A joint optimization method of sensing, transmission and computing for networked control systems based on information timeliness

Abstract

The present invention discloses a joint optimization method of sensing, transmission and computing of a networked control system based on information timeliness, including the following steps: S1, constructing information timeliness models in resource independent allocation scenarios and resource sharing scenarios; S2, calculating generalized information timeliness, equipment transmission energy consumption and equipment computing energy consumption in resource independent allocation scenarios; S3, quantifying system performance and efficiency with equipment cost, establishing an optimization problem to minimize transmission and computing energy consumption while ensuring fairness, and maximizing information timeliness; solving the optimization problem to obtain the optimal sampling strategy and resource allocation strategy. The present invention jointly considers the three processes of data collection, transmission and computing in the information flow loop of the networked control system, derives information timeliness value indicators under different edge unloading modes, and designs perception strategies and communication and computing joint resource allocation schemes based on this to improve the overall performance and efficiency of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of communication resource scheduling, and in particular to a sensing, transmission and computing joint optimization method for a networked control system based on information timeliness. Background Art

[0002] With the advent of a new era of interconnected intelligence, today's networks are developing into integrated communication and computing systems, with information flowing periodically and continuously in the control loop formed by edge physical devices and computing servers. Widely distributed edge devices continuously collect time-varying environmental data, generate computationally intensive perception tasks, and offload them to the network upper layer servers to extract state information, which is further used for downstream task decisions such as real-time reconstruction or estimation.

[0003] In integrated communication and computing systems, traditional indicators such as throughput and latency can no longer fully characterize system performance. It is necessary to expand the goal of system design from error-free data transmission to the usefulness of information for subsequent control tasks, and establish new time-value performance indicators for the unified process of information collection and processing. In addition, in such systems, the data collection, transmission, and computing processes are highly coupled and mutually constrained. Under limited network resources, the separate design of communication and computing systems cannot match this feature, resulting in reduced resource utilization. Therefore, it is necessary to redesign the task-oriented communication and computing architecture and develop an efficient multi-dimensional resource joint allocation method.

[0004] Existing edge computing technologies distribute the computing, storage, and communication pressures of central nodes to edge nodes with weaker computing power by distributing storage and computing power on nodes at the edge of the network, thereby achieving low latency, high reliability, and low cost of services. In order to meet latency requirements and device energy constraints, it is necessary to design a reasonable computing offloading strategy to fully utilize the computing resources distributed on each node and balance the workload between different nodes. For single-user scenarios, strategy design focuses on balancing the energy consumption and completion latency of task offloading; for multi-user scenarios, due to resource competition among users, the offloading problem is more complicated, and it is necessary to consider the joint optimization of communication and computing resources among users.

[0005] There are usually two modes for existing computing task offloading: integrated offloading and partial offloading. In the integrated offloading mode, highly integrated or relatively simple tasks cannot be divided and must be executed as a whole on the device or server side. In the partial offloading mode, the computing task is split into different components and executed on the terminal and server side respectively, which can improve the offloading efficiency by optimizing the data volume distribution on both ends.

[0006] In existing work, the design of offloading strategies mainly focuses on the resource utilization and system efficiency of single offloading. However, in networked control scenarios with strict time requirements, the state update information in the calculated tasks is time-dependent, and it is necessary to analyze the long-term time evolution of the state information in the continuous task flow. Due to the randomness of computing task generation and the time-varying nature of workload, simply applying existing computing offloading strategies to process continuously generated tasks separately will lead to system resource waste and performance degradation.

[0007] Age of Information (AoI), as the first proposed metric to measure the freshness of information, is defined as the time elapsed since the latest data received by the destination node was generated. It extends the traditional transmission delay metric and takes into account the periodic generation process of information. On this basis, Peak Age of Information (PAoI) focuses on the worst case of system timeliness performance and is an important metric in scenarios with strict timeliness requirements and low fault tolerance. The specific manifestation of PAoI is usually derived with the help of queuing theory. Under different business scenarios and transmission mechanisms, the generation of tasks is abstracted into different random processes, and the wireless network transmission process is modeled as various queues with different service times, buffer numbers, and packet management technologies. Since the queuing waiting process of tasks in the transmission queue will lead to unnecessary increase in age, the zero-wait sampling strategy, that is, sampling only when the channel is idle, has also received widespread attention.

[0008] In edge computing systems, considering the two continuous processes of task offloading and processing, the information age measurement model is extended from a single transmission queue to a transmission and computing series queue, which is divided into a transmission-computation series mode and a computing-transmission series mode according to the offloading strategy. Under different communication standards and computing schemes, the information processing process is modeled as different forms of series queues, and the expression of peak information age is derived to guide the resource allocation and update strategy design of the system.

[0009] Related work on peak information age mainly studies linear time-dependent models that grow at a unit rate in different scenarios, which only characterizes the temporal properties of information. However, in specific scenarios, the temporal change law of information is affected by many factors, such as the structural characteristics of the observation process, the rate of environmental change, and system resource limitations. In addition, different application scenarios have different requirements for data. Therefore, linear models cannot accurately represent the value of data and cannot be used to guide the design of actual systems.

[0010] In addition, most works only study single-user scenarios or multi-user scenarios oriented to the communication process, without considering the information flow fusion and resource competition between multiple users in the edge computing system during the transmission and computing processes. Summary of the invention

[0011] The purpose of the present invention is to propose a joint optimization method for sensing, transmission and computing of a connected control system based on information timeliness, jointly consider the three processes of data acquisition, transmission and calculation in the information flow loop of the connected control system, derive the information timeliness value index under different edge unloading modes, and based on this, design a perception strategy and a communication and computing joint resource allocation scheme to improve the overall performance and efficiency of the system.

[0012] In order to achieve the above object, the present invention provides the following technical solutions:

[0013] A sensor-transmission-computation joint optimization method for a networked control system based on information timeliness comprises the following steps:

[0014] S1. Constructing a generalized information timeliness model in resource independent allocation scenarios:

[0015]

[0016] Among them, λ is the average task generation rate, μ t is the average task transmission service rate, μ c Calculate the service rate for the average task;

[0017] S2, generalized information timeliness, transmission energy consumption of devices, and computing energy consumption of devices in the scenario of independent allocation of computing resources;

[0018] S3. Quantify system performance and efficiency using equipment cost, and establish an optimization problem to minimize transmission and computing energy consumption while ensuring fairness, while maximizing information timeliness; solve the optimization problem to obtain the optimal sampling strategy and resource allocation strategy.

[0019] Further,

[0020] In the special mode of zero-wait strategy, the formula for generalized information timeliness in the resource independent allocation scenario is:

[0021]

[0022] Furthermore, the information timeliness of the equipment also includes the following models: process-oriented information timeliness in resource independent allocation scenarios, generalized information timeliness in resource sharing scenarios, and process-oriented information timeliness in resource sharing scenarios.

[0023] Furthermore, the formula for process-oriented information timeliness in the resource independent allocation scenario is:

[0024]

[0025] Among them, κ is the structural parameter related to the regression rate, σ 2is the variance of the observation process, λ is the average task generation rate, μ t is the average task transmission service rate, μ c Calculate the service rate for the average task;

[0026] In the special mode of zero-wait strategy, the formula for process-oriented information timeliness in the resource independent allocation scenario is:

[0027]

[0028] Furthermore, the formula for the information timeliness of generalized information timeliness in the resource sharing scenario under the zero-wait strategy is:

[0029]

[0030] where μ i，t is the average task transmission service rate of device i, μ -i，t is the sum of the average task transmission service rates of the remaining devices, μ c Calculate the service rate for the average task.

[0031] Furthermore, the upper bound of the process-oriented information timeliness in the resource sharing scenario under the zero-wait strategy is:

[0032]

[0033] in,

[0034]

[0035]

[0036]

[0037]

[0038] κ is a structural parameter related to the regression rate, σ 2 is the variance of the observation process, μ i，t is the average task transmission service rate of device i, μ -i，t is the sum of the average task transmission service rates of the remaining devices, μ c Calculate the service rate for the average task.

[0039] Furthermore, the formula for the transmission energy consumption of device k in the resource independent allocation scenario in step S2 is:

[0040]

[0041] where p k represents the transmission power of device k, β kIndicates the ratio of the bandwidth allocated to device k to the total available bandwidth, is the average transmission rate of device k, B represents the total available bandwidth, N0 represents the noise power spectral density, and D k represents the size of the task package generated by device k, which follows the mean The exponential distribution of Represents a collection of devices, h k Indicates the uplink channel gain of the edge device;

[0042] The formula for calculating the energy consumption of tasks offloaded to device k is:

[0043]

[0044] Where α is a coefficient related to the chip structure, f k Indicates the CPU frequency pre-allocated to device k, c k Indicates the number of CPU cycles required to process 1 bit of data;

[0045] The generalized information timeliness of device k is expressed as:

[0046]

[0047] λ k is the average task generation rate, is the average task transmission service rate, Calculate the service rate for the average task.

[0048] Furthermore, in step S3, the equipment cost in the resource independent allocation scenario is expressed as:

[0049]

[0050] Where ω is a continuous variable, and ω∈[0,1], which is used to adjust the trade-off between information timeliness and total energy consumption of transmission calculation. is the transmission energy consumption of device k, The computing energy consumption of the device.

[0051] Furthermore, in step S3, the optimization problem in the resource independent allocation scenario is expressed as:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] Among them, C k For equipment cost.

[0064] Furthermore, the problem solving process of step S3 is:

[0065] Introduce an auxiliary variable τ and transform the original problem into Problem 2:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] Introduce a series of auxiliary variables Problem 2 is simplified, and continuous convex approximation is performed on the non-convex terms to convert Problem 2 into convex optimization problem 3 at the current solution:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] in To optimize the set of variables:

[0092] Given an initial feasible solution Use the convex optimization solver to repeatedly solve Problem 3 at the current solution until convergence, and obtain the final resource allocation and task generation strategy.

[0093] Compared with the prior art, the present invention has the following beneficial effects:

[0094] The present invention provides a joint optimization method for sensing, transmission and calculation of networked control systems based on information timeliness. First, the linear information age model that only considers time attributes is extended to other dimensions, and the statistical characteristics of the monitored physical process are analyzed to establish a mathematical modeling framework for task-oriented information timeliness indicators. By analyzing the structural characteristics of the information source, the mean square estimation error is used as a measure of information timeliness. Taking the common Gauss-Markov process as an example, the linear minimum mean square error estimation method is used to derive the nonlinear functional relationship between the mean square estimation error and the information age, thereby establishing a connection between the timeliness of information and the actual system design indicators.

[0095] Secondly, considering the two different modes of independent allocation and shared use of computing resources among multiple users in edge computing systems, the paper analyzes the dual resource limitations of communication and computing when multi-user computing resources are shared, as well as the combined impact of other user data inflows on the system latency of a single user, and creatively derives the expressions of information timeliness in the two scenarios. Considering the randomness of communication and computing resources, the perception data cannot be calculated and processed in time, forming multiple waiting queues in the system. Therefore, the data transmission and computing process is modeled as a serial multi-queue model. Based on queuing theory and probability theory, the mathematical expression of information timeliness under resource constraints is derived by analyzing the joint probability density of data sampling intervals and system time in the queues, as well as the coupling relationship between serial queues.

[0096] Finally, based on the information timeliness measurement index derived above, the problem of minimizing the information timeliness and system energy consumption of edge computing offloading based on user fairness under the dual resource constraints of communication and computing is proposed. The task generation, communication resource allocation and computing resource allocation are jointly optimized to achieve end-to-end performance optimization of sensing, transmission and computing integration. Compared with the independent optimization of the three stages in existing work, the overall efficiency of the system is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0098] Figure 1 A schematic diagram of the system scenario.

[0099] Figure 2 Schematic diagram of the time evolution of the estimation error.

[0100] Figure 3 It is a queue model for parallel computing mode.

[0101] Figure 4 It is a serial computing mode queue model. DETAILED DESCRIPTION

[0102] The present invention establishes a task-oriented information timeliness measurement index by analyzing the structural characteristics of the observed physical process to reveal the real-time estimation error of the system. At the same time, the different utilization mechanisms of computing resources in edge computing are considered, and the impact of resource competition among users is analyzed. Based on the established timeliness index, an efficient communication computing resource joint allocation and information update strategy is designed. In order to better understand the present technical solution, the method of the present invention is described in detail below with reference to the accompanying drawings.

[0103] 1. System scenario

[0104] Consider edge computing-assisted computationally intensive connected control systems, such as Figure 1 As shown in the figure, widely distributed sensors monitor the relevant physical processes in their surrounding environment. The multi-sensor data fusion device collects the data information collected by the sensors monitoring the same physical process, encapsulates it into a perception task, and uploads it to the edge server. The edge server extracts the state information in the perception task through calculation to estimate the real-time state of the environment, and deduce the control decision of the downstream task based on it. Due to the dynamic changes of communication and computing resources and the influence of other users on resource occupation, the communication and computing resources available to a single data fusion device change randomly. Therefore, the generated perception tasks cannot be transmitted and processed in time, and may form a sending waiting queue on the device side or a computing waiting queue on the edge server.

[0105] Based on the different ways of allocating computing resources, the following two common computing modes are considered. 1) Parallel computing mode: The computing resources in the edge server are pre-allocated to each connected device by setting up a virtual machine. Specifically, each device independently generates a perception task and sends it to the edge server. Each server has multiple virtual machines, which are virtual computers configured with a certain amount of server hardware resources (such as CPU, memory, and I / O bus). To this end, the server can provide independent services for the connected devices and perform parallel computing of perception tasks. 2) Serial computing mode: Each device independently generates a perception task and sends it to the edge server. The edge server uses all computing resources to process each task in the order of arrival.

[0106] 2. Information Timeliness Evolution Model

[0107] In the above real-time control system, information timeliness is an important indicator that affects system performance. It is directly related to the time since the data at the receiving end was generated, and reveals the degree of mismatch between the state estimation result and the real-time state. In the present invention, we use the state estimation error as a measurement indicator and use two forms to describe the timeliness of information: 1) generalized information timeliness (Δ), when the relevant prior knowledge of the observed process cannot be obtained, it is assumed that the estimation error grows linearly with time; 2) process-oriented information timeliness (V), that is, using the physical characteristics of the actual process to obtain a more targeted estimation error expression. Under this definition, the smaller the estimation error, the higher the information timeliness.

[0108] 2.1 Generalized Information Timeliness Model

[0109] For dynamic time-varying processes, generally speaking, the fresher the information obtained by the receiver, the more accurately it can infer the current real-time state and the smaller the estimation error. Therefore, in the absence of prior knowledge about the monitoring process, we assume that the estimation error grows linearly over time.

[0110] For any device, assuming that at any time t, the generation time of the latest task being calculated and processed is u(t), then the estimation error of the edge server is the time elapsed since the latest state information was generated, which can be expressed as a random process Δ(t) = tu(t). Figure 2 As shown in (a), under continuous information flow, Δ(t) is a sawtooth function with respect to time. When the new system state is not obtained, the estimation error Δ(t) increases linearly with time and drops sharply at the moment of obtaining the new system state. The peak estimation error (Δ n ) is the maximum value of the estimation error associated with task n, that is, the estimation error at the moment before the next task is calculated. Let X n represents the generation interval between tasks n and n-1, T n is the system delay of task n (including two continuous processes of transmission and calculation), For observing The number of tasks generated within the time interval. The average peak estimation error of all perception tasks is taken as the measure of generalized information timeliness, which can be expressed as:

[0111]

[0112] 2.2 Process-oriented information timeliness model

[0113] If prior knowledge of the observation process is known, the intrinsic structure and temporal correlation of the observed signal can be exploited to obtain a more targeted measure of information timeliness, rather than just the linear relationship mentioned above.

[0114] We consider a stationary Gaussian-Markov process Z t , whose variance is σ 2 , the kernel function is in exponential form. This type of process can usually be used to represent physical processes such as node movement in mobile self-organizing networks, robot swarms, and drone systems. For any device, assuming that at any time t, the generation time of the latest task being calculated and processed is u(t), the server extracts the state information Z at the time u(t) from it u(t) , the linear minimum mean square error estimation method is used to predict the real-time state Z of the information source t , the estimated result is The estimated error is where κ is a structural parameter related to the regression rate. Figure 2(b) shows the time evolution trend of the estimation error V(t) in this case. Assuming that the nth perception task is at t n Generated at time t′ n The time at which the task n is processed by the server is the same as the generalized information timeliness index mentioned above. We also consider the worst extreme case of system performance, that is, the peak estimation error of any task n before the calculation is completed. The average peak estimation error of all perception tasks is used as an indicator of information timeliness:

[0115]

[0116] 3. Timeliness evaluation of dual randomness of communication and computing resources

[0117] Next, we analyze the specific expressions of the two types of information timeliness indicators in 2 for the two computing scenarios described in 1.

[0118] 3.1 Timeliness Evaluation in Independent Allocation of Computing Resources

[0119] Since the computing resources are independently allocated, the server provides parallel computing services to the connected devices, and the task calculations of each device are independent of each other, so only the situation of a single device needs to be analyzed. Due to the use of multi-sensor fusion technology, the sampling frequency and data packet size of each sensor are different. At the same time, considering the actual hardware errors such as the frequency drift of the crystal oscillator, the generation of perception tasks can be assumed to be a Poisson process with an average generation rate of λ. Assuming that the uplink communication link is a quasi-static channel and the server calculation frequency remains unchanged, due to the randomness of the perception task packet size, it can be assumed that the service time of transmission and calculation obeys the average rate of μ t and μ c In addition, assuming that the queue lengths at both the transmission and computation locations are not limited, and that the transmission and computation processes of tasks follow the first-come, first-served (FCFS) rule, the parallel computing model with independent allocation of computing resources can be abstracted as an M / M / 1-M / M / 1 series queue, such as Figure 3 Next, we derive the closed-form expressions of the two information timeliness models in this scenario.

[0120] 3.1.1 Generalized Information Timeliness Evaluation

[0121] As shown in formula (1), the general expression of generalized information timeliness is Where T n It can be broken down into two parts: Transmission queue system time T n，t And calculate the queue system time T n，c Therefore, formula (1) can be further expressed as Where Poisson distribution X n The mean value of

[0122] Since both the transmission and computation queues are standard M / M / 1 queues, according to the existing conclusions of queuing theory:

[0123]

[0124] From this we can know

[0125] In summary, the generalized information timeliness expression in the parallel computing mode is:

[0126]

[0127] Zero-wait sampling strategy: We further studied the special case of zero-wait sampling strategy, in which the server sends an acknowledgment signal to the device immediately after receiving the task package, and the device generates and transmits a new task immediately after receiving the acknowledgment signal. This strategy avoids queuing and idleness of the transmission queue.

[0128] Let S n，t represents the service time of the sensing task in the transmission queue, which, as mentioned above, follows the average rate μ t Since the transmission system will not be idle or queued under the zero waiting strategy, there is X n =S n-1，t , T n，t =S n，t In addition, the service times in the M / M / 1 system are statistically independent, that is, S n，t = st S n-1，t , combined with formula (1), the generalized information timeliness of the parallel computing mode under the zero-wait strategy is:

[0129]

[0130] 3.1.2 Process-oriented information timeliness evaluation

[0131] When the observation process can be modeled as a Gaussian Markov process, based on known structural features, we can define more targeted information timeliness As shown in formula (2), the nonlinear function makes it impossible to separate the transmission and calculation processes, which increases the complexity of the analysis.

[0132] Total system time T n It can be divided into four parts: Transmission queue waiting time W n，t , transmission queue service time S n，t , calculate the queue waiting time W n，c, calculate the queue service time S n，c , that is, T n =W n，t +S n，t +W n，c +S n，c . Due to S n，c is independent of other variables, so It can be written as:

[0133]

[0134] The last term on the right side of the equation can be obtained by S n，c The probability density function of is calculated as:

[0135]

[0136] The former can be transformed into the total probability formula:

[0137]

[0138] Next, we analyze the unknown quantity W n，t +W n，c There are four possible combinations.

[0139] (1)W n，t >0,W n，c >0: Let D n，t represents the time interval between task n and task n-1 leaving the transmission queue. n，t >0, then D n，t =S n，t . Considering W n，t With W n，c are independent of each other, then W n，t +W n，c The probability density function of can be calculated by convolution:

[0140]

[0141] Taking the first term of convolution as an example, if T n-1，t >X n , that is, when task n is generated, task n-1 has not yet left the transmission queue, then W n，t =T n-1，t -X n On the contrary, W n，t = 0. Therefore, the waiting time of task n can be expressed as:

[0142] W n，t =(T n-1，t -X n ) + (10)

[0143] Due to T n-1，t and X n Independent of each other, we have:

[0144]

[0145]

[0146] D n，t Considered as calculating the arrival interval of the queue, the second term of the convolution is the same as the above analysis. Therefore, equation (9) can be calculated:

[0147]

[0148] (2)W n，t >0,W n，c =0: Due to W n，t and S n，t Independent of each other, according to equations (11) and (12), the probability density function in this case can be calculated:

[0149]

[0150] (3)W n，t =0,W n，c >0: Introduce D n，t As an intermediate variable, W n，t +W n，c The conditional probability distribution of can be expressed as:

[0151]

[0152] The second term in the integral on the numerator The calculation of is similar to formula (11).

[0153] For the first term in the integral, let B n，t It represents the time interval from when task n-1 leaves the transmission queue to when task n is generated, which can be expressed as X n -T n-1，t , and is independent of S n，t , so we have:

[0154]

[0155] The numerator and denominator can be obtained from formula (3) and formula (12) respectively.

[0156] Since it is known that W n，t = 0 and S n，t =s, then D n，t =B n，t +s, so we can get the first term in the integral as:

[0157]

[0158] At this point, the numerator in equation (15) can be obtained by integration. Its denominator can be offset in subsequent calculations, so there is no need to calculate the specific expression here.

[0159] (4)W n，t =0,W n，c = 0: If and only if in this case the waiting time of both queues is 0, so we can calculate W n，t +W n，c >0 to indirectly analyze this situation.

[0160] W n，t +W n，c >0 includes the above three situations, namely:

[0161]

[0162] The three probability density functions are calculated in the first three cases as shown in equations (13), (14), and (15).

[0163] For the three probabilities, taking the first one as an example, it can be transformed into:

[0164] P(W n，t >0,W n，c >0|S n，t =s,X n =x) (19)

[0165] =P(W n，t >0|S n，t =s,X n = x)P(W n，c >0|W n，t >0,S n，t =s,X n = x)

[0166] The first term on the right side of the equation is equivalent to equation (12), and the second term can be calculated as:

[0167]

[0168] The remaining two probabilities can be calculated similarly. Note that the third probability can be partially offset by the subsequent probability density function (as shown in equation (15)). At this point, the closed-form expression of equation (18) can be obtained:

[0169]

[0170] Thus, W is indirectly calculated n，t =W n，c =0:

[0171]

[0172] Comprehensively analyzing the above four situations, based on equations (21) and (22), the expectation in equation (8) It can be calculated as:

[0173]

[0174] Based on this, by calculating equation (8) and equation (6) in turn, we can get the process-oriented information timeliness expression in the parallel computing mode:

[0175]

[0176] Zero-wait sampling strategy: We also consider the special case of zero-wait sampling strategy, in which X n =S n-1，t , W n，t = 0. Since the transmission service time of the n-1th task is independent of the nth packet, equation (2) can be transformed into

[0177]

[0178] in and According to S n，t and S n，c The probability density function of is calculated.

[0179] about Still based on the total probability formula, the conditional expectation is derived, that is:

[0180]

[0181] in Similar to formula (11).

[0182] From this, we can calculate the process-oriented information timeliness of the parallel computing mode under the zero-wait strategy as follows:

[0183]

[0184] 3.2 Timeliness Evaluation in Computing Resource Sharing Scenarios

[0185] In the computing resource sharing mode, the edge server uses all computing resources to process the tasks uploaded by all devices in sequence according to the FCFS rules. The queuing process of a task in the calculation stage will be affected by tasks from other devices, which increases the system delay of the calculation process of the task, and this performance degradation is uncontrollable. In order to make up for this performance loss, intuitively speaking, we can improve the timeliness as much as possible by adjusting the independently controllable communication process of each device. Therefore, in the present invention, we consider a zero-wait strategy, which can eliminate the queuing and waiting process of the communication queue and shorten the system delay of the communication process.

[0186] Assume that the transmission service time of device i is an exponential random variable, and its average service rate is μ i，t ; The service time of the edge server for the task packets from all devices is subject to the parameter μ c The exponential distribution of . Then the serial computing mode of computing resource sharing can be abstracted as M / M / 1-multi-source M / M / 1 serial queue, such as Figure 4 Next, we derive the closed-form expressions of the two information timeliness models of any device i in this scenario.

[0187] 3.2.1 Generalized Information Timeliness Evaluation

[0188] Similar to 3.1.1, we also divide the whole process into two parts: transmission and calculation. At the same time, under the zero-wait strategy, X i，n =S i，n-1，t , T i，n，t =S i，n，t , the average task arrival rate is the same as the average transmission service rate. Then for any device i, the general expression of generalized information timeliness in formula (1) is can be transformed into:

[0189]

[0190] in

[0191] For T i，n，c According to the existing conclusions, the departure and arrival processes of the M / M / 1 queue are statistically consistent, both of which are Poisson processes with the same expectation, and the aggregation of multiple Poisson processes is still a Poisson process. Therefore, the computing queue can be regarded as an M / M / 1 queue, and its average task arrival rate is the sum of the task arrival rates of all devices, that is, μ i，t +μ -i，t , where μ -i，t represents the total task arrival rate of other devices except device i. By analogy with the probability density function of system delay shown in formula (3), the generalized information timeliness of the serial computing mode under the zero-wait strategy can be calculated as:

[0192]

[0193] 3.2.2 Process-oriented information timeliness evaluation

[0194] In the serial computing mode, the process-oriented information timeliness index, in addition to the inseparable variables of waiting time and service time in each stage due to nonlinearity, also has the problem that in the computing queue, additional queuing will occur between adjacent unloaded tasks on the same device due to the convergence of tasks from other devices, making the analysis more complicated.

[0195] Following formula (25), for any device i, the general expression of process-oriented information timeliness in formula (2) is can be transformed into:

[0196]

[0197] in and It can be calculated based on the probability density function of Si,n-1,t and Si,n,c.

[0198] According to the total probability formula, It can be expressed as:

[0199]

[0200] About the only unknown quantity in the above formula W i，n，c It depends on the system time of the n-1th task from the same device i and the tasks imported from other devices. Let W′ in，c represents the waiting time caused by the previous task from the same device i in the computation queue, W″ in，c represents the waiting time caused by the convergence of other device tasks within the arrival interval of two tasks. Then W i，n， c=W′ i，n，c +W″ i，n，c Next, we consider W′ in，c and W″ in，c Four possible combinations to analyze W i，n，c .

[0201] (1)W′ i，n，c >0,W″ i，n，c =0: According to equations (11) and (12), we can calculate W in this case i，n，c The conditional probability density function is:

[0202]

[0203] (2)W′ i，n，c >0,W″i，n，c >0: Due to W′ i，n，c and W″ i，n，c Independent of each other, W i，n，c The conditional distribution of can be transformed into:

[0204]

[0205]

[0206] The first term of the convolution is equation (32).

[0207] Now let’s focus on the second term of the convolution. i，n，c > 0, that is, when the nth task of device i arrives at the computing queue, its previous task is still in the queue, so in this interval S i，n，t The tasks imported from other devices are still queued. Since the arrival rate of tasks from other devices is μ -i，t The Poisson process is a process of k tasks, so the probability that k tasks arrive in a period of time y is:

[0208]

[0209] Since the computing service time of each task is independent and all obey the average rate μ c The exponential distribution of k tasks can be used to calculate the probability density function of the total service time of k tasks, namely:

[0210]

[0211] Based on the above two equations, we can get W″ according to the total probability formula i，n，c The conditional probability distribution within a period of time y is:

[0212]

[0213] In addition, based on formula (34), we can know:

[0214]

[0215] In summary, by substituting equations (32), (36), and (37) into equation (33), we can obtain W in this case: i，n，c The mathematical expression of the conditional distribution of . In order to simplify the calculation in this process, we scale equation (36) as follows without affecting the relative numerical correctness:

[0216]

[0217] (3)W′ i，n，c =0, W″ i，n，c >0: Let M nIt indicates the number of tasks of other devices that are backlogged in the queue when the nth task of device i arrives at the computing queue. i，n，c =0, that is, S i，n，t >T i，n-1，c , when the nth task arrives, the previous task has been away for a while, S i，n，t During this period, some of the tasks arriving from other devices may have been processed, so M n Cannot be directly based on S i，n，t We note that between the departure of the n-1th task and the arrival of the nth task, the computation queue can be viewed as a queue with an arrival rate of μ -i，t For an M / M / 1 queue, when the system is stable, the departure process of tasks in the queue is statistically consistent with the arrival process, both with an average rate of μ -i，t Poisson process, that is, the queue length is stable in a statistical sense. Therefore, M n The number of other device tasks in the calculation queue when the n-1th task leaves is consistent with the number of other device tasks in the calculation queue when the n-1th task leaves. i，n，c The conditional distribution of can be transformed into:

[0218]

[0219] The integral term can be numerically calculated based on equation (36), and the probability in the denominator will be offset in subsequent calculations. Similar to case (2), in the numerical calculation process, we also use the simplified form shown in equation (38).

[0220] (4)W′ i，n，c =0, W″ i，n，c =0: Only in this case is W i，n，c =0, so:

[0221] P(W i，M =0|S i，n，t =y) = P(W′ i，n，c =0|S i，n，t =y)P(W″ i，n，c =0|W′ i，n，c =0, S i，n，t =y)(40)

[0222] For the first term on the right side of the equation, we can calculate according to equation (12):

[0223]

[0224] For the second term, given W′ in，c =0, W″ i，n，c = 0 if and only if T i，n-1，c There are no tasks imported from other devices during the time period, so there are:

[0225]

[0226] Multiplying the above two equations together gives the mathematical expression of equation (40), that is, in this case W i，n，c probability.

[0227] Combining the above four situations, we can calculate the unknown term in formula (31): Specifically, the first three cases together constitute W i，n，c >0, that is:

[0228]

[0229] The three probability density functions are calculated in the first three cases as shown in equations (32)(33)(39).

[0230] For the three probabilities, taking the first one as an example, it can be transformed into:

[0231] P(W′ i，n，c >0,W″ i，n，c =0|S i，n，t =y) = P(W′ i，n，c >0|S i，n，t =y)P(W″ i，n，c =0|W′ i，n，c >0,S i，n，t =y) (44)

[0232] The two terms on the right side of the equation can be calculated based on equation (41) and equation (37) respectively.

[0233] The remaining two probabilities can be calculated similarly. Note that the third probability can be partially offset by the subsequent probability density function (as shown in equation (39)).

[0234] Based on equations (40) and (43), the term to be determined is It can be expressed as:

[0235]

[0236] Finally, Substituting into equation (31), through the calculation of equation (31) and equation (30), we can obtain the upper bound of the process-oriented information timeliness of the serial computing mode under the zero-wait strategy:

[0237]

[0238] in,

[0239]

[0240]

[0241]

[0242] 4. Time-optimal joint resource allocation strategy

[0243] The information timeliness expressions for different scenarios and different information sources derived in 3 above intuitively reflect the coupling relationship between task generation, transmission and computation, and can be used as a new performance indicator to guide the overall design of the system. We consider the generalized information timeliness indicator in the parallel computing mode and design a three-stage computation offloading strategy to optimize the information timeliness and energy consumption trade-off between all devices.

[0244] 4.1 System Model

[0245] Consider a computationally intensive connected control system assisted by edge computing, such as Figure 1 As shown in (a), the system consists of an edge server and K connected devices. Represents a collection of devices, and has These devices are placed at monitoring points in different locations. They continuously monitor the surrounding environment through the sensors they are equipped with, generate perception tasks and upload them to the edge server. The server extracts the state information in the perception task through calculation to estimate the real-time state of the environment and make control decisions for downstream tasks based on this. Assume that the task generation rate of any device k is λ k The task offloading uses OFDMA technology, that is, a fixed subchannel is pre-allocated to each device. The server uses the pre-allocated computing resources through the virtual machine to process the offloading tasks of each device in parallel.

[0246] For the task offloading transmission process, it is assumed that the channel state remains unchanged during the observation period and the server knows the uplink channel gain of each edge device Let p k represents the transmission power of device k, whose maximum value does not exceed p max , β k It represents the ratio of the bandwidth allocated to device k to the total available bandwidth. Then the transmission rate of device k can be expressed as:

[0247]

[0248] Where B is the total available bandwidth and N0 is the noise power spectral density.

[0249] Let D k represents the size of the task package generated by device k, which follows the mean The exponential distribution of . Then the average task transmission service rate of device k can be expressed as:

[0250]

[0251] The energy consumption required for task offloading is:

[0252]

[0253] For the task calculation process on the server side, let f k Indicates the CPU frequency pre-allocated to device k, c k represents the number of CPU cycles required to process 1 bit of data. Then the average task calculation rate for device k can be expressed as:

[0254]

[0255] Based on existing work, we model the power consumption of the CPU as P = αf k 3 , where α is a coefficient related to the chip structure. Then the energy consumption in the calculation stage is:

[0256]

[0257] In addition, based on formula (4), the information timeliness of device k is expressed as:

[0258]

[0259] 4.2 System Objectives

[0260] In order to improve information timeliness while saving transmission and computing energy, we quantify system performance and efficiency in terms of device cost. We define device cost as follows:

[0261]

[0262] Where ω is a continuous variable, and ω∈[0, 1], which is used to adjust the trade-off between information timeliness and the total energy consumption of transmission calculation.

[0263] The goal of this invention is to find the optimal sampling strategy and resource allocation strategy to minimize the cost of all devices in the system. At the same time, it is also necessary to consider the fairness issue among multiple devices to avoid sacrificing individual devices to make the overall cost of the system too high. There are many ways to solve the fairness problem. In this invention, we minimize the maximum cost of all devices to achieve a balance between system efficiency and device fairness. The optimization problem can be expressed as follows:

[0264]

[0265] st(48)-(53)

[0266]

[0267]

[0268]

[0269]

[0270] Among them, (54a) ensures the stability of the transmission and computing queues, and (54b) and (54c) reflect the limited bandwidth and computing resources.

[0271] 4.3 Strategy Design

[0272] First, in order to solve the non-differentiable problem caused by the min-max form in problem (54), we introduce an auxiliary variable τ and transform the original problem into the following equivalent form:

[0273]

[0274]

[0275] (48)-(53), (54a)-(54d)

[0276] The difficulty in solving problem (55) lies in the complex coupling relationship between the variables in constraint (55a). In order to simplify the formula, we introduce a series of auxiliary variables In this way, although we have transformed the problem into a more tractable form, there is still The problem still cannot be solved directly in the non-convex form of variable division. To overcome this challenge, we use the convex-concave procedure (CCCP) algorithm. First, according to formula (48), Therefore, formula (49) can be transformed into a convex function difference (difference of conVex, DC) problem:

[0277]

[0278] For the non-convex terms Further adopting the method of continuous convex approximation, in the i-th iteration, based on the current point in the solution space solved in the previous round Linearly approximate the non-convex terms as convex constraints:

[0279]

[0280]

[0281] Then the original problem (55) can be approximately transformed into the following problem in the i-th iteration:

[0282]

[0283] st(48), (50)-(53), (54a)-(54d), (55a), (57)

[0284] in A set of variables for optimization.

[0285] In problem (58), except for (48) and (52), the remaining constraints and objective functions are all convex functions in polynomial form. (52) can be solved by solving The Hessian matrix of is proved to be a convex function. For (48), according to the convexity of the perspective function, it is Concavity and convexity of function About variable collections The concavity and convexity of is the same, which is obviously a convex function. Therefore, it can be proved that problem (58) is a convex optimization problem, which can be solved using convex optimization solving tools (such as CVX).

[0286] In summary, given the initial feasible solution Repeat solving problem (58) at the current solution until convergence, and the final resource allocation and task generation strategy can be obtained. The specific algorithm is shown below.

[0287]

Claims

1. A sensor-transmission-computation joint optimization method for a networked control system based on information timeliness, characterized in that: The following steps are involved: S1. Constructing a generalized information timeliness model in resource independent allocation scenarios: Among them, λ is the average task generation rate, μ t is the average task transmission service rate, μ c Calculate the service rate for the average task; S2, generalized information timeliness, transmission energy consumption of devices, and computing energy consumption of devices in the scenario of independent allocation of computing resources; S3. Quantify system performance and efficiency using equipment cost, and establish an optimization problem to minimize transmission and computing energy consumption while ensuring fairness, while maximizing information timeliness; solve the optimization problem to obtain the optimal sampling strategy and resource allocation strategy.

2. The sensing, transmission and computing joint optimization method of a networked control system based on information timeliness according to claim 1 is characterized in that: In step S1, in the special mode of zero-wait strategy, the formula for generalized information timeliness in the resource independent allocation scenario is:

3. The sensing, transmission and computing joint optimization method of a networked control system based on information timeliness according to claim 1 is characterized in that: The information timeliness of equipment also includes the following models: process-oriented information timeliness in resource independent allocation scenarios, generalized information timeliness in resource sharing scenarios, and process-oriented information timeliness in resource sharing scenarios.

4. The sensing, transmission and computing joint optimization method of a networked control system based on information timeliness according to claim 3 is characterized in that: The formula for process-oriented information timeliness in the resource independent allocation scenario is: Among them, κ is the structural parameter related to the regression rate, σ 2 is the variance of the observation process, λ is the average task generation rate, μ t is the average task transmission service rate, μ c Calculate the service rate for the average task; In the special mode of zero-wait strategy, the formula for process-oriented information timeliness in the resource independent allocation scenario is:

5. The sensing, transmission and computing joint optimization method of a networked control system based on information timeliness according to claim 3 is characterized in that: The formula for generalized information timeliness in resource sharing scenarios under the zero-wait strategy is: where μ i,t is the average task transmission service rate of device i, μ -i,t is the sum of the average task transmission service rates of the remaining devices, μ c Calculate the service rate for the average task.

6. The sensing, transmission and computing joint optimization method for a networked control system based on information timeliness according to claim 3 is characterized in that: The upper bound of process-oriented information timeliness in resource sharing scenarios under the zero-wait strategy is: in, κ is a structural parameter related to the regression rate, σ 2 is the variance of the observation process, μ i,t is the average task transmission service rate of device i, μ -i,t is the sum of the average task transmission service rates of the remaining devices, μ c Calculate the service rate for the average task.

7. The sensing, transmission and computing joint optimization method of a networked control system based on information timeliness according to claim 1 is characterized in that: The formula for the transmission energy consumption of device k in the resource independent allocation scenario in step S2 is: where p k represents the transmission power of device k, β k Indicates the ratio of the bandwidth allocated to device k to the total available bandwidth, is the average transmission rate of device k, B represents the total available bandwidth, N0 represents the noise power spectral density, and D k represents the size of the task package generated by device k, which follows the mean The exponential distribution of Represents a collection of devices, h k Indicates the uplink channel gain of the edge device; The formula for calculating the energy consumption of tasks offloaded from device k is: Where α is a coefficient related to the chip structure, f k Indicates the CPU frequency pre-allocated to device k, c k Indicates the number of CPU cycles required to process 1 bit of data; The generalized information timeliness of device k is expressed as: λ k is the average task generation rate, is the average task transmission service rate, Calculate the service rate for the average task.

8. The sensing, transmission and computing joint optimization method for a networked control system based on information timeliness according to claim 1 is characterized in that: In step S3, the equipment cost in the resource independent allocation scenario is expressed as: Where ω is a continuous variable, and ω∈[0,1], which is used to adjust the trade-off between information timeliness and total energy consumption of transmission calculation. is the transmission energy consumption of device k, The computing energy consumption of the device.

9. The sensing, transmission and computing joint optimization method of a networked control system based on information timeliness according to claim 1 is characterized in that: In step S3, the optimization problem in the resource independent allocation scenario is expressed as: Among them, C k For equipment cost.

10. The sensing, transmission and computing joint optimization method of a networked control system based on information timeliness according to claim 9 is characterized in that: The problem solving process of step S3 is: Introduce an auxiliary variable τ and transform the original problem into Problem 2: Introduce a series of auxiliary variables Problem 2 is simplified, and continuous convex approximation is performed on the non-convex terms to convert Problem 2 into convex optimization problem 3 at the current solution: in To optimize the variable set; Given an initial feasible solution Use the convex optimization solver to repeatedly solve Problem 3 at the current solution until convergence, and obtain the final resource allocation and task generation strategy.

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