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doi: 10.24411/2409-5419-2018-10170
METHOD OF SCHEDULING DEPLOYMENT MEANS OF GROUND AUTOMATED CONTROL COMPLEX OF SPACECRAFT
MIKHAIL A. KOLPIN1 ABSTRACT
Topical problem of scheduling deployment means of ground automated control complex PETR A. PROTSENKO2 of spacecraft is defined in this article. It is concluded that the use of the existing methods
research backup in the field of application scheduling ground control means complex is difficult for operation scheduling of several ground control complex in integrated system. Complexity is due to high dimensionality of the optimization task and the problem of formalized accounting of technical and technological limitations system for control of miscellaneous spacecraft. The proposed method of means deployment scheduling of ground control complex is based on the statement of this problem in terms of graph theory. Multitude variants of means deployment of ground automated control complex of spacecraft is represented in the form of an undirected graph in which the vertices are control operations, and arcs reflect the possibility of joint assignment of corresponding control operations connected to vertices. The task of finding the optimal means deployment plan of ground automated control complex is formulated as the search for the maximum clique - the maximum set of vertices that form the complete subgraph of the initial graph. The algorithm of search the connected components of the graph, allowing the decomposition of the original problem into several independent scheduling sub-tasks, is used to reduce the dimension of the problem. It is estimated that to find the maximum clique of graphs with less than 70 vertices, it is expedient to use the Bron-Kerbosh algorithm. In other cases, it is recommended suboptimal procedures to find acceptable solutions in polynomial time. The developed methodology is brought to the software and mathematical support, to obtain rational plans for engaging the ground control complex and assessing the effectiveness of their possible implementation based on the composition and structure of ground automated control complex.
Information about authors:
1PhD, Head at the laboratory - Senior Researcher
of the Military Space Academy,
St. Petersburg, Russia, [email protected]
2PhD, Head at the laboratory - Senior Researcher
of the Military Space Academy KEYWORDS: spacecraft; technological control cycle; scheduling engagement means;
St. Petersburg, Russia, [email protected] graph theory; graph connectivity; maximum click.
For citation: Kolpin M.A., Protsenko P.A. Method of scheduling deployment means of ground automated control complex of spacecraft. H&ES Research. 2018. Vol. 10. No. 5. Pp. 90-99. doi: 10.24411/2409-5419-2018-10170
1. Introduction
In the context of the variety and complexity of tasks to be solved in space and from space using spacecraft (SC) for various purposes, it is particularly important to ensure the effectiveness of their targeted operation.
The efficiency of the SC orbital groups (OG) operation directly depends on the quality of the SC control problem solution, which consists in the SC onboard systems control using ground-based technical means, which are organizationally integrated into the ground-based automated SC control complex (GACC). GACC is understood as a set of interrelated technical means, information, mathematical and software intended for the formation of ground control systems (GCS) of all types of domestic SCs. The tasks of ensuring the implementation of control programs for SC of a certain purpose, as well as the issuance of control actions based on the analysis of measuring information about the state of the SC are solved in the GCS.
Planning to involve the resource of GACC for operations management SC is characterized by cyclic technologically sophisticated multi-step procedure. The main purpose of planning the use of the GACC is a conflict-free distribution of its resource, and the result is a plan of operations for each SC for a day, which indicates the time of their implementation and the list of the involved SC controls.
Thus, from the structure of the GACC and the planning, allocation of resources directly affects the ability to meet the demands of mission control centres (MCC) for the involvement of some other means of control, i.e. the possibility of issuing control actions on Board the SC and the necessary volume measurements in the required time.
The existing technology of planning of attraction of means of GACC for management of SC consists in the decentralized planning of their involvement in MCC and the subsequent coordination of the received plans for resolution of conflict situations between applications of various MCC.
The methodological basis for planning and evaluating the effectiveness of such complex systems as GACC SC is based on the use of the methodology of the system approach, principles and methods of systems engineering, methods of optimal control theory and multimodel studies, as well as their applications to the management of space assets, called space Cybernetics. The development of this direction is devoted to the work of V. N. Kalinina, B.A. Reznikov, I. I. Delia and their students: B. V. Sokolov, Yu. s. Manuilov, A. N. Pavlov and other scientists [1-8]. A wide front of research in this direction were conducted and are conducted abroad. The most interesting results in the field of planning and management of complex technical systems were obtained by foreign scientists K. Schilling, M. Schmitt, R. Erwin and others [9-13].
However, most of these works are focused on planning the operation of the GCS SC of a certain purpose, for example, SC navigation or surveillance. The work of planning the oper-
ation of the GACC as a single SC control system, from which a resource is allocated for the operational time interval to solve the SC control problems of specific space complexes (systems) (SC(S)), is not given due attention.
This circumstance is due to the peculiarities of the extensive period of development of the GACC at the end of the twentieth century, which contributed to the emergence of a large range of types of onboard SC control systems and, accordingly, ground-based SC control, which led to a reasonable decomposition of the task of planning the operation of the GSC SC.
At the present stage of development of GACC there is a tendency to reduce the range of types of on-Board systems and ground controls, which together with the increase in the composition of the domestic OG SC leads to an increase in the number of conflicts between the MCC SC to use the General technical resource of GACC.
Results of the analysis of applicability of scientific and methodical reserve in the field of planning of functioning of separate GCS for ensuring management of SC show that their use is very problematic for planning of functioning of GACC as a whole.
First of all, this is due to the difficulties of formalization and solution of the problem of finding the optimal plan for the use of GACC funds to perform a set of operations of OG SC in the dynamic or static setting. These difficulties are due to the large dimension of the optimization problem and the problematic formalized accounting of the entire system of technological constraints imposed on the control process of SC for various purposes (different composition of control operations, sequence of operations, compatibility of operations, their duration, etc.).
In this regard, it becomes urgent to develop alternative approaches to plan the use of SC management tools, allowing on the basis of the composition, structure and parameters of the spacecraft, GACC, as well as the requirements and limitations of SC management technologies, to obtain rational, in the sense of the selected system of performance indicators, plans for the use of GACC SC.
2. Formalization of the tasks of the deployment
means of ground automated control complex
of spacecraft
SC control is carried out in accordance with the recommended by the developer cyclogram of planning and timely execution of the main SC control operations, which include:
- the holding and processing of measurements of current navigation parameters (MCNP) SC;
- reception from SC and processing telemetry information (TMI);
- loading of the command software information to the SC board (CSI);
- reconciliation of onboard time scale (RTS) and correction of on-Board SC generator.
Cyclically repeating sequence of specified operations with respect to the amount of their execution and relationships between them (of compatibility, incompatibility, route) is called manufacturing cycle management (MCM) SC [8].
The quality of the execution MCM SC depends on the ability to achieve the required values of indicators of efficiency of use of SSC(S). The management of SC is in the radio coverage zones (RCZ) of the GACC means. Each RCZ can be characterized by the following set of parameters:
- GACC tool number;
- SC number;
- RCZ entry time;
- RCZ output time;
- number visible by means of GACC daily round of the SC.
Within finding the SC in RCZ means the GACC may be
operated to perform various control operations. Each management operation has a time standard run set in MCM by the specific SC. In this case, the control operation can be carried out if the time required to perform it is less than the duration of the corresponding RCZ. For a sufficiently large duration of the RCZ plan the conduction of several management operations. The start time of the control operation can be planned within the range of the SC in the radio visibility zone.
Thus, each zone of radio visibility of SC by means of GACC can be represented as a set of alternatives by types of the carried-out operations of management and times of the beginning of their performance. The set of these alternatives in all areas of coverage OG SC means GACC forms many alternatives to the use of funds GACC, to ensure control:
z = {z } z = {o,k,s,h}
where k. — SC number;
i 7
s. — Tool number;
i 7
0.—Operation type;
t — The interval of staying in RCZ t = (t , t );
i JO v bX BBIX7 '
1.—Number of the SC revolution.
i
Due to the fact that the plan for the use of GACC means should reflect the control technology of the SC, up to z it can be narrowed to a variety of acceptable alternatives ZA, considering a set of technological limitations imposed on the control process of the SC. For this MCM SC can be conveniently represented in the form of multiple applications for maintenance on funds of GACC:
T = {j},
where t. = (k, o, l).
i x i i y
Here k. — SC number;
j
0 . — Type of the control operation;
1 — Number of the SC revolution where the operation should be fulfilled.
Then the set of acceptable alternatives to the use of GACC means, considering the SC control technology, is presented as Z. = ZflT={z }, where n = 1...N.
A n' '
It should be noted that the generated set does not consider the temporary location of the control operation in the radio visibility zone. To take this fact into account, each acceptable alternative of activation is represented as a set ZA of alternatives, which differs in the start times of the operation in the radio visibility zone. In order to take this fact into account each acceptable alternative of engagement zn is presented as a set of alternatives z[, differs by the time of the beginning of the operation o. in RCZ t., i.e. zn = {z'},k = 1,N.
Considering the technical limitations of planning the use of GACC ZA it is convenient to present as an undirected graph without loops G, in which the vertices are control operations, and the arcs reflect the possibility of joint assignment to the plan of using the GACC means corresponding to the connected vertices of control operations.
However, vertices cannot be connected by arcs if the control operations involve:
- simultaneous work with two funds GACC, one SC;
- holding the work with one tool the GACC SC in two;
- simultaneous means the GACC SC two control operations, one SC;
- the use of the same means of GACC shall be carried out with an interval of time between the operations of the office not exceeding the time required for its preparation for work. This system of constraints is sufficient to account for technology loads CSI and reception of SC TMI. Technology of fulfillment the MCNP requires to measure two or three funds for several consecutive orbits. The complexity of accounting for this technology is the need for group management operations in a strictly specified sequence. For these purposes, you want to make the following transformations of the graph:
1. For each operation of the MCNP is determined by the number of possible inclusions in different schemes of the MCNP, which is determined by the amount of funds involved in the round. For example, to account for the control technology of three means on two consecutive revolutions m=3, two means on three consecutive revolutions m=2, with the possibility of using both control technologies m=5.
2. The Vertices of the graph that correspond to the operations of the MCNP are duplicated m, and they are assigned an attribute—the number of the copy.
3. The Vertices of the graph i and j are not connected by arcs if they are a copy of one vertex, belong to different schemes (technologies) of carrying out MCNP, and also in cases if the condition is fulfilled |l; -l;-1 > n -1, where l — a loop number, where is the planned operation MCNP SC, but n — he number of consecutive revolutions in the scheme of the MCNP.
The generated graph contains many plans for the use of GACC funds. Each such plan is a complete subgraph, i.e. a
graph with all vertices connected to each other. Due to the fact that the plan for the use of funds of the GACC should contain the operations laid down in the MCM, the task of finding a rational plan for the use of funds of the GACC is to find in the constructed graph G the maximum complete subgraph (cliques) G* such that:
G* = argmax |G, |, i = ,
GteG
where I — a number of cliques in graph G.
At the same time, it is proposed to assess the quality of planning the use of GACC tools using the indicator of completeness of the MCM SC Q, equal to the ratio of the number of planned operations to the specified number of operations in the MCM SC T:
\G*\ Q = J\
3. Method of scheduling deployment means of ground automated control complex of spacecraft
It is known that the problem of finding the maximum clique is NP-complete [14]. To solve this problem, in 1973, the Bronn-Kerbosh algorithm was developed, the meaning of which is to find the most complete subgraph. Starting with a single vertex that forms a complete subgraph, the algorithm attempts to increment an already constructed complete subgraph by adding vertices from a set of candidates to it at each step.
The computational complexity of the algorithm is 0(3n/3) , where n is the number of vertices. The dependence of the maximum clique search time on the number of vertices in the graph using the Bronn-Kerbosh algorithm is illustrated in fig. 1.
180
j; 160 aT
jr 140 u
I 120
E
1 100 E
J 80
HO
£ 60 u
fO
X 40
Q1 £
>" 20
0
o 20 40 60 so
Number of uertides in the graph
Fig. 1. The dependence of time of search of the maximum clique from graph power
In the task of finding a plan to use the existing composition of the GACC to control the orbital grouping of SC, numbering, for example, 20 SC, the number of vertices in the graph is several thousand, which greatly complicates the use of the armor-Kerbosh algorithm due to the unacceptably long time required for the relevant calculations (a few months on a supercomputer).
The analysis of mathematical approaches to solving the problem of finding the maximum clique for large graphs shows that the problem of dimension can be solved by constructing and working with the addition G of the graph G. Due to the fact that the feature of the original graph G is its high connectivity, G, in turn, is a sparse disconnected graph, in which the edges are connected only those vertices that cannot be simultaneously included in the plan of using the means of GACC.
Incoherence of G/ is due to the presence of SC control operations, the planning of which should be carried out independently of each other. Such situations include, for example, planning of SC control operations on various visible revolutions, planning of SC control operations with GACC means intended for carrying out operations of only one type MCNP or TMI), etc.
Then the General approach to the search for the maximum clique is to construct an addition of the original graph, select a set of disconnected graphs for which additions are built, and then, in the search for the maximum clique. The formation of the maximum clique of the original graph is carried out by combining the maximum clique of its independent subgraphs.
On the basis of the presented methodological approach, the method of planning the use of GACC SC is developed, the structural and logical scheme of which is presented in fig. 2. The method consists of 6 main blocks.
The first block contains initial data on the composition, structure and parameters of the controlled OG SC, as well as the system of technical and technological limitations imposed on the SC control process.
Data on the orbital grouping contain information on the spatial position of each SC, the type of on-Board command and measurement system (CMS), as well as the structure and parameters of the process control cycle established by the SC manufacturer in the operational documentation.
In the presented technique MCM SC are set by mapping each operation of the control room visible diurnal round, which means the GACC got to do it.
Due to the fact that the duration of the operation of verification, phasing and correction of the onboard time scale in comparison with other control operations is small, and its implementation is usually carried out in conjunction with the operation of the CSI loading, these operations are combined into a single operation.
The ground-based automated control system of the SC is set by the geographical coordinates of the command measuring
Fig. 2. Structural-logical scheme of the method
points (CSI) and their equipment by the SC control means. Each control tool is described by a certain functionality-the types of control operations that it performs, as well as the type of on-Board CMS, with which the tool interacts.
In the second block of the technique the formation of an array of applications for operations of laying CSI, receiving TMI and MCNP based on the technological cycle of control of each SC. The application includes the following set of parameters:
- SC number;
- the type of operation control;
- room visible diurnal revolution on which you want to perform the operation control;
- duration of the control operation.
In the third block, the spatial-temporal characteristics of the CMP-SC interaction are calculated. As a result of the calculations, an array of potential zones for the use of GACC means for control operations is compiled, considering the technical compatibility of the control means with the onboard CMS. Each potential zone of use of the GACC is defined by the following set of parameters:
- OCMS number;
- number of the control means;
- SC number;
- the type of operation control;
- time to enter the radio visibility zone;
- time of exit from the zone of radio visibility;
- number the daily round;
- number of the visible diurnal round (visible coils dustproof numbered sequentially).
In the fourth block of the technique the search of all zones of radio visibility of SC by means of GACC and formation on their basis of a set of alternatives on performance of operations of management is carried out. Each control operation is a set of parameters including the potential zone parameters and two additional parameters:
- time to start using the tool;
- the end time of the trigger means.
Thus, from each zone of involvement is formed a set of potential control operations, differing in one or more parameters. Each potential control operation becomes the vertex of the graph G. Vertices are not connected by edges if operations cannot be performed together.
In the fifth block of the methodology, the search for a rational plan for the use of GACC funds is carried out. The procedure for finding a plan is to do the following:
1) Building the add-on G source graph G.
2) The allocation in G of the aggregate of disconnected subgraphs Gl,G2...Gn,n = 1,N . This action is performed using the graph connectivity algorithm to decompose the original problem into subtasks. To search for a set of unrelated subgraphs, it is convenient to use algorithms for finding graph
connectivity components (for example, in depth or width) [10], which are graph traversal methods that allow to identify such subsets of vertices in a graph that for any two vertices of these subsets there is a path from one vertex to another and there are no paths to vertices belonging to other subsets of vertices. The advantage of these algorithms is the linear convergence time relative to the number of vertices and edges in the graph
3) To found independentsub-graphs G1,G2...Gn,n = 1,N the relevant additions are being built G1,G2...Gn,n = 1,N and the number of vertices in graphs is determined |Gn |, n = 1, N .
4) Search for maximum clicks G1 ,G2...Gn,n = 1,N . At the same time, to solve the problem of finding the maximum clicks of graphs with less than 70 vertices, it is proposed to use the Bron-Kerbosh algorithm [15]. In other cases, it is recommended to use suboptimal procedures to find acceptable solutions in polynomial time [16].
5) Formation of the maximum clique of the original graph according to the following rule:
G' = G1* uG2* u...uGn,n = 1N.
Found clique G* it will contain the desired rational plan for the use of GACC SC funds.
In the sixth block of the technique, a rational plan for the use of the GACC means is drawn up by comparing the vertices of the found greatest clique of control operations from the set of permissible alternatives to the use of the GACC means.
4. Analysis of the effectiveness of the method of
scheduling deployment means of ground automated
control complex of spacecraft
To study the effectiveness of the proposed method in the article developed a software tool that allows you to automate the process of searching for rational plans for the use of GACC SC.
On the basis of the developed software a number of experiments for different versions of the original data. The main goal of the experiment was the comparison of the values of the indicator of the completeness of control of the SC, obtained using the developed technique and methodological approaches to the formation of plans for the utilization of funds GACC, implementing the heuristic procedures of FIFO and LIFO [17].
The initial data for the experiments were considered:
1) Three variants of OG SC, consisting of 10, 15 and 20 low-orbit SC, which can have the first or second type of onboard CMS.
2) The technological cycle of control of SC including the CSI tab and reception of TMI at the beginning and the end of day of planning, and also carrying out sessions of MCNP two measuring means on three consecutive revolutions or three measuring means on two consecutive revolutions.
3) Means of GACC SC placed on 8 command and measuring points (CMP) evenly distributed on latitude along the territory of the Russian Federation. In this case, each CMP is placed on one set of tools that have the functionality to perform SC control operations, equipped with the first or second type of onboard CMS.
The modeling of the following configurations of the GACC SC is carried OUT:
- the full composition of the funds GACC (configuration 1);
- funds GACC4 CMP Western part of Russia (configuration 2);
- GACC means 4 CMP of the Eastern part of the Russian Federation (configuration 3).
The results of planning are displayed in a table (fig. 3) and graphic (fig. 4) forms. In addition, it is possible to observe the interaction of controls with the SC in the development of the resulting plan for the use of the NAC in 3D mode (fig. 5).
According to the results of the experiments were obtained the plans for the utilization of funds GACC SC for different variants of initial data on the composition of the OG SC and GACC, along with their assessment of the completeness of the execution MCM SC.
SC OCMS Mean type Procedure Start Time | End Time Visible Revolution
SC7-2 CSI 8 ТВ MCNP 11:44:00 11:45:40 7
SC7-2 CSI 7 ТВ MCNP 11:45:45 11:47:25 7
SC7-2 CSI 8 ТВ MCNP 13:14:50 13:16:30 8
SC7-2 CS I 7 T8 MCNP 13:16:45 13:18:25 8
SC7-2 CSI 6 ТВ MCNP 14:50:15 14:51:55 9
SC7-2 CSI 5 ТВ MCNP 14:52:25 14:54:05 9
SC7-2 CSI 7 ТВ CSI 02:42:00 02:47:25 1
SC7-2 CSI 5 ТВ TM1 04:15:55 04:19:10 2
SC7-2 CSI 2 ТВ CSI 18:01:25 18:06:50 11
SC7-2 CSI 4 ТВ TM1 19:29:15 19:32:30 12
SC7-1 CSI 5 МА9 NMI 03:28:00 03:31:15 2
SC7-1 CSI 4 SC CSI 18:42:35 18:48:00 10
SC7-1 CSI 1 МА9 TMI 20:20:00 20:23:15 13
SC6-3 CSI 8 ТВ MCNP 09:54:05 09:55:45 6
Fig. 3. Tabular presentation of the plan for the use of GACC means
so-i
Г • 1 • ' Î • • 1 • ! • 1 ' • ! 1 • ' • i ' 1 11 • ! 11 1 11 • ! • ' • • I 1 • • " I • 1 s жш»
8-00:00-00 e-0}:4t:40 «-№31:20 »08:10:00 1)1:06:40 llJiS);» ('16:40:00 »19:»; 40 »'21:13:10
Fig. 4. Graphical representation of the plan for the use of GACC means
Comparative analysis of the results (Fig. 6) allows you to draw the following conclusions:
- in conditions of excess management SC values for the indicator completeness of the performance MCM SC for the resulting plans, leveraging funds GACC using the proposed methodology and the considered heuristic procedures differ slightly, with the developed method allows to increase Q on the level of 3-4%;
- in the conditions of the reduced composition of the SC control facilities, the values of the completeness index of MCM SC execution for the obtained plans of the GACC funds utilization according to the proposed method are on average 10-15%
higher than for the heuristic algorithms FIFO and LIFO, which is due to the use of optimization procedures in the developed method for solving the problem of finding the maximum clique;
- the time spent on the build plan of use of funds GACC SC using the developed technique, much higher (tens of minutes) than for the heuristics FIFO and LIFO (tens of seconds). Therefore, in the operational planning of the use of GACC TOOLS in conditions of lack of time or excessive composition of controls, it is rational to use heuristic algorithms FIFO or LIFO.
It should be noted that, despite the computational complexity, the proposed method has a number of significant advantages, the main ones are:
Fig. 5. The display in the 3D mode of implementation of the plan functioning of the GACC
Fig. 6. Assessment of the completeness of the execution MCM SC for various compositions GACC and OG SC
- simplified procedure of formalized accounting of technological limitations differing in composition and structure imposed on the control process of different types of SC;
- optimization of the technology of constructing a plan for the use of GACC TOOLS through the possibility of using optimal and suboptimal methods for finding the maximum clique of the graph;
- the possibility of simultaneous conflict-free planning of the use of heterogeneous OG SC, which makes it possible to transform a complex multi-stage procedure of decentralized planning and coordination of GACC SC into a technology of planning and resource allocation of the SC controls from a single center.
Conclusion
The developed method is the development of scientific and methodological apparatus of planning and evaluation of the efficiency of the GACC SC and can be used to assess the target capabilities of different configurations of the GACC considering the complex system of technical, technological and space-time constraints imposed on the SC control process.
The proposed methodology allows to correctly formulate and solve a number of relevant scientific and practical problems of analysis and synthesis of automated control systems of SC:
1) assessment of the effectiveness of the GACC SC different conditions;
2) assessment of target opportunities promising GACC SC and promising technologies for SC control;
3) planning the use of funds of both individual GCS and the GACC SC a whole for the implementation of SC management programs;
4) the rationale for the various requirements as to particular types of controls SC, and to the GACC SC in General;
5) substantiation of the directions of development and improvement of the GACC SC, etc.
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МЕТОДИКА ПЛАНИРОВАНИЯ ЗАДЕЙСТВОВАНИЯ СРЕДСТВ НАЗЕМНОГО АВТОМАТИЗИРОВАННОГО КОМПЛЕКСА УПРАВЛЕНИЯ КОСМИЧЕСКИМИ АППАРАТАМИ
КОЛПИН Михаил Александрович, КЛЮЧЕВЫЕ СЛОВА: космический аппарат; технологический
г. Санкт-Петербург, Россия, [email protected] цикл управления; планирование задействования технических
средств; теория графов; связность графа; максимальная клика.
ПРОЦЕНКО Пётр Александрович,
г. Санкт-Петербург, Россия, [email protected]
АННОТАЦИЯ
В работе обоснована актуальность задачи планирования задействования средств наземного автоматизированного комплекса управления космическими аппаратами. Сделан вывод о том, что использование существующего научно-методического задела в области планирования средств отдельных наземных комплексов управления затруднительно для планирования задействования функционирования наземного автоматизированного комплекса управления в целом. Сложности обусловлены большой размерностью оптимизационной задачи и проблематичностью формализованного учета всей системы технических и технологических ограничений, накладываемых на процесс управления космическими аппаратами различного целевого назначения. Предложена методика планирования задействования средств наземного автоматизированного комплекса управления, основанная на постановке указанной задачи в терминах теории графов, что позволило применить алгоритмы данной теории для ее решения. Множество вариантов задействования средств наземного автоматизированного комплекса управления для управления космическими аппаратами представлено в виде неориентированного графа без петель, в котором вершинами являются операции управления, а дуги отражают возможность совместного назначения в план соответствующих соединяемым вершинам операций управления. Задача поиска оптимального плана задействования средств наземного автоматизированного комплекса управления сформулирована как поиск максимальной клики - максималь-
ного множества вершин, которые образуют полный подграф начального графа. Для уменьшения размерности задачи используется алгоритм поиска компонент связности графа, позволяющий провести декомпозицию исходной задачи на несколько независимых подзадач планирования. Установлено, что для отыскания максимальной клики графов, имеющих мощность менее 70 вершин, целесообразно использовать алгоритм Брона-Кербоша. В других случаях рекомендуется применять субоптимальные процедуры, позволяющие находить приемлемые решения за полиномиальное время. Разработанная методика доведена до уровня программно-математического обеспечения, позволяющего исходя из состава и структуры наземного автоматизированного комплекса управления, орбитальной группировки космических аппаратов, используемых технологий управления космическими аппаратами получать рациональные планы задействования наземного автоматизированного комплекса управления и оценки эффективности их возможной реализации.
СВЕДЕНИЯ ОБ АВТОРАХ:
Колпин М.А., к.т.н., начальник лаборатории - старший научный сотрудник военного института (научно-исследовательского) Военно-космической академии имени А.Ф.Можайского. Проценко П.А., к.т.н., начальник лаборатории - старший научный сотрудник военного института (научно-исследовательского) Военно-космической академии имени А.Ф.Можайского.
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Для цитирования: Колпин М.А., Проценко П.А. Методика планирования задействования средств наземного автоматизированного комплекса управления космическими аппаратами // Наукоемкие технологии в космических исследованиях Земли. 2018. Т. 10. № 5. С. 90-99. doi: 10.24411/2409-5419-2018-10170 (English)
