Measurement and control arc section optimization selection method and system based on mathematical programming

Abstract

The invention provides a measurement and control arc section optimal selection method and system based on mathematical programming, and the method comprises the following steps: building a mathematical model through measurement and control resource use constraint conditions; and calculating and solving by utilizing the mathematical model to obtain an optimal solution for the arc section in the task cycle. According to the technical scheme, a complex engineering problem and a task scene are condensed into a scientific problem, a selection range of a visible time window does not need to be delimited by paying attention to a task initial arrangement result any more, task attributes are represented through an accurate mathematical model, and then an optimal selection result is directly obtained through problem solving; and the use efficiency of measurement and control resources is improved.

Description

Background Art

[0002] TT&C resources are mainly ground-based TT&C resources, while deep space TT&C scheduling mainly uses ground-based TT&C resources, and scheduling constraints are relatively simple. After the addition of relay satellite TT&C resources, the two types of TT&C resources have different TT&C performance and usage characteristics, and are complementary in some aspects, which makes TT&C scheduling present new characteristics. In order to meet the needs of multi-target TT&C, a variety of technical solutions have emerged, such as single-beam multiple access, multi-beam multi-target, and relay satellite terminal stations; at the same time, in order to solve the problem of tight TT&C equipment resources, the method of adding TT&C equipment to the TT&C station is usually adopted, which also brings problems such as increased costs and waste of resources.

[0003] As the number of spacecraft in orbit increases rapidly, the contradiction of competition for aerospace tracking and control resources becomes increasingly prominent. It is unrealistic to meet the demand by increasing the number of tracking and control stations. How to make full use of the existing tracking and control resources is an important practical problem that urgently needs to be studied. The optimization problem of aerospace tracking and control resources is a scheduling problem with time window constraints, which involves the scheduling of a limited number of resources and a large number of time-related requests. Its computational complexity is proved to be NP-complete. The solution methods can usually be divided into three categories: optimization algorithms based on mathematical programming, heuristic algorithms, and intelligent optimization algorithms.

[0004] The optimization algorithm based on mathematical programming is a complete search algorithm with the characteristics of strong logic, rigorous structure, accurate description of problems, and the ability to obtain optimal solutions. It is widely used in power grids, aviation, transportation, and finance. In the field of aerospace, the Air Force Satellite Control Network (AFSCN) of the United States used mixed integer programming models as early as the 1980s to solve the contradiction between insufficient resources and increased measurement and control needs, continuously optimized the solution strategy, and applied the results in multiple tasks such as the Tracking and Data Relay Satellite System (TDRSS) of the United States. Mathematical programming includes two key scientific issues: one is how to model and translate complex decision-making problems into concise and effective mathematical expressions, which determines the effectiveness of the method; the other is how to solve and solve the mathematical model quickly and accurately, which determines the computational efficiency of the method. In the field of aerospace, due to the characteristics of tight coupling of constraints and high engineering reliability, it is rare to use accurate solution methods to support research results related to complex decisions.

[0005] The heuristic algorithm defines a heuristic function through targeted analysis of the problem, which is used to solve the feasible solution of the problem, and uses feature knowledge to construct a scheduling solution that is approximately optimal. This processing method greatly reduces the problem-solving space and does not require complex mathematical calculations. This type of method is the most widely used method in current engineering tasks. It can comprehensively consider various influencing factors and quickly solve feasible solutions. For example, patent CN 117829360 A considers arc segment priority and task priority, CN 111950870 B considers task priority, related application priority and time flexibility, and CN 117639894 A considers the impact of task parameters, priority of tasks to be executed and measurement and control parameters on the tasks to be executed. The disadvantage is that as the scale of the problem increases, the deviation between the feasible solution and the optimal solution will increase, and the optimal combination of resources cannot be achieved, resulting in a waste of resources.

[0006] Intelligent algorithms are approximate solution algorithms, including greedy algorithms, taboo search algorithms, simulated annealing algorithms (SA), etc. They have both asymptotic convergence and the intelligence to jump out of local optimal solutions. They are widely used in various scheduling optimization problems and have derived a series of hybrid strategies. For example, the introduction of genetic algorithms and ant colony algorithms to solve the task scheduling problem of relay satellites, combined with reinforcement learning methods to solve task scheduling problems, etc., are the mainstream methods used to solve the current multi-satellite measurement and control problems. The disadvantage is that it is difficult to propose a general intelligent algorithm construction strategy that can take into account the differences in problem constraints, application scenarios, etc., and intelligent algorithms need to do more work in targeted improvement strategies.

[0007] The three methods have their own advantages and disadvantages, and are suitable for different mission scenarios. With the increasing number of spacecraft in orbit, my country's measurement and control resources have faced the problem of tight resource allocation. In certain periods of time, only high-priority tasks can be guaranteed and low-priority tasks are forced to be abandoned. There is an urgent need to improve resource utilization efficiency and ensure the monitoring and control capabilities of various targets. In response to the above problems, the feasible solutions obtained by the heuristic algorithm and the approximate optimal solutions obtained by the intelligent algorithm cannot meet the above requirements. Summary of the invention

[0008] The present application provides a method and system for optimizing the selection of measurement and control arc segments based on mathematical programming, so as to improve the utilization efficiency of measurement and control resources.

[0009] In a first aspect, a method for optimizing the selection of a measurement and control arc segment based on mathematical programming is provided, comprising the following steps:

[0010] Construct mathematical models by measuring and controlling resource usage constraints;

[0011] The mathematical model is used to complete the calculation and solution to obtain the optimal solution for arc segment usage within the mission cycle.

[0012] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources.

[0013] In a specific embodiment, it also includes:

[0014] Analyze modeling conditions for engineering problems, propose model assumptions, and define problem boundaries;

[0015] The measurement and control resource usage constraint conditions are set.

[0016] In a specific implementation scheme, the model assumptions include:

[0017] At the same time, different antennas of the same satellite are regarded as different tracking and control stations;

[0018] The tracking arc duration actually used by the spacecraft is shorter than the visible window length;

[0019] Flight control events are the basic objects of planning, and each flight control event is an independent measurement, control and tracking task;

[0020] According to the duration of the mission, flight control events include continuous tracking missions and non-continuous tracking missions;

[0021] Non-continuous tracking tasks include periodic events, key point tasks, and general tasks;

[0022] During a given mission cycle, each tracking and control station can track the target spacecraft multiple times, and each tracking occupies an exclusive visible time window.

[0023] In a specific implementation scheme, the measurement and control resource usage constraints include:

[0024] Each mission must be tracked once by the tracking and control station;

[0025] Each task must have a tracking plan corresponding to that task;

[0026] The current tracking and control arc can only serve one type of flight control event;

[0027] The start time of the measurement and control tracking task falls within the measurement and control arc time interval;

[0028] The order of using the measuring stations in the tracking and using plan of the measurement and control network is unique;

[0029] The order of flight control events in the tracking and use plan of the measurement and control network is unique;

[0030] For the same mission, the tracking and control network only tracks and serves one primary target spacecraft at the same time.

[0031] In a specific implementation scheme, a landmark-based branch and bound algorithm is used to perform computational solutions.

[0032] In a specific implementation scheme, the mathematical model includes parameters, variables, constraint equations and objective functions.

[0033] In a specific implementation scheme, the formula of the mathematical model includes:

[0034]

[0035]

[0036] in, Represent different decision variables; t i represents the time variable;

[0037] H is the large number introduced to determine the continuous tracking task; S is the set of spacecraft; M is the set of tracking and control stations;

[0038] N 1 ={1,…,N 1} is a set of non-continuous tracking tasks; N 2 ={n 1 +1,…,n 1 +n 2} is a set of continuous tracking tasks; N = N 1 ∪N 2 is the set of all flight control events; K sm ={1,…,k sm} is the visible time window set of the tracking and control station m for the target spacecraft s, m∈M,s∈S; M j is the corresponding measurement and control station set of flight control event j, j∈N; is the set of all available visible time windows; σ m b is the switching time between two consecutive flight control events at the control station m, m∈M; j The spacecraft corresponding to flight control event j, j∈N,b j ∈S;p j is the execution time of flight control event j, j∈N; [r jk ,d jk ] is the measurement and control arc segment of flight control event j in the visible time window k, j∈N,k∈K;

[0039] is the set of all feasible continuous tracking plans, j∈N 2 .

[0040] In the second aspect, a system for optimizing the selection of measurement and control arc segments based on mathematical programming is provided, comprising:

[0041] Modeling condition analysis module, used to analyze modeling conditions of engineering problems, propose model assumptions, and define problem boundaries;

[0042] A constraint condition module, used to set the constraint conditions for the use of the measurement and control resources;

[0043] Mathematical model module, used to construct mathematical models by measuring and controlling resource usage constraints;

[0044] The calculation and solution module is used to complete the calculation and solution using the mathematical model to obtain the optimal solution for arc segment usage within the task cycle.

[0045] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources.

[0046] In a third aspect, an electronic device is provided, comprising a processor, wherein the processor is coupled to a memory, wherein at least one computer program is stored in the memory, and the at least one computer program is loaded and executed by the processor so that the electronic device implements any one of the methods for optimizing the selection of measurement and control arc segments based on mathematical programming.

[0047] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources.

[0048] In a fourth aspect, a computer-readable storage medium is provided, in which at least one computer program is stored. The at least one computer program is loaded and executed by a processor so that the computer-readable storage medium implements any one of the mathematical programming-based measurement and control arc segment optimization selection methods.

[0049] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A flowchart of a method for optimizing the selection of measurement and control arc segments based on mathematical programming provided in an embodiment of the present application;

[0051] Figure 2 A structural block diagram of a measurement and control arc segment optimization selection system based on mathematical programming provided in an embodiment of the present application;

[0052] Figure 3 A specific flow chart of the method for optimizing the selection of measurement and control arc segments based on mathematical programming provided in an embodiment of the present application. DETAILED DESCRIPTION

[0053] The present application is further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present application will become clearer and more specific.

[0054] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0055] In addition, the technical features involved in different embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.

[0056] To facilitate understanding of the method and system for optimizing the measurement and control arc segment selection based on mathematical programming provided in the embodiment of the present application, its application scenario is first explained. The method and system for optimizing the measurement and control arc segment selection based on mathematical programming provided in the embodiment of the present application are used to improve the efficiency of measurement and control resource utilization. The optimization algorithm based on mathematical programming is a complete search algorithm with the characteristics of strong logic, rigorous structure, accurate description of problems, and the ability to obtain optimal solutions. It is widely used in power grids, aviation, transportation, and finance. In the field of aerospace, the Air Force Satellite Control Network (AFSCN) of the United States Air Force adopted a mixed integer programming model as early as the 1980s to solve the contradiction between insufficient resources and increased measurement and control needs, continuously optimize the solution strategy, and apply the results in multiple tasks such as the Tracking and Data Relay Satellite System (TDRSS) of the United States. Mathematical programming includes two key scientific issues: one is how to model and translate complex decision-making problems into concise and effective mathematical expressions, which determines the effectiveness of the method; the other is how to solve and quickly and accurately solve the mathematical model, which determines the computational efficiency of the method. In the field of aerospace, due to the influence of the characteristics of tight coupling of constraints and high engineering reliability, there are few research results related to complex decision-making supported by precise solution methods. Heuristic algorithms define heuristic functions through targeted analysis of problems, which are used to solve feasible solutions to problems and use feature knowledge to construct approximately optimal scheduling solutions. This processing method greatly reduces the problem-solving space and does not require complex mathematical calculations. This type of method is the most widely used method in current engineering tasks. It can comprehensively consider various influencing factors and quickly solve feasible solutions. For example, patent CN 117829360 A considers arc priority and task priority, CN 111950870 B considers task priority, related application priority and time flexibility, and CN 117639894A considers the impact of task parameters, priority of tasks to be executed and measurement and control parameters on the tasks to be executed. The disadvantage is that as the scale of the problem increases, the deviation between the feasible solution and the optimal solution will increase, and the optimal combination of resources cannot be achieved, resulting in a waste of resources. Intelligent algorithms are approximate solution algorithms, including greedy algorithms, taboo search algorithms, simulated annealing algorithms (SA), etc. They have both asymptotic convergence and the intelligence to jump out of local optimal solutions. They are widely used in various scheduling optimization problems and have derived a series of hybrid strategies. For example, the introduction of genetic algorithms and ant colony algorithms to solve the task scheduling problem of relay satellites, combined with reinforcement learning methods to solve the task scheduling problem, etc., are the mainstream methods used to solve the current multi-satellite measurement and control problems.The disadvantage is that it is difficult to propose a universal intelligent algorithm construction strategy that can take into account the differences in problem constraints, application scenarios, etc., and the intelligent algorithm needs to do more work in targeted improvement strategies. The three methods each have their own advantages and disadvantages, and are adapted to different mission scenarios. With the increasing number of spacecraft on orbit, my country's measurement and control resources have faced the problem of tight resource allocation. In certain periods of time, only high-priority tasks can be guaranteed and low-priority tasks are forced to be abandoned. There is an urgent need to improve resource utilization efficiency and ensure the monitoring and control capabilities of various targets. In response to the above problems, the feasible solutions obtained by the heuristic algorithm and the approximate optimal solutions obtained by the intelligent algorithm cannot meet the above requirements. For this reason, the embodiment of the present application provides a method and system for optimizing the selection of measurement and control arc segments based on mathematical programming to improve the efficiency of measurement and control resource utilization. The following is a detailed description of the embodiments in conjunction with specific drawings.

[0057] Terminology explanation:

[0058] (1) Measurement and control station

[0059] my country's measurement and control resources include two parts: space-based relay satellite system and ground-based measurement and control network.

[0060] Relay satellites include relay-1 satellites and relay-2 satellites, which carry single-address antennas and multi-address antennas respectively. Their technical status constraints mainly consider the differences in forward and return link characteristics caused by differences in antenna performance; the ground-based tracking and control network includes standard TT&C tracking and control stations and full downlink receiving tracking and control stations, which track deep space spacecraft and near-Earth spacecraft respectively according to the size of the antenna aperture. For near-Earth orbit spacecraft, the factors that have a greater impact on tracking are the installation position and installation angle of the onboard tracking and control antenna, as well as the configuration and flight attitude of the spacecraft.

[0061] It can be seen that the measurement and control antenna is the most important condition affecting the use of measurement and control resources. In the present invention, for the ground-based measurement and control network, the antenna is used as the basic measurement and control unit, and each antenna is regarded as a measurement and control station; for the space-based measurement and control network, the requirements for the use of the forward return link in the flight control event are combined with the number of antennas carried by the relay satellite to make a judgment, and the set of antennas that can be used simultaneously by the satellite is regarded as a measurement and control station. For example, a certain satellite of Tianlian is equipped with 2 single-address antennas and 2 multiple-address antennas. During important flight control missions, the spacecraft target requires the use of the S-band of the forward 2 return 2 to provide a high-speed transmission link. The relay satellite needs 2 single-address antennas to achieve the above goal, and the other 2 multiple-address antennas can be used separately. In general, the satellite can be regarded as 3 measurement and control stations.

[0062] (2) Visible time window and measurement and control arc

[0063] The communication line between the spacecraft and the tracking and control station is not blocked by the earth, that is, the two are in a visible state. This time interval is called the visible time window. The tracking and control station needs to establish intersatellite link communication with the spacecraft within the visible time window. For a specific spacecraft, it may have multiple visible time windows with the tracking and control station, and the visible time windows between different spacecraft and the tracking and control station may overlap.

[0064] The selected visible time window is called the measurement and control arc. Considering factors such as equipment preparation time, the measurement and control arc needs to fall within the corresponding visible time window.

[0065] (3) TT&C tracking tasks and TT&C network tracking use plan

[0066] The TT&C tracking mission refers to the tasks of measuring, controlling and transmitting data to the spacecraft. Ground personnel need to complete the TT&C tracking mission according to the TT&C network tracking plan. The elements include mission ID, tracking target, tracking start time, tracking duration, link usage requirements, mission priority, etc.

[0067] Generally speaking, there is a one-to-one correspondence between the measurement and control arc and the measurement and control task. For long-period measurement and control tasks, such as space teaching, ground personnel need to split them up and regard them as a set of measurement and control tasks connected by multiple starting times. The measurement and control arc is a set of visible windows that overlap each other.

[0068] refer to Figures 1 to 3 , Figure 1 A flowchart of a method for optimizing the selection of measurement and control arc segments based on mathematical programming provided in an embodiment of the present application; Figure 2 A structural block diagram of a measurement and control arc segment optimization selection system based on mathematical programming provided in an embodiment of the present application; Figure 3 A specific flow chart of the method for optimizing the selection of measurement and control arc segments based on mathematical programming provided in an embodiment of the present application.

[0069] exist Figure 1 In the embodiment of the present application, a method for optimizing the selection of a measurement and control arc segment based on mathematical programming is provided, comprising the following steps:

[0070] Construct mathematical models by measuring and controlling resource usage constraints;

[0071] The mathematical model is used to complete the calculation and solution to obtain the optimal solution for arc segment usage within the mission cycle.

[0072] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources.

[0073] In a specific embodiment, it also includes:

[0074] Analyze modeling conditions for engineering problems, propose model assumptions, and define problem boundaries;

[0075] The measurement and control resource usage constraint conditions are set.

[0076] In a specific implementation scheme, the model assumptions include:

[0077] At the same time, different antennas of the same satellite are regarded as different tracking and control stations;

[0078] The tracking arc duration actually used by the spacecraft is shorter than the visible window length;

[0079] Flight control events are the basic objects of planning, and each flight control event is an independent measurement, control and tracking task;

[0080] According to the duration of the mission, flight control events include continuous tracking missions and non-continuous tracking missions;

[0081] Non-continuous tracking tasks include periodic events, key point tasks, and general tasks;

[0082] During a given mission cycle, each tracking and control station can track the target spacecraft multiple times, and each tracking occupies an exclusive visible time window.

[0083] In a specific implementation scheme, the measurement and control resource usage constraints include:

[0084] Each mission must be tracked once by the tracking and control station;

[0085] Each task must have a tracking plan corresponding to that task;

[0086] The current tracking and control arc can only serve one type of flight control event;

[0087] The start time of the measurement and control tracking task falls within the measurement and control arc time interval;

[0088] The order of using the measuring stations in the tracking and using plan of the measurement and control network is unique;

[0089] The order of flight control events in the tracking and use plan of the measurement and control network is unique;

[0090] For the same mission, the tracking and control network only tracks and serves one primary target spacecraft at the same time.

[0091] In a specific implementation scheme, a landmark-based branch and bound algorithm is used to perform computational solutions.

[0092] In a specific implementation scheme, the mathematical model includes parameters, variables, constraint equations and objective functions.

[0093] In a specific implementation scheme, the formula of the mathematical model includes:

[0094]

[0095] in, Represent different decision variables; t i represents the time variable;

[0096] H is the large number introduced to determine the continuous tracking task; S is the set of spacecraft; M is the set of tracking and control stations;

[0097] N 1 ={1, ..., N 1} is a set of non-continuous tracking tasks; N 2 ={n 1 +1,…,n 1 +n 2} is a set of continuous tracking tasks; N = N 1 ∪N 2 is the set of all flight control events; K sm ={1,…,k sm} is the visible time window set of the tracking and control station m for the target spacecraft s, m∈M, s∈S; M j is the corresponding measurement and control station set of flight control event j, j∈N; is the set of all available visible time windows; σ m b is the switching time between two consecutive flight control events at the control station m, m∈M; j The spacecraft corresponding to flight control event j, j∈N,b j ∈S;p j is the execution time of flight control event j, j∈N; [r jk , d jk ] is the measurement and control arc segment of flight control event j in the visible time window k, j∈N, k∈K;

[0098] is the set of all feasible continuous tracking plans, j∈N2.

[0099] Specifically, refer to Figure 3 The method for optimizing the selection of the measurement and control arc segment based on mathematical programming includes:

[0100] Step 1: Analyze the modeling conditions of the engineering problem, propose "model assumptions", and limit the boundaries of the problem.

[0101] Based on the current status of the measurement and control network, this application proposes 6 assumptions, which are applicable to all scenarios of current engineering tasks. The details are as follows:

[0102] (1) At the same time, different antennas of the same satellite can be regarded as different tracking and control stations;

[0103] (2) Considering factors such as antenna tracking and acquisition, communication link establishment, etc., the actual tracking arc length used by the spacecraft is less than the visible window length;

[0104] (3) Flight control events are the basic objects of planning. Each flight control event is an independent measurement, control and tracking task. Its attributes specify the event name, event ID, target spacecraft, duration, priority, expected start time and resource requirements.

[0105] (4) According to the duration of the mission, flight control events can be divided into two categories. One is a continuous tracking mission, such as astronauts leaving the cabin, which requires the use of multiple tracking and control arcs for continuous tracking, with overlaps in time intervals to ensure uninterrupted tracking of the target spacecraft. The other is a non-continuous tracking mission, such as the command to open the sailboard when entering or leaving the shadow area, which needs to be executed at a specified time point or time interval and occupies a separate tracking and control arc.

[0106] (5) Non-continuous tracking tasks include: a. Periodic events, i.e., instructions that need to be executed periodically at a fixed time in each cycle, such as the power on / off instructions for entering and exiting the measurement and control area within the mission cycle; b. Key point tasks, i.e., instructions at a specified execution time, such as spacecraft attitude adjustment, which have the highest priority; c. General tasks, i.e., conventional remote control instructions. The above three types of flight control events are considered as the same type of planning objects;

[0107] (6) Within a given mission cycle, each tracking and control station can track the target spacecraft multiple times, and each tracking occupies an exclusive visible time window.

[0108] Step 2: Set the measurement and control resource usage constraints. The constraints set in this step will be directly converted into the constraint equations in step 3.

[0109] Specifically include:

[0110] (1) Each mission must be tracked once by the tracking and control station;

[0111] (2) Each task must have a corresponding tracking plan;

[0112] (3) The current measurement and control arc can only serve one type of flight control event. For example, if a certain arc has been included in the periodic measurement and control tracking task, no other tracking tasks will be arranged even if there is remaining time in the arc. This agreement will cause some waste of the arc, but it provides better reliability for engineering tasks;

[0113] (4) The start time of the measurement and control tracking task needs to fall within the measurement and control arc time interval;

[0114] (5) The order of using the stations in the tracking and use plan of the measurement and control network is unique;

[0115] (6) The order of flight control events in the tracking and use plan of the measurement and control network is unique;

[0116] (7) For the same mission, the tracking and control network only tracks and serves one primary target spacecraft at the same time, that is, multiple flight control events need to be executed serially.

[0117] Step 3: Construct a mathematical model for the optimal selection of measurement and control arc segments, including parameters, variables, constraint equations and objective functions.

[0118] (1) Define the parameters as follows:

[0119]

[0120]

[0121] Table 1 Parameters

[0122] (2) Define the variables as follows:

[0123] Boolean decision variables, m∈M, j∈N, k∈K, when the tracking and control station m serves the flight control event j in the kth visible time window, otherwise,

[0124] Boolean decision variable, u∈U j ,j∈N 2 , when the u-th continuous tracking plan serves the continuous tracking task j, otherwise,

[0125] Boolean decision variables, m∈M, i∈N, j∈N. When the tracking and control station m completes the service of task i and then serves task j, otherwise,

[0126] Boolean decision variables, m∈M, k∈K, when the tracking station m is used in the kth visible time window, otherwise,

[0127] t j : Time variable, the start tracking time of flight control event j, j∈N;

[0128] Let A j , B j is the earliest possible start time and the latest possible start time of the flight circle of target j in all visible arcs, then H = B i -A j ,i≠j∈N.

[0129] (3) The optimization goal of the problem is defined as: on the basis of completing all tracking requests within the task cycle, minimize the number of measurement and control windows used and improve the efficiency of measurement and control resource utilization.

[0130] (4) The complete mathematical model is as follows:

[0131]

[0132] st

[0133]

[0134]

[0135] Formula (1) indicates that the optimization goal is to occupy the least measurement and control resources, that is, to use the least measurement and control arc segments, while satisfying all flight control event arrangements. Constraint (2) defines each non-continuous tracking task j∈N 1 All must be tracked once by the tracking station. Constraint (3) limits each continuous tracking task j∈N 2 There must be a continuous tracking plan for the task. Constraint (4) indicates that the current tracking arc can only serve one type of flight control event. Constraints (5) and (6) limit the tracking arc to fall within the visible event window time interval. Constraint (7) ensures the uniqueness of the station usage order in the tracking usage plan of the tracking network. Constraints (8) to (10) are constraints. The linearization of ensures the uniqueness of the flight control event arrangement order in the tracking plan. Constraint (11) limits the uniqueness of the tracking arc. Constraint (12) ensures a simple temporal relationship between adjacent tracking tasks, that is, the successor task j can only start after the predecessor task i is completed. Constraints (13)-(17) represent the decision variables and t i The value range of .

[0136] Step 4: Use the landmark-based branch and bound algorithm to calculate and solve.

[0137] Branch and bound is a method based on search and iteration. It is the most commonly used method for solving mixed integer programming models. Its main idea is to search by selecting different branch variables and sub-problems to find the integer solution that makes the objective function value reach the optimal value in the feasible domain. The algorithm processing flow generally includes steps such as problem initialization, branch selection, iterative search, and generation of optimal solution. During the solution process, the algorithm will traverse the search space. With the increase of variables and constraints, the calculation space will expand sharply, resulting in reduced solution efficiency.

[0138] This application proposes a landmark-based branch-and-bound algorithm, which sets a dynamic guidance strategy in the "branch selection" step of the traditional algorithm to guide and optimize the search path and improve the efficiency of the algorithm solution. The specific method is to set the branch selection strategy according to the criterion of "minimum difference between the length of the measurement and control arc segment and the execution time of the flight control event", so as to reduce the fragmentation of the measurement and control arc segment and avoid the situation where a shorter task occupies a larger time window as much as possible.

[0139] set up It represents the difference between the length of the measurement and control arc and the execution time of the flight control event. The landmark is adjusted in real time according to the settlement result. If some paths are found to be feasible optimal solutions multiple times during the search process, the landmark is updated and the potential upper bound of the solution is calculated to help the algorithm prune the unfavorable search path faster and realize the dynamic adjustment of the search strategy. and are time windows k 1 and k 2 When selecting the branch to be processed, the heuristic function is used. Determine the direction of the next search. If Then the time window k is considered 1 is a better local solution; otherwise, it is considered that the time window k 2 is a better local solution.

[0140] Step 5: Output the results.

[0141] In the mathematical model constructed in step 3, the flight control events and the measurement and control arc segments are associated. The program processing result example is shown below:

[0142]

[0143] In the above results, the time format uses the UTC (Universal Coordinated Time) time format.

[0144] In this embodiment, for the optimization problem of tracking and control resource scheduling of multi-objective low-orbit spacecraft, a mixed integer programming method is used to achieve rapid selection of tracking and control arc segments, including:

[0145] (1) In terms of modeling, we comprehensively consider the task attributes, resource requirements and other conditions, and propose to relax the two tightly coupled issues of arc segment selection and task scheduling in complex engineering problems from three perspectives: "model assumptions", "usage constraints" and "arc segment usage configuration". We define the problem boundaries and condense complex engineering problems and task scenarios into scientific problems. We no longer need to focus on the results of task scheduling to define the selection range of the visible time window. Instead, we can use precise mathematical models to represent task attributes and then directly obtain the optimal selection results through problem solving.

[0146] (2) In terms of mathematical models, objective functions and constraint equations are constructed. The constructed mathematical model covers the basic requirements for the use of measurement and control resources and realizes a general model architecture for the rapid selection of measurement and control resources for low-orbit multi-target spacecraft.

[0147] (3) In terms of solution, the landmark method is introduced into the traditional branch and bound algorithm for solving mixed integer equations, and a dynamic discriminant heuristic strategy for branch selection is set, which effectively reduces the computational space and improves computational efficiency.

[0148] exist Figure 2 In the embodiment of the present application, a system for optimizing the selection of measurement and control arc segments based on mathematical programming is provided, comprising:

[0149] Modeling condition analysis module, used to analyze modeling conditions of engineering problems, propose model assumptions, and define problem boundaries;

[0150] A constraint condition module, used to set the constraint conditions for the use of the measurement and control resources;

[0151] Mathematical model module, used to construct mathematical models by measuring and controlling resource usage constraints;

[0152] The calculation and solution module is used to complete the calculation and solution using the mathematical model to obtain the optimal solution for arc segment usage within the task cycle.

[0153] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources.

[0154] An embodiment of the present application also provides an electronic device, which includes a processor, the processor is coupled to a memory, and the memory stores at least one computer program. The at least one computer program is loaded and executed by the processor so that the electronic device can implement any one of the methods for optimizing the selection of measurement and control arc segments based on mathematical programming.

[0155] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources.

[0156] An embodiment of the present application also provides a computer-readable storage medium, in which at least one computer program is stored. The at least one computer program is loaded and executed by a processor so that the computer-readable storage medium implements any one of the mathematical programming-based measurement and control arc segment optimization selection methods.

[0157] In the above technical solution, a mathematical model is constructed through the constraints on the use of measurement and control resources; the mathematical model is used to complete the calculation and solution to obtain the optimal solution for the use of arc segments within the task cycle; complex engineering problems and task scenarios are condensed into scientific problems. It is no longer necessary to focus on the results of the initial task arrangement to define the selection range of the visible time window, but to use accurate mathematical models to represent the task attributes, and then directly obtain the optimal selection result through problem solving, thereby improving the efficiency of the use of measurement and control resources.

[0158] Those skilled in the art will appreciate that the present application may be implemented as a system, method or computer program product.

[0159] Therefore, the present disclosure may be specifically implemented in the following forms, namely: it may be completely hardware, it may be completely software (including firmware, resident software, microcode, etc.), or it may be a combination of hardware and software, generally referred to herein as a "circuit", "module" or "system". In addition, in some embodiments, the present application may also be implemented in the form of a computer program product in one or more computer-readable media, and the computer-readable medium may contain computer-readable program code.

[0160] Any combination of one or more computer-readable media can be used. Computer-readable media can be computer-readable signal media or computer-readable storage media. Computer-readable storage media can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or devices, or any combination of the above. More specific examples (non-exhaustive list) of computer-readable storage media include: electrical connections with one or more wires, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, portable compact disk read-only memories (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above. In this document, computer-readable storage media can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it.

[0161] Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art can change, modify, replace and modify the above embodiments within the scope of the present application. On this basis, a variety of replacements and improvements can be made to the present application, all of which fall within the scope of protection of the present application.

Claims

1. A method for optimizing the selection of measurement and control arc segments based on mathematical programming, characterized in that: The following steps are involved: Construct mathematical models by measuring and controlling resource usage constraints; The mathematical model is used to complete the calculation and solution to obtain the optimal solution for arc segment usage within the mission cycle.

2. The method for optimizing the selection of measurement and control arc segments based on mathematical programming according to claim 1 is characterized in that: Also includes: Analyze modeling conditions for engineering problems, propose model assumptions, and define problem boundaries; The measurement and control resource usage constraint conditions are set.

3. The method for optimizing the selection of measurement and control arc segments based on mathematical programming according to claim 2 is characterized in that: The model assumptions include: At the same time, different antennas of the same satellite are regarded as different tracking and control stations; The tracking arc duration actually used by the spacecraft is shorter than the visible window length; Flight control events are the basic objects of planning, and each flight control event is an independent measurement, control and tracking task; According to the duration of the mission, flight control events include continuous tracking missions and non-continuous tracking missions; Non-continuous tracking tasks include periodic events, key point tasks, and general tasks; In a given mission cycle, each tracking and control station can track the target spacecraft multiple times, and each tracking occupies an exclusive visible time window.

4. The method for optimizing the selection of measurement and control arc segments based on mathematical programming according to claim 3 is characterized in that: The measurement and control resource usage constraints include: Each mission must be tracked once by the tracking and control station; Each task must have a tracking plan corresponding to that task; The current tracking and control arc can only serve one type of flight control event; The start time of the measurement and control tracking task falls within the measurement and control arc time interval; The order of using the measuring stations in the tracking and using plan of the measurement and control network is unique; The order of flight control events in the tracking and use plan of the measurement and control network is unique; For the same mission, the tracking and control network only tracks and serves one primary target spacecraft at the same time.

5. The method for optimizing the selection of measurement and control arc segments based on mathematical programming according to claim 4 is characterized in that: A landmark-based branch and bound algorithm is used to calculate the solution.

6. The method for optimizing the selection of measurement and control arc segments based on mathematical programming according to claim 5 is characterized in that: The mathematical model includes parameters, variables, constraint equations and objective functions.

7. The method for optimizing the selection of measurement and control arc segments based on mathematical programming according to claim 6 is characterized in that: The formula of the mathematical model includes: in, Represent different decision variables; t i represents the time variable; H is the large number introduced to determine the continuous tracking task; S is the set of spacecraft; M is the set of tracking and control stations; N1={1,…,N1} is the set of non-continuous tracking tasks; N2={n1+1,…,n1+n2} is the set of continuous tracking tasks; N=N1∪N2 is the set of all flight control events; K sm ={1,…,k sm } is the visible time window set of the tracking and control station m for the target spacecraft s, m∈M,s∈S; M j is the corresponding measurement and control station set of flight control event j, j∈N; is the set of all available visible time windows; σ m b is the switching time between two consecutive flight control events at the control station m, m∈M; j The spacecraft corresponding to flight control event j, j∈N,b j ∈S;p j is the execution time of flight control event j, j∈N; [r jk ,d jk ] is the measurement and control arc segment of flight control event j in the visible time window k, j∈N,k∈K; is the set of all feasible continuous tracking plans, j∈N2.

8. A system for optimizing the selection of measurement and control arc segments based on mathematical programming, characterized in that: include: Modeling condition analysis module, used to analyze modeling conditions of engineering problems, propose model assumptions, and define problem boundaries; A constraint condition module, used to set the constraint conditions for the use of the measurement and control resources; Mathematical model module, used to construct mathematical models by measuring and controlling resource usage constraints; The calculation and solution module is used to complete the calculation and solution using the mathematical model to obtain the optimal solution for arc segment usage within the task cycle.

9. An electronic device, characterized in that: The electronic device includes a processor, the processor is coupled to a memory, at least one computer program is stored in the memory, and the at least one computer program is loaded and executed by the processor so that the electronic device implements the method for optimizing the selection of measurement and control arc segments based on mathematical programming as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: At least one computer program is stored in the computer-readable storage medium, and the at least one computer program is loaded and executed by the processor so that the computer-readable storage medium implements the method for optimizing the selection of measurement and control arc segments based on mathematical programming as described in any one of claims 1 to 7.

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