Joint optimization method for task unloading and power control in satellite edge computing network

Abstract

The invention discloses a joint optimization method for task unloading and power control in a satellite edge computing network, and provides a time delay-energy consumption balance optimization framework oriented to dynamic task arrival aiming at the long-term random optimization problem in satellite edge computing task unloading. Through fusion of Lyapunov optimization and a virtual queue mechanism, the long-term delay constraint is successfully converted into a time slot level optimization target which can be executed online, and a self-adaptive decision process is realized. And aiming at the generated non-convex optimization problem, constructing a robust solution algorithm under a PDD framework, and integrating secondary transformation and an SCA technology to realize efficient solution. Simulation experiments show that the method can obviously reduce the energy consumption in a random task arrival scene, and strictly meets the delay constraint requirement at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication, and specifically, relates to a joint optimization method for task offloading and power control in a satellite edge computing network. Background Art

[0002] With the rapid development of satellite technology, Low Earth Orbit (LEO) satellites have been widely deployed to support diverse applications such as remote sensing, Earth observation, and cooperative monitoring. However, the exponential growth of observation data and frequent downlink communication have imposed a huge pressure on the limited space-ground communication bandwidth, resulting in increased transmission delay, rising energy consumption, and network congestion. To address these challenges, Satellite Edge Computing (SEC), inspired by Mobile Edge Computing (MEC) on the ground, has emerged. SEC enables satellites to process on-board tasks and only transmit important processed data back to the ground station. Despite these advantages, SEC still faces inherent constraints related to on-board computing capabilities, storage, and energy resources, which makes it difficult to optimally balance local computing and task offloading while achieving high computing efficiency and energy conservation.

[0003] The dynamic movement of satellites causes continuous fluctuations in channel conditions, and unpredictable task arrivals introduce additional uncertainties. These factors significantly increase the complexity of accurately predicting workload requirements and efficiently allocating resources, thus posing several key challenges: First, they interfere with effective resource management and further exacerbate the difficulty of optimizing the balance between energy consumption and delay. Therefore, a flexible and adaptive offloading strategy must be adopted. Second, sudden changes in the amount of task arrivals may lead to resource shortages, further causing increased delay or low resource utilization efficiency. In addition, the limited on-board computing and energy resources of the satellite platform require precise trade-offs between energy consumption and delay. During the task offloading process, increasing the transmission power can enhance the transmission rate, shorten the transmission time, and thus reduce the end-to-end delay. However, since energy consumption depends on both power and duration, there objectively exists an optimal transmission power level that minimizes the total energy consumption. Existing research has not fully revealed this dynamic balance mechanism, especially lacking a systematic optimization framework in scenarios where task arrivals are random. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a joint optimization method for task offloading and power control in a satellite edge computing network, which fully considers the uncertainties of task arrivals and transmission conditions, making it highly robust in a dynamic environment.

[0005] The purpose of the present invention is achieved by the following technical solutions:

[0006] A joint optimization method for task offloading and power control in a satellite edge computing network, comprising:

[0007] Establish a system model, where the system model includes a space-ground network composed of S satellites and a ground server;

[0008] Construct a system objective function and constraint conditions to form an optimization problem P1 to minimize the total energy consumption of all satellites while satisfying the long-term average delay constraint;

[0009] Use the Lyapunov optimization method to transform the optimization problem P1 into a single-slot deterministic optimization problem and solve it to obtain the optimal satellite offloading decision and the optimal power allocation.

[0010] Furthermore, the system objective function is:

[0011]

[0012] The constraint conditions are:

[0013]

[0014] Among them,

[0015] The system objective function represents minimizing the total energy consumption of all satellites during the total operation period of the system;

[0016] E(t) represents the total energy consumption of all satellites at time slot t;

[0017] S represents the total number of satellites, T represents the total number of time slots during the system operation period;

[0018] p s (t) represents the transmission power of satellite s at time slot t; represents the maximum transmission power of satellite s;

[0019] a s (t) represents the offloading decision variable. When a s (t) = 0, it means that the data received by satellite s at time slot t is locally computed. When a s (t) = 1, it means that the data received by satellite s at time slot t is offloaded to the ground server;

[0020] D s (t) represents the amount of data received by satellite s at time slot t;

[0021] represents the achievable data rate of satellite s to the ground server at time slot t; The link bandwidth B is divided into S subcarrier numbers, Denotes the channel gain between satellite s and the ground server at time slot t, σ 2 Denotes the noise power, g tx And g rx Denote the gains of the satellite transmitter and the ground server receiver respectively; β denotes the wavelength of the communication signal; d s (t) denotes the distance between satellite s and the ground server at time slot t; F rain Denotes the rain attenuation;

[0022] k s Denotes the effective switching capacitance when satellite s performs local calculations; w denotes the number of CPU cycles per bit; f s Denotes the CPU processing frequency of satellite s;

[0023] Denotes the long-term average delay of all satellites during the entire operating cycle;

[0024] Denotes the maximum delay allowed by the system;

[0025] Denotes the average delay of all satellites;

[0026] Denotes the total delay of satellite s;

[0027] Denotes the total delay during offloading of satellite s, f g Denotes the processing frequency of the ground server; c denotes the speed of light.

[0028] Furthermore, using the Lyapunov optimization method, solving the objective function includes:

[0029] Using the Lyapunov optimization framework, convert problem P1 into a single-time-slot deterministic optimization problem P2, that is

[0030]

[0031] The constraint conditions are:

[0032]

[0033] Among them, Q(t) represents the virtual queue, which is used to track the cumulative unmet delay. The evolution formula of this virtual queue is: Among them, Q(0) = 0;

[0034] V is a constant, which is used to control the balance between the minimum energy consumption of all satellites and the stability of the virtual queue;

[0035] For any time slot \(t\), obtain the current state of queue \(Q(t)\), and solve problem \(P2\) based on the penalty dual decomposition method to generate the optimized power allocation and offloading decisions for all satellites in time slot \(t\).

[0036] According to the optimized power allocation and offloading decisions obtained at time slot \(t\), update the queue state of the next time slot according to the evolution formula of the virtual queue, and solve problem \(P2\) again based on the penalty dual decomposition method to generate the optimized power allocation and offloading decisions for the next time slot until all time slots are optimized.

[0037] Furthermore, solving problem \(P2\) based on the penalty dual decomposition method includes:

[0038] First, convert problem \(P2\) into problem \(P3\):

[0039]

[0040] The constraint conditions are:

[0041]

[0042] where is an auxiliary variable;

[0043] Next, convert problem \(P3\) into problem \(P4\):

[0044]

[0045] The constraint conditions are:

[0046]

[0047] where

[0048] P ρ is a penalty term,

[0049] \(\rho\) represents the penalty parameter used to control the scaling of the penalty term;

[0050] and respectively represent the dual variables of the equality constraints and ;

[0051] Through the nested optimization framework, co-optimize the optimization of the dual variables and the penalty parameter with the variables in problem \(P4\) to obtain the solution result of problem \(P2\).

[0052] Furthermore, the nested optimization framework has a two-layer structure, namely an outer loop and an inner loop,

[0053] The outer loop is used for dual variables and as well as the update of the penalty parameter ρ, and the update method is expressed as:

[0054]

[0055]

[0056] ρ←τρ,

[0057] where 0 ≤ τ ≤ 1, representing the control parameter for controlling the value of the outer iteration penalty term P ρ ;

[0058] In the inner loop, the alternating optimization technique is adopted to optimize the variables in the inner loop. The variables in the inner loop are divided into three blocks: and For one optimization process of the variables in the inner loop, it includes:

[0059] First, fix the second and third blocks to obtain the closed-form solution of :

[0060]

[0061] Then, fix the first and third blocks, and the optimization of the second block is expressed as problem P5:

[0062]

[0063] The constraint conditions are:

[0064]

[0065] Solve problem P5 through the convex optimization tool to obtain a s (t);

[0066] Then, fix the first and second blocks, and the optimization of the third block is expressed as problem P6:

[0067]

[0068] The constraint conditions are:

[0069]

[0070] Solve problem P6 through the method based on quadratic transformation and SCA to obtain p s (t).

[0071] Furthermore, the solution of problem P2 specifically includes:

[0072] In the inner loop, by generating each time through optimization a s (t) and p s (t) to determine the objective function value in problem P4;

[0073] Using the a s (t) and p s (t) region updates the variables in the inner loop for the next optimization, generating the a s (t) and p s (t), and determines the objective function value in problem P4 again. When the reduction rate of the objective function value in problem P4 is lower than the preset threshold ε I then, the optimization process of this inner loop;

[0074] Using the and a s (t) determined by the final generation of this inner loop, determine the maximum constraint violation:

[0075]

[0076] If then use the dual variables and update method to update the dual variables and , where k0 represents a preset value;

[0077] Otherwise, use the update method of the penalty parameter ρ to update the penalty parameter ρ;

[0078] After the outer loop update is completed, use and the update results of ρ and the a s (t) and p s (t) generated by this inner loop to determine the objective function value in problem P2;

[0079] Repeat the parameter update of the outer loop and the parameter optimization process of the inner loop until the reduction rate of the objective function value in problem P2 is lower than the preset threshold ε0. Thus, the solution to problem P2 is completed.

[0080] Furthermore, solving problem P6 by the method based on quadratic transformation and SCA includes:

[0081] Adopt the quadratic transformation method to transform into where y s (t) is an auxiliary variable for auxiliary transformation;

[0082] Transform Perform a linear transformation;

[0083] According to the result of the linear transformation, convert the objective function in Problem P6 into a convex function;

[0084] Use a convex optimization tool to solve the objective function converted into a convex function by the SCA method, so as to obtain the final solution result of p s (t) in Problem P6.

[0085] Furthermore, solving Problem P6 by the method based on quadratic transformation and SCA specifically includes:

[0086] At the k-th iteration, obtain and respectively represent p at the k-th iteration s (t), R s (t) and y s (t);

[0087] At the given point Apply the first-order Taylor approximation to obtain “ ” represents the definition symbol, represents the linearized upper bound of;

[0088] Use to replace in

[0089] According to and determine so as to obtain

[0090] Replace E(t) with E′(t), where

[0091]

[0092] Then, replace Problem P6 with Problem P7:

[0093]

[0094] The constraint conditions are:

[0095]

[0096] Among them, R in the objective function of Problem P7 s (t) and y s (t) are respectively replaced with and respectively,

[0097] Solve problem P7 using convex optimization tools to obtain the optimized p generated in this iteration s (t);

[0098] Use the optimized p s (t) generated in this iteration to update p s (t) for the next iteration and update R s (t) and y s (t) successively. Solve problem P7 again and repeat the above iterative process until the termination iteration requirement is met. The finally generated p s (t) is the solution to problem P6

[0099] The present invention also provides a joint optimization system for task offloading and power control in a satellite edge computing network. The system includes:

[0100] A memory configured to store a computer program;

[0101] A processor configured to execute the computer program to implement the joint optimization method for task offloading and power control in the satellite edge computing network as described above

[0102] The present invention also provides a computer-readable storage medium with a computer program stored thereon. When the computer program is executed by a processor, it implements the joint optimization method for task offloading and power control in the satellite edge computing network as described above

[0103] The beneficial effects of the present invention are:

[0104] The present invention first constructs a multi-stage stochastic optimization model that jointly optimizes satellite offloading decisions and power allocation to minimize energy consumption while strictly satisfying the long-term average delay constraint. Moreover, the model explicitly considers the uncertainty of task arrival and transmission conditions, making it highly robust in a dynamic environment

[0105] The present invention also proposes a Lyapunov optimization method with a virtual queue mechanism, which transforms the long-term delay constraint into a manageable per-slot optimization objective. For the resulting non-convex optimization problem, an efficient algorithm is designed within the Penalty Dual Decomposition (PDD) framework, combined with quadratic transformation and Successive Convex Approximation (SCA) techniques, to achieve iterative optimization of offloading decisions and power allocation

[0106] Other advantages, objects, and features of the present invention will be set forth in part in the following description, and in part will be obvious to those skilled in the art upon examination of the following, or may be learned by practice of the present invention. The objects and other advantages of the present invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] In order to make the objectives, technical solutions, and advantages of the present invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, where:

[0108] Figure 1 is a schematic flowchart of a joint optimization method for task offloading and power control in a satellite edge computing network;

[0109] FIG. 2(a) is a simulation result of the convergence characteristics based on the PDD algorithm;

[0110] FIG. 2(b) is a simulation result of the variation relationship between the objective function value (i.e., the objective value) of problem P2 and the transmission power;

[0111] FIG. 3(a) is the average transmission power simulation result of the satellite under different D max ;

[0112] FIG. 3(b) is the average offloading rate of the satellite under different D max ;

[0113] FIG. 4(a) is the total energy consumption simulation result when the method proposed in the present invention and other comparison methods vary with D max ;

[0114] FIG. 4(b) is the simulation result of the long-term average delay when the method proposed in the present invention and other comparison methods vary with D max ; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0115] The following will refer to the accompanying drawings to describe the preferred embodiments of the present invention in detail. It should be understood that the preferred embodiments are only for illustrating the present invention, rather than limiting the protection scope of the present invention.

[0116] A joint optimization method for task offloading and power control in a satellite edge computing network, in combination with Figure 1 , the method includes:

[0117] Establishing a system model, where the system model includes a space-ground network composed of S satellites and a ground server;

[0118] Constructing a system objective function and constraint conditions to form an optimization problem P1 to minimize the total energy consumption of all satellites while satisfying the long-term average delay constraint;

[0119] The optimization problem P1 is transformed into a single-slot deterministic optimization problem and solved using the Lyapunov optimization method to obtain the optimal satellite offloading decision and the optimal power allocation.

[0120] In this system model, each satellite performs various tasks, including earth remote sensing, meteorological monitoring, and environmental monitoring. During these operations, the satellite captures data, which can include videos, images, or other types of sensing data. The size of the captured data is random and affected by the dynamics of the observation environment and the specific tasks being performed. The captured data usually requires a large amount of computing resources for processing, such as image or video analysis, object detection, or environmental modeling, to extract useful information. However, due to the limited computing power on the satellite, the satellite faces significant challenges in processing large-scale tasks while meeting the latency constraints, and the variation in data size further exacerbates this problem, especially for large datasets involving high-resolution videos or images, which may exceed the satellite's processing capacity. To address these limitations, the satellite can offload its data to the ground server G, which has greater computing power.

[0121] The total operating time (or "operating cycle") of the system is divided into T time slots with a time slot interval of δ. The amount of data arriving at satellite s within any time slot t can be denoted as D s (t), which is a random variable. The size of the data volume D s (t) is bounded by 0 ≤ D s (t) ≤ D max , where D max represents the maximum amount of data that the satellite can process at any given time.

[0122] In the satellite-ground communication network, the channel between the LEO satellite and the ground server G is described by the channel gain of satellite s within time slot t, where g tx and g rx represent the gains of the satellite transmitter and the ground server receiver, respectively; β represents the wavelength of the communication signal; d s (t) represents the distance between satellite s and the ground server at time slot t; F rain represents the rain fade and follows the Weibull distribution.

[0123] To facilitate efficient communication, the available uplink (in this scenario, the uplink refers to the link from the satellite to the ground server) bandwidth B is divided into S subcarriers (i.e., the number of subcarriers is the same as the number of satellites). This division enables parallel transmission, thereby reducing interference and increasing throughput. The achievable data rate from satellite s to the ground server within time slot t can be expressed as where p s(t) represents the transmission power of satellite s at time slot t, and σ 2 represents the noise power.

[0124] The present invention adopts a binary offloading method to determine the processing strategy for each task. Since partial offloading is usually impractical in the LEO scenario due to limited connection duration and coordination overhead between on-board and ground processing, the present invention introduces a binary offloading decision variable a s (t) ∈ {0, 1}, where when a s (t) = 0, it means that the data received by satellite s at time slot t is locally computed, and a s (t) = 1 means that the data received by satellite s at time slot t is offloaded to the ground server.

[0125] Within time slot t, the total energy consumption of satellite s includes communication energy consumption (i.e., communication energy consumption) and computing energy consumption. Among them, the communication energy consumption of satellite s at time slot t is expressed by formula (1) as:

[0126]

[0127] When the task is locally computed on satellite s, the computing energy consumption is given by the following formula: k s w s D s (t)f s 2 , where k s represents the effective switching capacitance when satellite s performs local computing; w represents the number of CPU cycles per bit (this parameter is a quantity related to the task); f s represents the CPU processing frequency of satellite s.

[0128] Therefore, considering the communication energy consumption and computing energy consumption, the total energy consumption (i.e., total energy consumption) of all satellites within time slot t can be expressed as:

[0129]

[0130] The total delay experienced by the satellite depends on the processing strategy.

[0131] If satellite s locally computes the task, the delay calculation formula is

[0132] If satellite s offloads the task to the ground server, the total delay includes transmission delay, propagation delay, and computing delay. The transmission delay is The one-way propagation delay is (then, the two-way propagation delay is ), where c represents the speed of light, and the computing delay of the ground server is where, f gIndicates the processing frequency of the ground server.

[0133] Therefore, the total delay during unloading is:

[0134] The total delay of satellite s within time slot t is

[0135] To evaluate the overall performance of the satellite network, the present invention calculates the average delay of time slot t by averaging the delays of all satellites, that is:

[0136]

[0137] Then, the long-term average delay over the entire operation period can be expressed as:

[0138] By ensuring that the long-term average delay remains within an acceptable range, it is possible to guarantee the smooth operation of critical services without interruption. Therefore, it is necessary to set is the maximum allowable delay.

[0139] The objective of the present invention is to minimize the total energy consumption of all satellites while ensuring low and stable delays. To achieve this goal, it is necessary to optimize the satellite communication power, i.e., and the offloading decision Then the above optimization problem can be expressed as problem P1:

[0140]

[0141] The constraint conditions are:

[0142]

[0143]

[0144]

[0145] Among them, represents the maximum transmission power of satellite s, S represents the total number of satellites, T represents the total number of time slots within the system operation period.

[0146] It should be noted that solving problem P1 is somewhat challenging, which stems from the randomness characteristics of the data arrival of each satellite. Due to the data volume D s (t) is a random variable, and the delay of each time slot is also random. This randomness brings significant complexity in meeting the long-term average delay requirement (5). The combination of this randomness with the binary offloading decision and the non-convex nature of the objective function makes this problem a multi-stage stochastic optimization problem, which is difficult to solve.

[0147] Based on this, the present invention proposes a solution based on the Lyapunov algorithm to achieve online optimization with queue stability. Specifically, the original problem is transformed into a more tractable single-slot deterministic optimization problem through the Lyapunov optimization framework, and then an efficient algorithm based on the PDD, quadratic transformation, and SCA methods is proposed.

[0148] Specifically, to solve the multi-stage stochastic optimization problem (P1), the present invention adopts a method based on the Lyapunov optimization framework (i.e., the Lyapunov optimization framework).

[0149] The present invention introduces a virtual queue Q(t) to track the accumulated unmet latency. The accumulated unmet latency is the cumulative result over time of the excess of the average latency over the maximum tolerable latency in each time slot. of the excess part.

[0150] The evolution formula of this queue is as follows:

[0151]

[0152] where Q(0) = 0, indicating that there is no accumulated unmet latency initially in the system, and L(t) can be regarded as the arrival rate of the queue, which can be obtained from formula (2).

[0153] Next, the following lemma is used to ensure that the stability of the virtual queue can satisfy the long-term trial constraint condition (5).

[0154] Lemma 1: If the queue Q(t) is strongly stable, i.e., then the constraint (5) is satisfied, where, denotes taking the expected value.

[0155] Proof: For the queue evolution formula given by formula (6), obviously Summing from t = 1 to t = T, we get If Q(t) is stable, then When T → ∞, we can obtain Therefore, the constraint (5) is satisfied.

[0156] Define a quadratic Lyapunov function to represent the congestion degree of the queue. The Lyapunov drift captures the change in the congestion degree, which is given by the formula Next, a drift-penalty function is introduced to balance the goals of minimizing energy consumption and maximizing queue stability, i.e., Here, V ≥ 0 is a constant that controls the balance between minimizing energy consumption and maintaining queue stability. The goal is to minimize the drift-penalty function for each time slot, which optimizes energy consumption while ensuring long-term average delay. However, directly minimizing the Lyapunov drift function is complex. To overcome this problem, an upper bound is established for the drift function.

[0157] Lemma 2: The upper bound of the drift-penalty function can be established as Where C is a bounded constant.

[0158] Proof: By squaring equation (6) and applying the inequality (max{ab,0}+c)≤a 2 +b 2 +c 2 +2a(cb), we can get

[0159] Among them, the constant term is a finite value.

[0160] Therefore, the drift function is restricted to: Adding penalty terms on both sides gives the target expression.

[0161] This upper bound enables us to minimize the upper bound, thus providing a practical method to balance energy consumption and long-term delay constraints. Therefore, we finally get an optimization problem applicable to each time slot t, that is, converting problem P1 into a single time slot deterministic optimization problem P2, that is,

[0162]

[0163] The constraints are:

[0164]

[0165]

[0166] By introducing the Lyapunov optimization framework, the original multi-slot stochastic optimization problem is transformed into a more tractable single-slot deterministic optimization problem, which simplifies the optimization process and enables online adjustment.

[0167] For any time slot t, obtain the current state of the queue Q(t), solve problem P2 based on the penalty dual decomposition method, and generate the optimized power allocation and unloading decisions of all satellites in time slot t;

[0168] According to the optimized power allocation and offloading decisions obtained at time slot \(t\), based on the evolution formula of the virtual queue, update the queue state for the next time slot, and then solve problem P2 again based on the method of penalty dual decomposition to generate the optimized power allocation and offloading decisions for the next time slot until all time slots are optimized. The algorithm details are summarized in Algorithm 1.

[0169]

[0170] To solve the binary constraint (3), the present invention uses the method of penalty dual decomposition (PDD) to solve problem P2. Introduce the auxiliary variable and there are the following constraint conditions:

[0171]

[0172]

[0173] Obviously, only when the equality constraint holds, and including these equality constraints will not change the actual feasible solution space of the problem. Therefore, problem P2 is transformed into problem P3:

[0174]

[0175] The constraint conditions are:

[0176]

[0177] It should be noted that is added in formulas (9) and (10), while is not added in the constraint conditions of problem P3. This is because also needs to be satisfied, and in the context of the specific problem P3, the multi-time-slot (i.e., stage) stochastic optimization problem has been transformed into a single-time-slot deterministic optimization problem in P3. Therefore, the constraint is not required here.

[0178] Next, to solve the equality constraint problem, problem P3 is transformed into problem P4:

[0179]

[0180] The constraint conditions are:

[0181]

[0182] where

[0183] P ρ is the penalty term,

[0184] ρ represents the penalty parameter, which is used to control the scaling of the penalty term; as ρ decreases, the penalty associated with the violation of the constraint increases, thus ensuring the discreteness of the variables;

[0185] and respectively represent the dual variables of the equality constraint and ;

[0186] Through the nested optimization framework, the optimization of the dual variables and the penalty parameter is co - optimized with the variables in Problem P4, so as to obtain the solution result of Problem P2.

[0187] Furthermore, the nested optimization framework has a two - layer structure, namely, an outer loop and an inner loop,

[0188] The outer loop is used for updating the dual variables and as well as the penalty parameter ρ, and the update method is expressed as:

[0189]

[0190]

[0191] ρ←τρ, (14)

[0192] where 0 ≤ τ ≤ 1 represents the control parameter, which is used to control the value of the outer - iteration penalty term P ρ ;

[0193] In the inner loop, the alternating optimization technique is adopted to optimize the variables in the inner loop. The variables in the inner loop are divided into three blocks: and One optimization process of the variables in the inner loop includes:

[0194] First, fix the second and third blocks to obtain the closed - form solution of :

[0195]

[0196] Then, fix the first and third blocks, that is, fix The optimization of the second block (i.e., ) is expressed as Problem P5:

[0197]

[0198] The constraint conditions are:

[0199]

[0200] Solve problem P5 using a convex optimization tool (such as existing optimization tools like CVX) to obtain a s (t);

[0201] Next, fix the first and second blocks, that is, fix The optimization of the third block (i.e., ) is expressed as problem P6:

[0202]

[0203] The constraints are:

[0204]

[0205] Solve problem P6 using a method based on quadratic transformation and SCA to obtain p s (t).

[0206] Furthermore, for the solution of problem P2, refer to Algorithm 2, which specifically includes:

[0207] In the inner loop, by generating a s (t) and p s (t) each time for optimization, determine the objective function value in problem P4;

[0208] Use the a s (t) and p s (t) generated in this optimization to update the variables in the inner loop for the next optimization, and generate the a s (t) and p s (t) for the next optimization, and determine the objective function value in problem P4 again. When the reduction rate of the objective function value in problem P4 is lower than the preset threshold ε I , end the optimization process of this inner loop;

[0209] Use the finally generated and a s (t) in this inner loop to determine the maximum constraint violation:

[0210]

[0211] If then update the dual variables and using the update method of the dual variables and , where k0 represents a preset value;

[0212] Otherwise, update the penalty parameter ρ using the update method of the penalty parameter ρ;

[0213] After the outer loop update is completed, use and the updated results of ρ, as well as a s (t) and p s (t) generated in this inner loop to determine the objective function value in Problem P2;

[0214] Repeat the parameter update of the outer loop and the parameter optimization process of the inner loop until the reduction rate of the objective function value in Problem P2 is lower than the preset threshold ε0. Thus, the solution to Problem P2 is completed.

[0215]

[0216] For Problem P6, this problem optimizes the transmit power given the offloading decision. Note that the objective function contains a fractional term which introduces significant computational complexity. To solve this problem, a quadratic transformation method is adopted, which has stability and equivalence in dealing with such non-convex terms. Specifically, is rewritten as where y s (t) is an auxiliary variable used for auxiliary transformation. During the optimization process, y s (t) and p s (t) are iteratively updated.

[0217] At the k-th iteration, we get:

[0218]

[0219] This enables the communication energy to be expressed as:

[0220] Therefore, the quadratic transformation decouples the numerator and denominator. Although is still non-convex, applying the first-order Taylor approximation at the given point p s (k) (t), we obtain “ ” represents the definition symbol, represents the linearized upper bound of. By replacing with effectively converts the original non-convex term into a linear form, making the problem easier to handle.

[0221] This process is further simplified by applying the first-order Taylor approximation at the given point. Therefore, the energy consumption expression is approximated as:

[0222]

[0223] Specifically, solving problem P6 through the method based on quadratic transformation and SCA may include the following process:

[0224] Adopt the quadratic transformation method to transform into

[0225] Transform by linear transformation;

[0226] According to the result of the linear transformation, convert the objective function in problem P6 into a convex function;

[0227] Use the convex optimization tool to solve the objective function converted into a convex function through the SCA method, so as to obtain the final solution result of p s (t) in problem P6.

[0228] Furthermore, specifically including solving problem P6 through the method based on quadratic transformation and SCA:

[0229] At the k-th iteration, obtain and respectively represent p s (t), R s (t) and y s (t) at the k-th iteration;

[0230] Apply the first-order Taylor approximation at the given point p s (k) (t) to obtain

[0231] Use to replace in

[0232] According to and determine so as to obtain

[0233] Replace E(t) with E′(t);

[0234] Then, problem P6 can be approximately replaced by problem P7:

[0235]

[0236] The constraint conditions are:

[0237]

[0238] Among them, R s (t) and ys (t) are respectively replaced with and to replace,

[0239] Use a convex optimization tool (such as the CVX optimization tool) to solve problem P7 (P7 is a convex optimization problem), so as to obtain the optimized p generated in this iteration s (t);

[0240] Use the optimized p s (t) generated in this iteration to update p s (t) for the next iteration and update R s (t) and y s (t) in turn, and solve problem P7 again. Repeat the above iteration process until the termination iteration requirement is met (for example, the reduction rate of the objective function value in P7 is lower than the preset threshold ε p ). The finally generated p s (t) is the solution result of problem P6. The complete algorithm for solving sub-problem (P6) is shown in Algorithm 3, and this algorithm iteratively updates the value of p s (t) until convergence.

[0241]

[0242] The present invention also provides a joint optimization system for task offloading and power control in a satellite edge computing network, and this system includes:

[0243] A memory, configured to store a computer program;

[0244] A processor, configured to execute the computer program to implement the joint optimization method for task offloading and power control in the satellite edge computing network as described above.

[0245] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the joint optimization method for task offloading and power control in the satellite edge computing network as described above.

[0246] The effectiveness of the proposed method is verified through simulation experiments. Consider a cooperative working scenario consisting of 5 satellites operating at the same orbital altitude. The simulation is implemented using the Satellite Tool Kit (STK), and the typical LEO satellite parameters are set with reference to the paper "Q. Wang, X. Chen, Q. Qi, M. Li, and W. Gerstacker, “Multiple-satellite cooperative information communication and location sensing in leo satellite constellations,” IEEE Trans. Wireless Commun., pp. 1–1, 2025": Each satellite maintains an orbital altitude of approximately 500 km from the Earth's surface, and the position of the ground station is set to ensure that the satellites pass overhead dynamically, thus realistically simulating the change of the space-ground distance d s (t). The space-ground communication link operates in the Ka band with a carrier frequency of 20 GHz. The number of computing tasks arriving at the satellite in each time slot is modeled as a random value with an upper limit D max . Unless otherwise specified, the system parameters are set as follows: B = 50 MHz, σ 2 = -203 dBm / Hz, the maximum transmit power P of each satellite max = 10 W (i.e., ), The total operating period is 100 seconds (i.e., T = 100), δ = 1 s, f s = 1 GHz, f g = 10 GHz.

[0247] Figure 2(a) shows that Algorithm 1 based on Penalty Dual Decomposition (PDD) converges within 10 iterations, demonstrating fast and efficient optimization characteristics. Figure 2(b) further evaluates the algorithm performance under different transmit powers: As the transmit power increases, the enhanced data transmission rate shortens the transmission delay, but the energy consumption change shows a non-linear characteristic - when the power is low, the significant reduction in transmission time dominates the energy consumption reduction; while when the power exceeds the critical value, the marginal benefit of time reduction weakens, and the positive effect of power increase dominates, resulting in an increase in total energy consumption. This non-linear relationship makes the objective function show a convex characteristic of first decreasing and then increasing, verifying the importance of choosing the optimal power level for the delay-energy efficiency trade-off. The method of the present invention realizes a significant improvement in system performance by accurately identifying this optimal balance point.

[0248] Figures 3(a) and 3(b) show the average transmit power and task offloading ratio of the five satellites within the total time range. It can be clearly observed from Figures 3(a) and 3(b) that as D maxWith the increase of [[ID=]], both the transmission power and the offloading ratio show an upward trend. This indicates that when the scale of the computing task increases, the satellite tends to offload tasks to the ground station with higher power, thereby alleviating the local computing load and ensuring that the latency constraint is met.

[0249] To demonstrate the performance advantages of the proposed algorithm, the following benchmark schemes are selected for comparison: Maximum Power Full Offloading (MPFO) (see "K. Wang, Y. Zhou, J. Li, L. Shi, W. Chen, and L. Hanzo, “Energy-efficient task offloading in massive mimo-aided multi-pair fog computing networks,” IEEE Trans. Commun., vol. 69, no. 4, pp. 2123–2137, 2021"), Maximum Power Random Offloading (MPRO) (see J. Zhou, J. Liang, L. Zhao, S. Wan, H. Cai, and F. Xiao, “Latency-energy efficient task offloading in the satellite network-assisted edge computing via deep reinforcement learning,” IEEE Trans. Mobile Comput., vol. 24, no. 4, pp. 2644–2659, 2025.) and Genetic Algorithm-based method (GA) (see "J. Tian, D. Wang, H. Zhang, and D. Wu, “Service satisfaction-oriented task offloading and uav scheduling in uav-enabled me networks,” IEEE Trans. Wireless Commun., vol. 22, no. 12, pp. 8949–8964, 2023.” and “L. He, J. Li, Y. Wang, J. Zheng, and L. He, “Balancing total energy consumption and mean makespan in data offloading for space-air-ground integrated networks,” IEEE Trans. Mobile Comput., vol. 23, no. 1, pp. 209–222, 2024.”). The comparison results are shown in Figs. 4(a) and 4(b). Fig. 4(a) shows that as the maximum task size D maxWith the increase of , the energy consumption of all solutions shows an upward trend. The method proposed in the present invention is based on an optimized task offloading decision and an adaptive power control mechanism, showing significant advantages in terms of delay-energy consumption balance, and its energy consumption level is always lower than that of the comparison solutions. Figure 4(b) reveals the delay characteristics under different task scales: when D max is relatively small, all methods can meet the delay constraint; however, as the task scale increases, the MPRO and GA solutions quickly exceed the delay threshold. The MPFO solution maintains delay guarantee through a high-power full offloading strategy, but at the cost of excessive energy consumption. In contrast, the algorithm in the present invention dynamically adjusts the power and offloading strategy based on the Lyapunov optimization framework, achieving energy consumption minimization while strictly meeting the delay constraint. The experimental results show that this method can maintain robust performance under different load conditions, verifying the effectiveness of the proposed balance mechanism.

[0250] In summary, for the long-term stochastic optimization problem in satellite edge computing task offloading, the present invention proposes a delay-energy consumption balance optimization framework for dynamic task arrivals. By integrating the Lyapunov optimization and virtual queue mechanisms, the long-term delay constraint is successfully transformed into an online executable time-slot level optimization goal, realizing an adaptive decision-making process. For the resulting non-convex optimization problem, a robust solution algorithm is constructed under the PDD framework, integrating quadratic transformation and SCA techniques to achieve efficient solution. The simulation experiments show that the proposed method can significantly reduce the energy consumption in the scenario of random task arrivals while strictly meeting the delay constraint requirements.

[0251] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A joint optimization method for task offloading and power control in a satellite edge computing network, characterized in that Including: Establish a system model, where the system model includes a satellite-ground network composed of S satellites and a ground server; Construct a system objective function and constraint conditions to form an optimization problem P1 to minimize the total energy consumption of all satellites while satisfying the long-term average delay constraint; Use the Lyapunov optimization method to transform the optimization problem P1 into a single-slot deterministic optimization problem and solve it to obtain the optimal satellite offloading decision and optimal power allocation.

2. The joint optimization method for task offloading and power control in the satellite edge computing network according to claim 1, wherein The optimization problem P1 is expressed by the formula: The constraint conditions are: Where, The system objective function represents minimizing the total energy consumption of all satellites during the total operation period of the system; E(t) represents the total energy consumption of all satellites at time slot t; S represents the total number of satellites, T represents the total number of time slots during the system operation period; p s (t) represents the transmission power of satellite s at time slot t; represents the maximum transmission power of satellite s; a s (t) represents the offloading decision variable. When a s (t) = 0, it means that the data received by satellite s at time slot t is locally computed. a s (t) = 1 means that the data received by satellite s at time slot t is offloaded to the ground server; D s (t) represents the amount of data received by satellite s at time slot t; represents the achievable data rate of satellite s to the ground server at time slot t; the link bandwidth B is divided into S sub - carriers, represents the channel gain between satellite s and the ground server at time slot t, σ 2 represents the noise power, g tx and g rx represent the gains of the satellite transmitter and the ground server receiver respectively; β represents the wavelength of the communication signal; d s (t) represents the distance between satellite s and the ground server at time slot t; F rain represents the rain fade; k s represents the effective switched capacitance when satellite s performs local calculations; w represents the number of CPU cycles per bit; f s represents the CPU processing frequency of satellite s; Represents the long-term average delay of all satellites over the entire operating cycle; Indicates the maximum time delay allowed by the system; Represents the average delay of all satellites; Represents the total time delay of satellite s; represents the total time delay during the offloading of satellite s, f g represents the processing frequency of the ground server; c represents the speed of light.

3. The joint optimization method for task offloading and power control in the satellite edge computing network according to claim 2, characterized in that, Using the Lyapunov optimization method, solving the objective function includes: Using the Lyapunov optimization framework, transform the optimization problem P1 into a single-slot deterministic optimization problem P2, that is The constraint conditions are: Among them, Q(t) represents the virtual queue, which is used to track the cumulative unmet delay. The evolution formula of this virtual queue is: Among them, Q(0) = 0; V is a constant used to control the balance between the minimum energy consumption of all satellites and maintaining the stability of the virtual queue; For any time slot t, obtain the current state of the queue Q(t), and solve the problem P2 based on the penalty dual decomposition method to generate the optimized power allocation and offloading decision of all satellites in the time slot t; According to the optimized power allocation and offloading decision obtained at time slot t, update the queue state of the next time slot according to the evolution formula of the virtual queue, and again solve the problem P2 based on the penalty dual decomposition method to generate the optimized power allocation and offloading decision for the next time slot until all time slots are optimized.

4. The joint optimization method for task offloading and power control in the satellite edge computing network according to claim 3, wherein Solving the problem P2 based on the penalty dual decomposition method includes: First, transform the problem P2 into the problem P3: The constraint conditions are: wherein, is an auxiliary variable; Then, transform the problem P3 into the problem P4: The constraint conditions are: Where, P ρ is the penalty term, ρ represents the penalty parameter used to control the scaling of the penalty term; and respectively represent the dual variables of the equality constraint and ; Through the nested optimization framework, co-optimize the optimization of the dual variable and the penalty parameter with the variables in the problem P4 to obtain the solution result of the problem P2.

5. The joint optimization method for task offloading and power control in the satellite edge computing network according to claim 4, characterized in that The nested optimization framework has a two-layer structure, namely an outer loop and an inner loop, The outer loop is used for updating the dual variables and as well as the penalty parameter ρ, and the update method is expressed as: where \(0\leqslant\tau\leqslant1\) represents a control parameter for controlling the value of the outer iteration penalty term \(P\). ρ value; In the inner loop, an alternating optimization technique is used to optimize the variables in the inner loop. The variables in the inner loop are divided into three blocks: and For one optimization process of the variables in the inner loop, it includes: First, fix the second and third blocks to obtain the closed-form solution of Then, fix the first block and the third block, and the optimization of the second block is expressed as the problem P5: The constraint conditions are: The problem P5 is solved by a convex optimization tool to obtain a s (t); Then, fix the first block and the second block, and the optimization of the third block is expressed as the problem P6: The constraint conditions are: Solve problem P6 through a method based on quadratic transformation and SCA to obtain p s (t).

6. The joint optimization method for task offloading and power control in the satellite edge computing network according to claim 5, wherein The specific solution of the problem P2 includes: In the inner loop, by generating each time through optimization a s (t) and p s (t), the objective function value in problem P4 is determined; Generated by this optimization a s (t) and p s (t) updates the variables in the inner loop during the next optimization to generate the a s (t) and p s (t), and determines the objective function value in problem P4 again. When the reduction rate of the objective function value in problem P4 is lower than the preset threshold ε I the optimization process of this inner loop is terminated; Finally generated using this inner loop and a s (t), determine the maximum constraint violation: If then use the update method of the dual variables and to update the dual variables and , where k0 represents a preset value; Otherwise, update the penalty parameter ρ using the update method of the penalty parameter ρ; After the outer loop update is completed, using and the update results of ρ, and the a s (t) and p s (t), determine the objective function value in problem P2; Repeat the parameter update of the outer loop and the parameter optimization process of the inner loop until the reduction rate of the objective function value in the problem P2 is lower than the preset threshold ε0. At this point, the solution of the problem P2 is completed.

7. The joint optimization method for task offloading and power control in the satellite edge computing network according to claim 5, characterized in that Solving the problem P6 through the method based on quadratic transformation and SCA includes: Using a secondary transformation method, transform into where y s (t) is an auxiliary variable used for assisting the transformation; Perform a linear transformation; Convert the objective function in the problem P6 into a convex function according to the result of the linear transformation; Using convex optimization tools, the objective function converted into a convex function is solved by the SCA method, so as to obtain the final solution result of p s (t) in Problem P6.

8. The joint optimization method for task offloading and power control in the satellite edge computing network according to claim 7, wherein The specific solution of the problem P6 through the method based on quadratic transformation and SCA includes: At the k-th iteration, we obtain and represent p at the k-th iteration s (t), R s (t) and y s (t); At a given point p s (k) (t), applying the first-order Taylor approximation gives " ” denotes the definition symbol, denotes the linearized upper bound of; Use Replace in According to and determine so as to obtain Replace E(t) with E′(t), where, Then, replace the problem P6 with the problem P7: The constraint conditions are: Among them, R in the objective function in problem P7 s (t) and y s (t) are respectively replaced by and respectively. Solve problem P7 using convex optimization tools to obtain the optimized p generated in this iteration s (t); Use the optimized p s (t) generated in this iteration to update p s (t) for the next iteration, and then update R s (t) and y s (t) in sequence. Solve problem P7 again, repeat the above iterative process until the iterative termination requirement is met, and the finally generated p s (t) is the solution to problem P6.

9. A joint optimization system for task offloading and power control in a satellite edge computing network, characterized in that, Including: A memory configured to store a computer program; A processor, configured to execute the computer program to implement the joint optimization method for task offloading and power control in the satellite edge computing network according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the joint optimization method for task offloading and power control in the satellite edge computing network according to any one of claims 1 to 8.

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