Method for analyzing feasibility of non-precise mixed key system scheduling under deadline constraint

Abstract

The application discloses a deadline-constrained imprecise mixed critical system scheduling feasibility analysis method, which comprises the following steps: determining a system mode conversion strategy according to a deadline-constrained imprecise mixed critical task scheduling model; obtaining sufficient conditions for scheduling feasibility of the imprecise mixed critical system in a low mode; determining processor requirements of low critical level jobs according to a first preset formula or a second preset formula, and then calculating processor requirements of low critical level tasks τ i in the high mode; determining processor requirements of high critical level jobs according to a third preset formula, and then calculating processor requirements of high critical level tasks τ j in the high mode; and obtaining sufficient conditions for scheduling feasibility of the imprecise mixed critical system in the high mode according to the relationship between the length of a task interval and the processor requirements of the imprecise mixed critical task set Γ in the high mode. The deadline-constrained model is used to analyze and determine the processor requirements of the tasks by using a requirement limiting function, so that the scheduling feasibility of the system is improved.

Description

Technical Field

[0001] This invention relates to the field of real-time scheduling technology for real-time systems and hybrid critical systems, and in particular to a method for feasibility analysis of scheduling of imprecise hybrid critical systems with deadline constraints. Background Technology

[0002] With the rapid development of computer technology, the trend in embedded real-time systems is to integrate multiple applications at different levels onto a single shared platform to meet limitations in power consumption, size, and weight, thus forming hybrid critical systems. Hybrid critical systems typically define their own safety levels. For example, in the automotive safety certification standard ISO 26262, there are four critical levels: ASIL (Automotive Safety and Integrity Level) and AD, where D is the highest critical level and A is the lowest. In the avionics safety certification standard DO-178C, there are five critical levels: AE, where A is the highest critical level and E is the lowest. Therefore, the most typical applications of hybrid critical systems are in the automotive electronics and aerospace fields; for example, autonomous vehicle control systems and unmanned aerial vehicle (UAV) control systems are typical applications of hybrid critical systems.

[0003] For hybrid critical systems, it is essential not only to ensure that the system can output the correct results, but also to ensure that the tasks are completed within the specified time. Therefore, the scheduling feasibility of the system is of paramount importance and is the most important means of ensuring system security.

[0004] Most commonly used feasibility analysis methods for hybrid critical systems currently available are designed for classic hybrid critical task models and assume that the relative deadlines of tasks are equal to their cycles, which does not align with actual industrial products. More importantly, the feasibility analysis methods for hybrid critical systems employed by existing technologies suffer from high time complexity and low system scheduling ratios, failing to meet the scheduling and verification requirements of hybrid critical systems. Summary of the Invention

[0005] The main objective of this invention is to provide a feasibility analysis method for scheduling of imprecise hybrid critical systems with deadline constraints. This method aims to solve the technical problems of high time complexity and low system scheduling ratio in existing feasibility analysis methods for hybrid critical systems, which cannot meet the scheduling and verification requirements of hybrid critical systems.

[0006] To achieve the above objectives, this invention provides a feasibility analysis method for scheduling an imprecise hybrid critical system with deadline constraints, comprising the following steps: determining a system mode switching strategy based on a deadline-constrained imprecise hybrid critical task scheduling model; deriving sufficient conditions for the feasibility of scheduling the imprecise hybrid critical system in low mode based on the relationship between the length of the task interval and the processor requirements of the imprecise hybrid critical task set Γ in low mode; and determining low-criticality level tasks according to a first preset formula or a second preset formula. The processor requirements then need to compute low-critical-level tasks τ. i High processor requirements in high-mode; high-criticality tasks are determined according to the third preset formula. The processor requirements, and then the computation of high-critical-level tasks τ j High-mode processor requirements; based on low-critical-level tasks. i High-mode processor requirements, high-critical-level tasks j The processor requirements in high mode are obtained, and the processor requirements of the inaccurate mixed critical task set Γ in high mode are derived. Based on the relationship between the length of the task interval and the processor requirements of the inaccurate mixed critical task set Γ in high mode, sufficient conditions for the feasibility of scheduling the inaccurate mixed critical system in high mode are obtained.

[0007] Optionally, based on the deadline-constrained imprecise hybrid critical task scheduling model, a system mode transition strategy is determined, specifically including: the deadline-constrained imprecise hybrid critical system consists of n independent imprecise hybrid critical incidental tasks τ i Composition, that is, Γ={τ1,τ2,…,τ n}, where 1≤i≤n, and i is an integer; inexact mixed critical incidental task τ i Represented by a quadruple (Ti, Li, Ci(*), Di), where T i For τ i The cycle time is such that a task releases only one job within its cycle; L i For τ i The key level, when L i When the value is LO, τ i For low-criticality tasks, when L i When the value of τ is HI, i For high-criticality tasks; in Ci(*), * represents LO or HI, when * represents LO, C i (LO) is τ i In the worst-case execution time of low mode, * is HI, C i (HI) is τ i In the worst-case execution time of high mode; D i For τ i The relative deadline, D i≤T i If τ i It is a high-critical-level task, namely L i =HI,C i (HI)≥C i (LO); otherwise, C i (HI)≤C i (LO); The system's mode switching strategy is as follows: the system starts in low mode; when a high-critical-level task τ... i The execution time exceeds τ i In low mode, the worst execution time C i If (LO) is not completed, the system switches from low mode to high mode.

[0008] Optional, low mode refers to any task τ i The execution time does not exceed τ i In low mode, the worst execution time C i (LO); High mode refers to any task τ i The execution time does not exceed τ i In the worst execution time C of high mode i (HI).

[0009] Optionally, the system switches from low mode to high mode by using a critical level-aware dynamic priority strategy to schedule the inaccurate mixed critical task set Γ. Specifically, the high critical level-aware dynamic priority strategy uses the earliest deadline priority strategy to schedule all tasks, and delays the execution of low critical level tasks while ensuring that low critical level tasks do not miss their deadlines.

[0010] Optionally, based on the relationship between the length of the task interval and the processor requirements of the inaccurate hybrid critical task set Γ in low mode, sufficient conditions for the feasibility of scheduling the inaccurate hybrid critical system in low mode are derived. Specifically, these conditions include: scheduling is feasible when the processor requirements of the inaccurate hybrid critical task set Γ in low mode are less than or equal to the length of the task interval; otherwise, scheduling is not feasible. That is, the sufficient conditions for the feasibility of scheduling the inaccurate hybrid critical system in low mode are as follows:

[0011]

[0012] in, Let be the length of the task interval, and H represents the hypercycle of the task set. This represents the processor requirements of task set Γ in low mode, calculated using the following formula:

[0013]

[0014] in, For task τi The processor requirements in low mode are calculated as follows:

[0015]

[0016] Optionally, low-criticality tasks can be determined according to either the first or the second preset formula. The processor requirements then need to compute low-critical-level tasks τ. i In high-mode processor requirements, at least the following are included: If A i <A m Then, the first preset formula is used to determine the low-criticality level operations. processor requirements If A i ≥A m Then, the second preset formula is used to determine the low-criticality level operations. processor requirements Among them, A i It is a low-criticality operation. Arrival time, A m It is a high-critical-level task. m The time to release the job, and the job in t s The system mode transition is triggered at all times; the first preset formula is as follows:

[0017]

[0018] Where mod(τ) i A m ) represents a low-criticality task τ i Release time and A m The time interval between them, according to A m τ i Period T i The calculation yields the following second preset formula:

[0019]

[0020] Where mod(τ) i ,t s ) represents a low-criticality task τ i Release time and t s The time interval between them depends on the time t when the system mode transitions. s τ i Period T i Calculated; Calculation of low-criticality task τ i High-mode processor requirements Specifically, the calculation is based on the following formula:

[0021]

[0022] in,

[0023] Optional, mod(τ) i A m The specific calculation formula is as follows:

[0024] mod(τ i ,t s The specific calculation formula is as follows:

[0025] Optionally, high-criticality tasks can be determined according to a third preset formula. The processor requirements, and then the computation of high-critical-level tasks τ j In high-mode processor requirements, specifically including: determining high-criticality tasks based on a third preset formula. processor requirements The third preset formula is as follows:

[0026]

[0027] Among them, C j (LO), for high-criticality tasks τ j In the worst-case execution time of low mode, A j For high-critical-level operations Arrival time, D j For high-critical-level tasks j The relative deadline, C j (HI) represents a high-critical-level task. j Worst execution time in high mode;

[0028] Computing high-criticality task τ j High-mode processor requirements Specifically, the calculation is based on the following formula:

[0029]

[0030]

[0031]

[0032] Among them, T j For high-critical-level tasks j The cycle, For high-critical-level tasks j Release time and The time interval, according to The difference, T j Calculated.

[0033] Optional, The specific calculation formula is as follows:

[0034] Optionally, based on low-criticality task τ i High-mode processor requirements, high-critical-level tasks j Based on the processor requirements in high mode, the processor requirements of the inaccurate mixed-critical-task set Γ in high mode are obtained. And based on the relationship between the length of the task interval and the processor requirements of the inaccurate mixed-critical-task set Γ in high mode, sufficient conditions for the feasibility of scheduling the inaccurate mixed-critical-task system in high mode are derived. Specifically, the processor requirements of the inaccurate mixed-critical-task set Γ in high mode are obtained according to the following formula:

[0035]

[0036] Among them, Γ LO For a set of low-critical-level tasks, Γ HI A set of high-critical-level tasks;

[0037] Scheduling is feasible when the processor requirement of the inaccurate mixed-critical task set Γ in high mode is less than or equal to the length of the task interval; otherwise, scheduling is not feasible. That is, the sufficient condition for scheduling of the inaccurate mixed-critical system in high mode is as follows:

[0038]

[0039] The beneficial effects of this invention are:

[0040] (1) The method of the present invention uses a deadline constraint model and a demand constraint function analysis to determine the processor requirements of the task, which improves the scheduling feasibility of the system. Compared with the existing schedulable analysis method, it has a higher scheduling ratio and can meet the scheduling requirements of hybrid critical systems.

[0041] (2) The method of the present invention has higher system stability compared with existing schedulable analysis methods. Attached Figure Description

[0042] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0043] Figure 1 This is a simplified flowchart of the feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints according to the present invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] like Figure 1 As shown, the present invention provides a feasibility analysis method for scheduling an imprecise hybrid critical system with deadline constraints, comprising the following steps: determining a system mode switching strategy based on a deadline-constrained imprecise hybrid critical task scheduling model; deriving sufficient conditions for the feasibility of scheduling the imprecise hybrid critical system in low mode based on the relationship between the length of the task interval and the processor requirements of the imprecise hybrid critical task set Γ in low mode; and determining low-criticality level tasks according to a first preset formula or a second preset formula. The processor requirements then need to compute low-critical-level tasks τ. i High processor requirements in high-mode; high-criticality tasks are determined according to the third preset formula. The processor requirements, and then the computation of high-critical-level tasks τ j High-mode processor requirements; based on low-critical-level tasks. i High-mode processor requirements, high-critical-level tasks j The processor requirements in high mode are obtained, and the processor requirements of the inaccurate mixed critical task set Γ in high mode are derived. Based on the relationship between the length of the task interval and the processor requirements of the inaccurate mixed critical task set Γ in high mode, sufficient conditions for the feasibility of scheduling the inaccurate mixed critical system in high mode are obtained.

[0046] Existing technologies consider the relative deadline to equal the period, which is pessimistic and does not align with actual industrial products. More importantly, the feasibility analysis methods for hybrid critical systems employed in existing technologies have high time complexity and low system scheduling ratios, failing to meet the scheduling requirements of hybrid critical systems. This invention, through a deadline constraint model and demand constraint function analysis, determines the processor requirements of tasks, improving the system's scheduling feasibility. Compared to existing schedulable analysis methods, it achieves a higher system scheduling ratio and can meet the scheduling requirements of hybrid critical systems.

[0047] In this embodiment, based on the deadline-constrained imprecise hybrid critical task scheduling model, a system mode transition strategy is determined, specifically including: the deadline-constrained imprecise hybrid critical system consists of n independent imprecise hybrid critical incidental tasks τ i Composition, that is, Γ={τ1,τ2,…,τ n}, where 1≤i≤n, and i is an integer; inexact mixed critical incidental task τ i Represented by a quadruple (Ti, Li, Ci(*), Di), where T i For τ i The cycle time is such that a task releases only one job within its cycle; L i For τ i The key level, when L i When the value is LO, τ i For low-criticality tasks, when L i When the value of τ is HI, i For high-criticality tasks; in Ci(*), * represents LO or HI, when * represents LO, C i (LO) is τ i In the worst-case execution time of low mode, * is HI, C i (HI) is τ i In the worst-case execution time of high mode; D i For τ i The relative deadline, D i ≤T i If τ i It is a high-critical-level task, namely L i =HI,C i (HI)≥C i (LO); otherwise, C i (HI)≤C i (LO); The system's mode switching strategy is as follows: the system starts in low mode; when a high-critical-level task τ... i The execution time exceeds τ i In low mode, the worst execution time C i If (LO) is not completed, the system switches from low mode to high mode.

[0048] It should be noted that in this embodiment, the subscripts i, j, and m of the task refer only to the task set Γ = {τ1, τ2, ..., τ}. n In the context of a task, the subscripts i, j, and m do not specifically refer to high-critical-level tasks or low-critical-level tasks. That is, the subscripts i, j, and m can all represent high-critical-level tasks, and the range of values ​​for the subscripts i, j, and m is 1 ≤ i ≤ n, where n is the number of tasks in the task set. This does not constitute an improper limitation on the present invention.

[0049] In this embodiment, low mode refers to any task τ i The execution time does not exceed τ i In low mode, the worst execution time C i (LO); High mode refers to any task τ i The execution time does not exceed τ i In the worst execution time C of high mode i (HI).

[0050] In this embodiment, the system switches from low mode to high mode by using a key level-aware dynamic priority strategy to schedule the imprecise mixed critical task set Γ. Specifically, the high key level-aware dynamic priority strategy uses an Earliest Dealine First (EDF) strategy to schedule all tasks, and delays the execution of low-key tasks while ensuring that they do not miss their deadlines. Tasks of the same key level are always scheduled according to the Earliest Dealine First strategy. The priority of a task is determined by the Earliest Dealine First algorithm; the smaller the absolute deadline, the higher the priority. For tasks with the same absolute deadline, the task with the earlier arrival time has the higher priority. For tasks with the same absolute deadline and arrival time, task τ... i The smaller the index i, the higher the priority; the absolute deadline is equal to the sum of the task's arrival time and the relative deadline.

[0051] In this embodiment, based on the relationship between the length of the task interval and the processor requirements of the inaccurate hybrid critical task set Γ in low mode, sufficient conditions for the feasibility of scheduling the inaccurate hybrid critical system in low mode are derived. Specifically, these conditions include: scheduling is feasible when the processor requirements of the inaccurate hybrid critical task set Γ in low mode are less than or equal to the length of the task interval; otherwise, scheduling is not feasible. That is, the sufficient conditions for the feasibility of scheduling the inaccurate hybrid critical system in low mode are as follows:

[0052]

[0053] in, Let be the length of the task interval, and H represents the supercycle of the task set, which is the least common multiple of the cycles of all tasks. This represents the processor requirements of task set Γ in low mode, calculated using the following formula:

[0054]

[0055] in, For task τ i The processor requirements in low mode are calculated as follows:

[0056]

[0057] In this embodiment, low-criticality tasks are determined according to a first preset formula or a second preset formula. The processor requirements then need to compute low-critical-level tasks τ. i In high-mode processor requirements, at least the following are included: If A i <A m Then, the first preset formula is used to determine the low-criticality level operations. processor requirements If A i ≥A m Then, the second preset formula is used to determine the low-criticality level operations. processor requirements Among them, A i It is a low-criticality operation. Arrival time, A m It is a high-critical-level task. m The time to release the job, and the job in t s The system mode transition is triggered at any time, i.e., t s This marks the moment of system mode transition.

[0058] Preferably, the first preset formula is as follows:

[0059]

[0060] Where mod(τ) i A m ) represents a low-criticality task τ i Release time and A m The time interval between them, according to A m τ i Period T i Calculated.

[0061] Preferably, mod(τ) i A m The specific calculation formula is as follows:

[0062] Preferably, the second preset formula is as follows:

[0063]

[0064] Where mod(τ) i ,t s ) represents a low-criticality task τ i Release time and t s The time interval between them depends on the time t when the system mode transitions. s τ i Period Ti Calculated; Calculation of low-criticality task τ i High-mode processor requirements Specifically, the calculation is based on the following formula:

[0065]

[0066] in,

[0067] Preferably, mod(τ) i ,t s The specific calculation formula is as follows:

[0068] In this embodiment, high-criticality tasks are determined according to a third preset formula. The processor requirements, and then the computation of high-critical-level tasks τ j In high-mode processor requirements, specifically including: determining high-criticality tasks based on a third preset formula. processor requirements The third preset formula is as follows:

[0069]

[0070] Among them, C j (LO), for high-criticality tasks τ j In the worst-case execution time of low mode, A j For high-critical-level operations Arrival time, D j For high-critical-level tasks j The relative deadline, C j (HI) represents a high-critical-level task. j Worst execution time in high mode;

[0071] Computing high-criticality task τ j High-mode processor requirements Specifically, the calculation is based on the following formula:

[0072]

[0073]

[0074]

[0075] Among them, T j For high-critical-level tasks j The cycle, For high-critical-level tasks jRelease time and The time interval, according to The difference, T j Calculated.

[0076] Preferred, The specific calculation formula is as follows:

[0077] In this embodiment, based on low-criticality task τ i High-mode processor requirements, high-critical-level tasks j Based on the processor requirements in high mode, the processor requirements of the inaccurate mixed-critical-task set Γ in high mode are obtained. And based on the relationship between the length of the task interval and the processor requirements of the inaccurate mixed-critical-task set Γ in high mode, sufficient conditions for the feasibility of scheduling the inaccurate mixed-critical-task system in high mode are derived. Specifically, the processor requirements of the inaccurate mixed-critical-task set Γ in high mode are obtained according to the following formula:

[0078]

[0079] Among them, Γ LO For a set of low-critical-level tasks, Γ HI A set of high-critical-level tasks;

[0080] Scheduling is feasible when the processor requirement of the inaccurate mixed-critical task set Γ in high mode is less than or equal to the length of the task interval; otherwise, scheduling is not feasible. That is, the sufficient condition for scheduling of the inaccurate mixed-critical system in high mode is as follows:

[0081]

[0082] In this embodiment, the set of tasks considered is shown in Table 1 below:

[0083]

[0084]

[0085] Table 1

[0086] Based on this task set, utilization analysis shows that it is unschedulable; other deadline-constrained demand bound function methods also show that it is unschedulable; however, the method of this invention shows that it is schedulable.

[0087] Therefore, it has been confirmed that the method of the present invention improves the scheduling feasibility of the system by using a deadline constraint model and demand constraint function analysis to determine the processor requirements of the task. Compared with existing schedulable analysis methods, it has a higher scheduling ratio and can meet the scheduling requirements of mixed critical systems. Compared with existing schedulable analysis methods, the method of the present invention has higher system stability.

[0088] Furthermore, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0089] The foregoing description illustrates and describes preferred embodiments of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept by means of the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints, characterized in that, include: Based on the deadline-constrained inaccurate hybrid critical task scheduling model, determine the system mode switching strategy; Based on the length of the task interval and an imprecise mixed critical task set Based on the relationship between processor requirements in low mode, sufficient conditions are derived for the feasibility of scheduling in low mode for inaccurate hybrid critical systems. Low-criticality tasks are determined based on either the first or second preset formula. The processor requirements then compute low-critical tasks. High-mode processor requirements; if A i <A m Then, the first preset formula is used to determine the low-criticality level operations. processor requirements If A i ≥A m Then, the second preset formula is used to determine the low-criticality level operations. processor requirements ;in, It is a low-criticality operation. Arrival time, It is a high-critical-level task The time to release the job, and the job in The system mode switch is triggered at any time. The first preset formula is as follows: in, for Worst execution time in low mode; for The relative deadline; for Worst execution time in high mode; Let be the length of the task interval, and H represents the hypercycle of the task set; Indicates low-criticality tasks Release time and The time interval between them, according to , cycle Calculated; The second preset formula is as follows: in, Indicates low-criticality tasks Release time and The time interval between them depends on the timing of the system mode transition. , cycle Calculated; Identify high-criticality tasks The processor requirements then compute high-critical-level tasks. High-mode processor requirements; Based on low-key level tasks High-mode processor requirements, high-critical-level tasks Under high-mode processor requirements, an imprecise mixed mission-critical set is obtained. High-mode processor requirements, and based on the length of the task interval and the non-precise mixed critical task set. Based on the relationship between processor requirements in high mode, sufficient conditions are derived for the feasibility of scheduling in high mode for inaccurate hybrid critical systems.

2. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints as described in claim 1, characterized in that: Based on the deadline-constrained inaccurate hybrid critical task scheduling model, the system mode transition strategy is determined, specifically including: Deadline-constrained inexact hybrid critical systems A series of independent, imprecise, mixed, critical, and sporadic tasks Composition, that is Where 1≤i≤n, and i is an integer; Inexact mixed critical incidental task With quadruplets ( , , , ) indicates that among them for The cycle is such that a task releases only one job within its cycle; for The key level, when The value is hour, For low-criticality tasks, when The value is hour, For high-critical-level tasks; middle, For LO or HI; ;like It is a high-critical-level task, that is , ;otherwise, ; The system's mode switching strategy is as follows: the system starts in low mode; when high-critical-level tasks... Execution time exceeds Worst execution time in low mode If the execution is not completed, the system switches from low mode to high mode.

3. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints as described in claim 2, characterized in that: Low mode refers to any task The execution time does not exceed Worst execution time in low mode High mode refers to any task The execution time does not exceed Worst execution time in high mode .

4. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints as described in claim 2, characterized in that: The system switches from low mode to high mode by using a critical level-aware dynamic prioritization strategy to schedule an imprecise hybrid mission set. ; The high-criticality-level-aware dynamic priority strategy specifically involves scheduling all tasks using the earliest deadline priority strategy, while delaying the execution of low-criticality-level tasks to ensure that they do not miss their deadlines.

5. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints as described in claim 2, characterized in that: Based on the length of the task interval and an imprecise mixed critical task set Based on the relationship between processor requirements in low mode, sufficient conditions are derived for the feasibility of scheduling in low mode for inaccurate hybrid critical systems, specifically including: When inaccurately mixed mission sets Scheduling is feasible when the processor requirement in low mode is less than or equal to the length of the task interval; otherwise, scheduling is not feasible. That is, the sufficient conditions for the feasibility of low-mode scheduling for an imprecise hybrid critical system are as follows: ； in, It is a task set The processor requirements in low mode are calculated using the following formula: ； in, For the task The processor requirements in low mode are calculated as follows: 。 6. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints according to claim 1, characterized in that: Computing low-critical-level tasks High-mode processor requirements Specifically, it is calculated according to the following formula: ； in, .

7. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints as described in claim 1, characterized in that: The specific calculation formula is as follows: ; The specific calculation formula is as follows: .

8. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints according to claim 1, characterized in that: Identify high-criticality tasks processor requirements Specifically, it is determined according to the following formula: in, For high-critical-level tasks In the worst-case execution time of low mode For high-critical-level operations Time of arrival For high-critical-level tasks The relative deadline, For high-critical-level tasks Worst execution time in high mode; Computing high-critical-level tasks High-mode processor requirements Specifically, it is calculated according to the following formula: ； ； ； in, For high-critical-level tasks The cycle, , ; For high-critical-level tasks Release time and The time interval, according to The difference Calculated.

9. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints as described in claim 8, characterized in that: The specific calculation formula is as follows: .

10. The feasibility analysis method for scheduling imprecise hybrid critical systems with deadline constraints as described in claim 8, characterized in that: Based on low-key level tasks High-mode processor requirements, high-critical-level tasks Under high-mode processor requirements, an imprecise mixed mission-critical set is obtained. High-mode processor requirements, and based on the length of the task interval and the non-precise mixed critical task set. Based on the relationship between processor requirements in high-mode, sufficient conditions for the feasibility of scheduling in high-mode for inaccurate hybrid critical systems are derived, specifically including: The inaccurate hybrid mission set is obtained according to the following formula. Processor requirements in high mode: ； in, This is a set of low-criticality tasks. A set of high-critical-level tasks; When inaccurately mixed mission sets Scheduling is feasible when the processor requirement in high mode is less than or equal to the length of the task interval; otherwise, scheduling is not feasible. That is, the sufficient conditions for the feasibility of high-mode scheduling in an imprecise hybrid critical system are as follows: 。

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