimensional plane, as shown below. Figure 3 The charger is represented by a circle with coordinates (1.2,0), (2,0), (0,0.8), (0.8,2.8) and (2.4,2.8), respectively. The rechargeable sensor is represented by a triangle with coordinates (0,1.6), (0.8,2.4), (0.8,1.2), (1.6,0.8), (1.6,1.6), (1.6,2.4), (2.4,1.6), and (2.4,2.4).

[0230] With α = 6.93, β = 0.34, and maximum charging distance D = 2m, the rechargeable sensor o j From wireless chargers i The obtained charging power is:

[0231]

[0232] d(s i ,o j Wireless chargers i With rechargeable sensor o j The distance between them. When d(s) i ,o j If )≤2, the rechargeable sensor always receives positive power.

[0233] The specific steps of S2 in this embodiment are as follows:

[0234] B1: Discretize the continuous time of 10000s into time slices using the time discretization method. The length of each time slot is 100s; the charging amount of the wireless charger set in time slot t when the activation strategy is X(t)=(x1(t),x2(t),x3(t),x4(t),x5(t)) is:

[0235]

[0236] Where R(t) is the set of sensors that make a request in time slot t, and the sensors only make a request when the power level is less than the threshold of 30J. The wireless charger only charges the rechargeable sensors that make the request.

[0237] The activation cost for each wireless charger is set to a random value c. i ∈020, 301; Battery capacity E of all rechargeable sensors MAX =100J, B j (t) represents the rechargeable sensor at the start of time slot t. j Battery level, E MAX -B j (t) represents the rechargeable sensor o in time slot t. j The maximum acceptable charging amount.

[0238] B2: Based on the decision made in the current time slot, the battery level in the next time slot can be expressed as:

[0239]

[0240] Among them, the t-slot rechargeable sensor o j The power consumption rate is set to a random value w in each time slot because it is affected by the environment. j (t)∈[15mj / s, 30mj / s1, where the energy consumption rate of the rechargeable sensor in each time slot is assumed to be the value at the beginning of the time slot.

[0241] B3: Define the total charging efficiency of a wireless rechargeable sensor network in time slot t as:

[0242]

[0243] Each wireless sensor has different sensing capabilities and different sensing effectiveness for different sensing tasks, so it is set to a random value λ. j ∈050 / J, 100 / J1.

[0244] The specific steps of S3 in this embodiment are as follows:

[0245] C1: Establish long-term charging budget constraints:

[0246]

[0247] Ensure that the average time-to-use cost of the wireless charger is less than the average time-to-use charging cost budget C. avg =57, of which Indicates the activation cost of the wireless charger in time slot t;

[0248] C2: Establish long-term response rate expectation constraints:

[0249]

[0250] Guarantee the average response rate is greater than the expected average response rate ζ avg =50%, where the set of rechargeable sensors for each time slot response can be represented as:

[0251]

[0252] C3: Taking maximizing average charging efficiency as the optimization objective, a unified formalized scheduling problem for optimizing average charging efficiency is obtained:

[0253]

[0254]

[0255]

[0256] x i (t)∈{0,1}

[0257] The specific steps of S4 in this embodiment are as follows:

[0258] D1: Before using the Lyapunov method, the time-averaged charging utility optimization scheduling problem is transformed into a real-time wireless charger switching scheduling problem within each time slot:

[0259]

[0260]

[0261]

[0262] x i (t)∈{0,1}

[0263] Where η avg =1-50%=50% is denoted as the expected non-response rate, U′(X(t))= -U(X(t)), and the two problems before and after the transformation are completely equivalent;

[0264] D2: Defines the virtual queue for wireless charger startup costs.

[0265] Q(t+1) = max{Q(t) + C(t) - 57, 0}

[0266] A virtual queue is used to describe each time slot exceeding the average hourly cost budget C. avg =57 cost backlog, where Q(0) is initialized to 0;

[0267] D3: Defines the virtual queue for enabling the wireless charger's response rate.

[0268]

[0269] To describe the expected average non-response rate η for each time slot exceeding the specified time. avg =50% of the non-response rate backlog, where ψ(t) is the set of rechargeable sensors that respond to the charging request in time slot t, that is, the set of rechargeable sensors that are charged by the wireless charger after issuing the charging request, and initialize Z(0) = 0.

[0270] D4: Introduce the Lyapunov function L(Θ(t)) and the drift function Δ(Θ(t)):

[0271]

[0272]

[0273] D5: The standardized stochastic optimization problem is transformed into a real-time optimization problem that combines charging cost, response rate, and charging utility. The goal of this problem is to minimize the drift penalty function in each time slot.

[0274]

[0275] The non-negative controllable parameter V = 100 is used to balance charging utility and the virtual queue.

[0276] D6: Further transform the target through queue definition and drift function:

[0277]

[0278] Where A is a constant.

[0279] D7: Transform the solution for the drift penalty function into finding the minimum value on the right side of the inequality in step C6:

[0280]

[0281] Since in each time slot Q(t), Z(t), η avg =50%, C avg=57 are both known constants, so after simplification and negation, it is equivalent to solving a maximization problem:

[0282]

[0283] In this embodiment, by Figure 2 As can be seen, the specific steps of step S5 are as follows:

[0284] E1: Input parameters: Controllable parameter V = 100, average hourly charging cost budget C avg =57, Expected average unresponsive rate η avg =50%, randomly select the sensing utility λ of each rechargeable sensor. j ∈[50 / J, 100 / J1 and initial charge B] j (0)∈[0J, 100J1 and the activation cost c of each wireless charger i ∈[20, 301;

[0285] E2 initializes the virtual queues Q(0) = 0 and Z(0) = 0, and sets the request queues for all time slots to an empty set.

[0286] E3: At the beginning of each time slot, the decision to initialize the current time slot is to turn off all wireless chargers X(t) = 0, and then observe the w of the current time slot. j (t), R(t), Q(t), Z(t) and B j (t);

[0287] E4: Let the objective function of problem P4 be F(S(X(t))). From the set of all inactive wireless chargers in the current time slot, select the wireless charger that brings the greatest benefit. Its corresponding activation strategy The default value is 0. The wireless charger will be turned on as long as its marginal value is greater than zero.

[0288] E5: Repeat step D4 until the marginal value brought by turning on the selected wireless charger is less than or equal to zero, and obtain the wireless charger activation strategy X for the current time slot. * (t).

[0289] E6: According to formula (7) Wireless charger activation strategy X for the current time slot * (t) Obtain the set of rechargeable sensors that responded, then calculate the number of unresponded requests |R(t)|-|ψ(t)| and the wireless charger activation cost. And update the virtual queue Q(t+1)=max{Q(t)+C(t)-C} for the next time slot according to the queue definitions (11)(12). avg ,0} and

[0290] E7: Calculate the charge level B of all rechargeable sensors in the wireless rechargeable sensor network in the next time slot according to formulas (2) and (3). j (t+1), if B j If (t+1) < 30, then the request is added to the request queue R(t+1) of the next time slot.

[0291] E8: Starting from time slot 0, repeat D3 to D7 for each time slot t until the 99th time slot ends.

[0292] E9: As shown in the diagram of the average charging efficiency optimization scheduling algorithm in 5(a), the wireless charger activation strategy X for each time slot t is obtained. * (t).

[0293] Example 3

[0294] To verify and illustrate the technical effectiveness of this method, this embodiment involves two schemes that are compared with the method of the present invention in actual tests:

[0295] (1) Maximum marginal utility algorithm: This algorithm iteratively selects the wireless charger with the maximum marginal utility to turn on in each time slot, under the condition that the average time cost of turning on the wireless charger does not exceed 57.

[0296] (2) Maximum cost-effectiveness algorithm: This algorithm iteratively selects the wireless charger with the highest ratio of marginal utility to activation cost in each time slot, under the condition that the average time-to-activation cost of the wireless charger does not exceed 57.

[0297] The strategies of the three algorithms are as follows Figure 4 (a) Graph of the time-averaged charging efficiency optimization scheduling algorithm Figure 4 (b) Maximum Marginal Utility Algorithm Graph Figure 4(c) As shown in the diagram of the maximum cost-effectiveness algorithm, a comparison reveals that the strategy obtained by the average charging utility optimization scheduling algorithm designed in this invention is concentrated in certain time slots. More specifically, the variance of the number of wireless chargers activated in all time slots using the average charging utility optimization scheduling algorithm of this invention is 3.98, while the other two algorithms are 0.46 and 0.49 respectively. This reflects that the average charging utility optimization scheduling algorithm of this invention focuses more on the long-term benefits of the future than the benefits of the current time slot. Therefore, it may sometimes sacrifice the charging benefits of the current time slot by not activating the wireless charger to save the charger activation cost budget for activating multiple wireless chargers simultaneously in the future to obtain higher charging utility. Conversely, the other two comparison algorithms are short-term optimization algorithms. They only focus on maximizing the utility of the current time slot. Therefore, each time slot will try to use up the activation cost budget of the wireless charger in the current time slot as much as possible, so the activation strategy results in a more even distribution of the number of wireless chargers activated in each time slot. Figure 5 As shown, the time-average charging utility optimization scheduling algorithm outperforms the maximum marginal benefit algorithm and the maximum cost-effectiveness algorithm by 46.31% and 47.56% respectively in terms of average charging utility per rechargeable sensor.

[0298] Example 4

[0299] Reference Figures 6-9 This is another embodiment of the present invention, in which simulation experiments are conducted to compare two existing algorithms proposed in the previous embodiment. It should be noted that the other two comparison algorithms do not have requirements for response rate, so only the average response rate of each time slot of the other two algorithms is recorded for comparison.

[0300] Parameter settings: The wireless charger and rechargeable sensor nodes are randomly distributed within a 50m*50m square two-dimensional plane. The number of time slots is set to T = 1500, and the length of each time slot is τ = 100s. The hardware parameters are set as follows: α = 100000, β = 40, D = 20m, δ = 30J, m = 50, n = 100, E MAX =100J, initial charge B of each rechargeable sensor (randomly). j (0)∈[0J,100J], perceived utility λ j ∈[50 / J, 100 / J1 and initial charge B] j (0)∈[0J, 100J] and the startup cost c of the wireless charger i ∈[20, 30], the energy consumption rate range w for each rechargeable sensor in each time slot j (t)∈[15mj / s, 30mj / s1, hourly cost budget C avg =300, expected average response rate ζ avg=50%, control parameter V=5000. Next, the values ​​of key parameters will be changed to explore their impact on the algorithm, with the average of each measurement exceeding 100 random topologies.

[0301] Comparing the time-average charging efficiency optimization scheduling algorithm with the other two algorithms, in terms of time-average response rate, such as... Figure 6 , Figure 6 This is a comparison chart of the average response rate of the present invention; the average response rate of the time-averaged charging utility optimization scheduling algorithm is 0.57%, which is 3.42% and 4.37% higher than the maximum marginal utility algorithm and the maximum cost-effectiveness algorithm, respectively; in terms of average charging utility, as the number of rechargeable sensors increases from 80 to 130, as shown in Figure 7(a) (charging sensor number graph), the average charging utility optimization scheduling algorithm is 19.64% and 18.72% higher than the maximum marginal utility algorithm and the maximum cost-effectiveness algorithm, respectively. As the average charging cost budget increases from 300 to 800, as... Figure 7 (b) As shown in the time-averaged charging budget diagram, a higher time-averaged charging cost budget results in higher time-averaged charging utility. However, charging utility also depends on the battery capacity of the rechargeable sensor nodes. When more wireless chargers can be turned on in each time slot, the rechargeable sensors can reach higher battery levels, and the number of charging requests issued by the rechargeable sensors will decrease. Therefore, as the time-averaged budget increases, the increase in time-averaged charging utility becomes slower, and the time-averaged charging utility optimization scheduling algorithm still generally has a higher time-averaged charging utility than the maximum marginal utility algorithm and the maximum cost-effectiveness algorithm. In terms of algorithm runtime, such as... Figure 7 (c) As shown in the graph of the number of wireless chargers, the running time of all algorithms increases as the number of wireless chargers increases from 30 to 80. This is because these algorithms need to search for the activation strategy for each time slot across the entire set of wireless chargers. Since the average charging utility optimization scheduling algorithm needs to maintain a virtual queue for each time slot, its running time is slightly longer than that of the maximum marginal utility algorithm and the maximum cost-effectiveness algorithm. Furthermore, as the number of wireless chargers increases, updating the virtual queue takes more time, so the running time of the average charging utility optimization scheduling algorithm increases even faster than that of the maximum marginal utility algorithm and the maximum cost-effectiveness algorithm. However, when there are 80 wireless chargers and 1500 time slots, the total time spent by the average charging utility optimization scheduling algorithm is within 294.39 seconds.

[0302] The effectiveness of the time-average charging utility optimization scheduling algorithm in this invention is also greatly affected by the control parameter V, such as Figure 8 , Figure 9 As shown, Figure 8 This is a comparison chart of the time-averaged charging efficiency of the present invention under different control parameters V. Figure 9The present invention presents a comparison of the time-averaged queue length under different control parameters V. The larger V is, the better the performance of the time-averaged charging utility optimization scheduling algorithm, but at the same time, the time-averaged queue length will also be larger, and the convergence speed will be slower. Since the Lyapunov method is based on queue stability, the slow convergence speed of the time-averaged queue will also slow down the convergence of the time-averaged charging utility. Therefore, the present invention provides an algorithm that can flexibly adjust the value of V according to the diverse needs for time-averaged charging utility and storage consumption.

[0303] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A wireless charger switch scheduling method for optimizing long-term charging efficiency, characterized in that, include: The rechargeable sensor battery level and charging efficiency within each time slot are obtained using a time discretization method. Formalizing the time-averaged charging utility optimization scheduling problem; The time-average charging efficiency optimization scheduling problem is transformed into a real-time wireless charger switching scheduling problem within each time slot. The time-average charging efficiency optimization scheduling algorithm is invoked to calculate the wireless charger activation strategy for each time slot; Before obtaining the rechargeable sensor battery level and charging efficiency within each time slot using the time discretization method, the method further includes: Define a collection of rechargeable sensors and wireless chargers; Define the charging power of the rechargeable sensor; The rechargeable sensor set is as follows: The wireless charger set includes: },in It is the number of rechargeable sensors. It refers to the number of wireless chargers; The charging power of the rechargeable sensor includes: The wireless charger From rechargeable sensors The obtained charging power is: （1） in, and These are two constants determined by the magnetic field environment and hardware parameters of the wireless charger and rechargeable sensor. This is the maximum charging distance of the wireless charger. For rechargeable sensors With wireless charger The distance between them, when The rechargeable sensor always receives positive power; The method of obtaining the rechargeable sensor battery level and charging efficiency in each time slot using the time discretization method includes: Discretize a continuous time segment into time slots ,in A set of time slices, with the number of time slots being... The length of each time slot is ; Wireless chargers are integrated into time slots The activation strategy is ,in Indicates in Time slot wireless charger Turn on, Indicates in Time slot wireless charger Without activation, the unit activation cost for each wireless charger is ; exist Time slots allow rechargeable sensors to operate only when the battery level is below a threshold. A request will be sent at any time; the rechargeable sensor that sends the request will do so. The wireless charger activation strategy is as follows: The charging amount at that time is: （2） in, for The set of rechargeable sensors that issue a time slot, and the wireless charger only charges the rechargeable sensors that issued the request. The battery capacity for the rechargeable sensor. Indicates the rechargeable sensor at the start of time slot t. Battery level, This indicates a rechargeable sensor in time slot t. The maximum acceptable charging amount; Based on the decision made in the current time slot, the battery level in the next time slot can be expressed as: （3） in, for Time-slot rechargeable sensor The power consumption rate; The total charging efficiency of a wireless rechargeable sensor network in time slot t is defined as: （4） in, For rechargeable sensors Perceived utility per unit; The formalized time-averaged charging utility optimization scheduling problem includes: Establish long-term charging budget constraints; Establish long-term response rate expectation constraints; With maximizing the average charging efficiency as the optimization objective, a formalized scheduling problem for the average charging efficiency optimization is obtained. The establishment of long-term charging budget constraints includes: Establish long-term charging budget constraints: （5） in, This is the average charging cost budget. express The cost of enabling wireless chargers in time slots; The established long-term response rate expectation constraints include: Establish long-term response rate expectation constraints: （6） in, The expected average response rate, the set of rechargeable sensors for each time slot response can be represented as: （7） The formalized scheduling problem for optimizing average charging efficiency, with the goal of maximizing average charging efficiency, includes: With maximizing average charging efficiency as the optimization objective, the following scheduling problem for optimizing average charging efficiency is obtained: （8） （9） The method for transforming the time-averaged charging efficiency optimization scheduling problem into a real-time wireless charger switching scheduling problem within each time slot includes: The time-average charging utility optimization scheduling problem P1 is transformed into a short-term optimization problem for each time slot using the Lyapunov method. Before using the Lyapunov method, the P1 problem is first transformed into a standard stochastic optimization problem: （10） （11） in The average non-response rate is recorded as the expected rate. ; Define a virtual queue for the activation cost of wireless chargers: （12） A virtual queue is used to describe each time slot exceeding the average hourly cost budget. The cost backlog, of which, initial ; Define a virtual queue for enabling the wireless charger's response rate: （13） To describe the expected average non-response rate for each time slot exceeding the specified time. The backlog of non-response rates, of which for The set of rechargeable sensors that respond to time-slot charging requests is initialized. ; Introducing Lyapunov functions and drift function : （14） （15） The original problem is transformed into a real-time optimization problem P2 that combines charging cost, response rate, and charging utility, with the goal of minimizing the drift penalty function in each time slot: （16） Where V is a non-negative controllable parameter used to balance charging utility and virtual queue; The optimization objective of P2 is further transformed using queue definitions (12) and (13) and the drift function (15): （17） in, It is a constant. It is the maximum charging cost that a time slot can generate; Since the expression on the right side of inequality (17) is the upper bound of the optimization objective of P2, and A is a constant, solving the P2 problem can be transformed into solving the following formula 18, and this formula is denoted as problem P3: （18） Due to each time slot , , , Since all are known constants, the optimization objective for P3, after simplification and negation, can be equivalently obtained by solving the following formula 19, and this formula is denoted as problem P4: (19).

2. The wireless charger switch scheduling method for optimizing long-term charging efficiency as described in claim 1, characterized in that: The call-time average charging efficiency optimization scheduling algorithm includes: A1: Input parameters: Controllable parameters Average charging cost budget Expected average non-response rate Each rechargeable sensor Perceived utility per unit and initial power and each wireless charger Startup cost ; A2: Initialize the virtual queue , And set the request queues for all time slots to empty sets. ; A3: The decision to initialize the current time slot at the beginning of each time slot is to turn off all wireless chargers. Observe the current time slot , , , as well as ; A4: Let the objective function of problem P4 be... From the set of all inactive wireless chargers in the current time slot, select the wireless charger that delivers the greatest marginal value. Its corresponding activation strategy The default value is 0. The wireless charger will be turned on as long as its marginal value is greater than zero. ; A5: Repeat step A4 until the marginal value of turning on the selected wireless charger is less than or equal to zero, and obtain the wireless charger activation strategy for the current time slot. ; A6: According to formula (7) Wireless charger activation policy for the current time slot Obtain the set of rechargeable sensors that responded, and then calculate the number of unresponded requests. and the cost of starting a wireless charger And update the virtual queue for the next time slot according to the queue definitions (11) and (12). and ; A7: Calculate the power level of all rechargeable sensors in the wireless rechargeable sensor network in the next time slot according to formulas (2) and (3). ,if Then add it to the request queue for the next time slot. ; A8: From the time slot Begin, for each time slot Repeat steps A3 through A7 until the last time slot ends; A9: Return each time slot Wireless charging activation strategy .

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