Исследование устойчивости планов применения средств управления активными подвижными объектами

Владимир Петрович Сугак; Валерий Федорович Волков; Владимир Иванович Салухов; Алексей Сергеевич Карайчев

doi:10.15622/sp.2019.18.3.614-644

Vladimir Sugak Mozhaisky Military Space Academy
Valery Volkov Mozhaisky Military Space Academy
Vladimir Salukhov St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences (SPIIRAS)
Aleksey Karaychev Mozhaisky Military Space Academy

DOI:

https://doi.org/10.15622/sp.2019.18.3.614-644

Keywords:

Stability Across Lyapunov, Stability on Probability, Lyapunov's Function, an Active Mobile Object, the Moment of the First Exit, Optimum Control

Abstract

The paper considers research of the sustainability plans of active moving objects (AMOs) control system application. AMOs are material objects moving in space and carrying out informational, material and energetic interaction with objects, control points and other AMOs.

Use of AMOs is usually regulated by strict requirements, so any time delay or incomplete achievement of target effect are unacceptable. The reason of failing to perform a purpose task can be the development of control using incorrect plans, so that realization of the plan is unstable due to random factors or targeted effects of the environment and other systems. The paper deals with problematic issues of complex research of active moving objects control application stability plans .

Quantitative and qualitative assessment methods of stability plans , ways and means of ensuring required levels of stability are proposed by the authors. In this case planning task is considered dynamic, which provides plan correction by means of organizational, structural and program-algorithmic measures to ensure stability. The most adequate model of plan implementation is appropriate system of differential equations. Notion of stability probability is defined to account stochastic character of disturbance effect . The expression for stability criterion is obtained. It allows to establish the fact of sustainability and unsustainability based on analysis of properties of a purposefully built Lyapunov function and disturbances characteristics.

References

1. Kalinin V.N. Teoriya upravleniya kosmicheskim apparatom (na osnove koncepcii aktivnogo ob"ekta [The theory of control of the spacecraft (on the basis of the concept of an active object)]. SPb.: VKA imeni A.F. Mozhajskogo. 2014. 182 p. (In Russ.).
2. Yeliseyev A.S., Gitman M.B. [Estimating of the production plan taking stability into account stochasticity of resource restrictions]. Upravlenie bol'shimi sistemami – Large-Scale Systems Control. 2013. vol. 42. pp. 252–272. (In Russ.).
3. Seck B. et al. Stability Analysis and Regularization of Uncertain Linear Multi-Objective Integer Optimization Problems. Engineering Optimization. 2012. vol. 44. no. 11. рр. 1279–1302.
4. Greshilov A.A. [On stability of the optimal solution of the linear programming problem under uncertainty of the problem parameters]. Vestnik MGTU im. N.E. Baumana. Seriya "Priborostroenie" – Bauman Moscow State Technical University (BMSTU). Series "Instrument Engineering". 2003. vol. 4 pp. 54–63. (In Russ.).
5. Ivanov D., Sokolov B., Pavlov A. Dual problem formulation and its application to optimal redesign of an integrated production–distribution network with structure dynamics and ripple effect considerations. International Journal of Production Research. 2013. vol. 51. no. 18. pp. 5386–5403.
6. Rakhmonov F.N., Khamzayev A.A., Ismagilov M.F. [The Study of static stability of the Navoi thermal power plant by the method of Lyapunov functions in quadratic form]. Molodoj uchenyj – Young scientist. 2017. vol. 43. pp. 58–65. (In Russ.).
7. Burkov V.N. Optimal'noe upravlenie kompleksami operacij [Optimum control of complexes of operations]. M.: Nauka. 1972. (In Russ.).
8. Zimin I.N., Ivanilov Yu.P. [The solution of problems of network planning by their data to problems of optimum control]. Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki – Computational Mathematics and Mathematical Physics. 1971. Issue 11. vol. 3. pp. 632–641. (In Russ.).
9. Pavlov O.V. [Dynamic optimization of production activity of the enterprise taking into account effect of a curve of training]. Vestnik Samarskogo gosudarstvennogo jekonomicheskogo universiteta – Vestnik of Samara State University of Economics. 2015. Issue 3. vol. 125. pp. 88–92. (In Russ.).
10. Kokorin S.V., Potryasaev S.A., Sokolov B.V. [Complexed method of operations scheduling and distributing of active moving objects sources management system]. Izvestiya vysshih uchebnyh zavedenij. Priborostroenie – Journal of Instrument Engineering. 2012. Issue 55. vol. 11. pp. 17–22. (In Russ.).
11. Kalinin V.N. [O some problems of optimum control of information exchange of the spacecraft with the Earth's surface]. Trudy SPIIRAN – SPIIRAS Proceedings. 2015. vol. 4(41). pp 34–56. (In Russ.).
12. Carvalho M., Syguiy T. Efficiency and Effectiveness Analysis of Public Transport of Brazilian Cities. Journal of Transport Literature. 2015. vol. 9(3). pp. 40–44.
13. Novikov D.A., Smirnov I.M., Shokhina T. E. Mekhanizmy upravleniya dinamicheskimi aktivnymi sistemami [Mechanisms of management of dynamic active systems]. M.: IPU RAN. 2002. 124 p. (In Russ.).
14. Trotsky D.V., Gorodetsky V.I. [Scenario-based knowledge model and language for situation assessment and prediction]. Trudy SPIIRAN – SPIIRAS Proceedings. 2009. vol. 8. pp. 94–127. (In Russ.).
15. Matinheikki Y., Pesonen T., Artto K., Peltokorpi A. New value creation in business networks: The role of collektive action in constructing system-level goals. Industrial Marketing Management. 2017. vol. 67. рp.122–133.
16. Yi Z., Xiuxia Y., Hewei Z., Weiwei Z. Tracking control for UAV trajectory. Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference. 2014. pp. 1889–1894.
17. Popovic Z. Basic mathematical models in economic-ecological control. Series: Economics and Organization. Facta Universitatis. 2008. vol. 5. no. 3. pp. 251–262.
18. Feoktistov V.V., Feoktistova O.P., Chernishova I.N. [Aleksandr Mihaylovich Liapuno, the General Problem of the Stability of Motion]. Nauka i obrazovanie: nauchnoe izdanie MGTU im. N.E. Baumana – Science & education: Scientific Edition of Bauman MSTU. 2015. vol. 7. pp. 65–76. (In Russ.).
19. Belov A.A., Andrianova O.G. Computation of anisotropic norm for descriptor systems using convex optimization. 2013 International Conference on Process Control (PC). 2013. pp. 173–178.
20. Saati T. Decision making with the analytic hierarchy process. International Journal of Services Sciences. 2008. vol. 1. no. 1. pp. 83–98.
21. Ashimov A.A., Gejda A.S., Lusenko I.V., Yusupov R.M. [Performance and other operational properties of systems: objectives and method of evaluation]. Trudy SPIIRAN – SPIIRAS Proceedings. 2018. vol. 5(60). pp. 241–270. (In Russ.).
22. Mirjalili S., Mirjalili S. M., Lewis A. Grey Wolf Optimizer. Advances in Engineering Software. 2014. vol. 69. pp. 46–61.
23. Sheeba P.S.,Ghose D. Optimal Resourse Allocation and Redistribution Strategy in Military Conflikts with Lanchester Squre Law Attrition. Naval Research Logistics (NRL). 2008. vol. 55. no. 6. pp. 581–591.
24. Lyapunov A.M. Obshchaya zadacha ob ustojchivosti dvizheniya [The general task about stability of the movement]. M.: Gostekhizdat. 1950. 472 p. (In Russ.).
25. Kramer J.S., Orlik L.K. [On the extension of the concept of Lyapunov stability]. Nauchno-metodicheskij elektronnyj zhurnal Koncept – Scientific and methodical electronic journal Concept. 2017. vol. 39. pp. 1871–1875. (In Russ.).
26. Kushner J. Stochastic stability and management. Academic Press. 1967. 176 p. (Russ. ed.: Kouchner G.Dzh. Stohasticheskaya ustojchivost' i upravlenie. M.: Mir. 1969. 200 p.).
27. Rantzer A. A dual to Lyapunov’s stability theorem. Systems & Control Letters. 2001. vol. 42. no. 3. pp. 161–168.
28. Ivanov A.K. [Optimization of stability of hierarchical control systems]. Avtomatizacija processov upravlenija – Automation of control processes. 2015. vol. 3. pp. 23–33. (In Russ.).
29. Imkeller P., Milstein G.N. Moment Lyapunov exponent for conservative systems with small periodic and random perturbations. Stochastic Dynamics. 2002. vol. 2. pp. 25–48.
30. Kurek J.E. Stability of nonlinear time-varying digital 2-D Fornasini-Marchesini system. Multidimensional Systems and Signal Processing. 2014. vol. 25. no. 1. pp. 235–244.
31. Andronov A.A., Vitt A.A., Hajkin S.E. Teoriya kolebanij [Theory of fluctuations]. M.: Nauka. 1981. 918 p. (In Russ.).
32. Kalashnikov V.V. Kachestvennyj analiz povedeniya slozhnyh sistem metodom probnyh funkcij [Qualitative analysis of behavior of difficult systems by method of trial functions]. M.: Nauka. 1978. 247 p. (In Russ.).
33. Kuz'kin A.A. [A technique of ensuring stability of the strategy of development for information technologies in the organizations]. Trudy SPIIRAN – SPIIRAS Proceedings. 2014. vol. 6(37). pp. 95–115. (In Russ.).
34. Yadykin I.B. [Frequency method of the analysis of stability slaboustoychivykh of linear dynamic systems]. Mehatronika, Avtomatizacija, Upravlenie – Mechatronics, Automation, Control. 2014. vol. 3. pp. 3–9. (In Russ.).
35. Kovalenko A.Yu. [Analysis of structural stability of diverse systems of spacecrafts]. Trudy SPIIRAN – SPIIRAS Proceedings. 2014. vol. 4(35). pp. 108–116. (In Russ.).
36. Solovyova I.V., Sokolov B.V. [Algoritm of correction of plans of work of a corporate information system on the basis of a method of position optimization]. Trudy SPIIRAN – SPIIRAS Proceedings. 2012. vol. 1(20). pp 153–164. (In Russ.).
37. Karsayev O.V. [Review of traditional innovative systems of planning of missions of spacecrafts]. Trudy SPIIRAN – SPIIRAS Proceedings. 2016. vol. 5(48). pp. 151–181. (In Russ.).
38. Arsenyev V.N., Silantyev S.B., Yadryonkin A.A. [Use of aprioristic information for correction of model of a stream of events in the difficult system]. Izvestija vysshih uchebnyh zavedenij. Priborostroenie – Journal of Instrument Engineering. 2017. Issue 60. vol. 5. pp. 391–397. (In Russ.).
39. Devyatkov V.V. [Development of methodology and technology of imitating researches of the difficult systems]. Trudy SPIIRAN – SPIIRAS Proceedings. 2014. vol. 5(36). pp. 44–58. (In Russ.).
40. Katagiri H. et al. Transactions of engineering technologies. International MultiConference of Engineers and Computer Scientists 2017. Springer. 2018. 403 p.
41. Yeganefar N., Yeganefar N., Ghamgui M., Moulay A. Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability. IEEE Transactions on Automatic Control. 2012. vol. 58. no. 5. pp. 1299–1304.
42. Gorban A.N. Coping with Complexity: Model Reduction and Data Analysis. Springer. 2010. 390 p.
43. Ivanov D., Pavlov A., Sokolov B. Exact and heuristic methods for integrated supply chain design reliability analysis. International Journal of Integrated Supply Management. 2016. vol. 10. no. 2. pp. 206–224.
44. Arhipov V. et al. Development of Event-Driven Models for Operation Data of Some Systems of Small Satellites. Computer Science On-line Conference. 2016. pp. 403–413.
45. Petuhov G.B., Yakunin V.I. Metodologicheskie osnovy vneshnego proektirovaniya celenapravlennyh processov i celeustremlennyh sistem [Methodological basis of external design of purposeful processes and purposeful systems]. M.: AST. 2006. 504 p. (In Russ.).
46. Najdenov V.G., Pershin E.V. [Study of interval measure of the accuracy of the trajectory measuring complex]. Vooruzhenie i jekonomika – Armament and Economics. 2017. vol. 3(40). pp. 14–21. (In Russ.).
47. Maltsev G.N., Nazarov V.A., Yakimov V.L. [Study of the process of diagnosing on-Board equipment of automatic spacecraft with ispolzovaniya-event simulation model]. Trudy SPIIRAN – SPIIRAS Proceedings. 2018. vol. 1(56). pp. 95–121. (In Russ.).
48. Kuntsevich V.M., Lychak M.M. Sintez sistem avtomaticheskogo upravleniya s pomoshch'yu funkcij Lyapunova [Synthesis of automatic control systems using Lyapunov functions]. M.: Nauka. 1977. 387 p. (In Russ.).
49. Matrosov V.M. Metod vektornyh funkcij Lyapunova: Analiz dinamicheskih svojstv nelinejnyh sistem [The method of vector Lyapunov functions: analysis of dynamical properties of nonlinear systems]. М.: Fizzmatlit. 2001. 381 p. (In Russ.).
50. Bellman P. Vector Lyapunov Functions. Journal of the Society for Industrial and Applied Mathematics. 1962. pp. 32–34.
51. Skobelev P.O. et al. [A New Approach to Managing Life Cycle of Aerospace Products using Complexity Theory]. Mekhatronika, avtomatizaciya, upravlenie – Mechatronics, Automation, Control. 2016. Issue 17. vol. 4. pp. 282–287. (In Russ.).
52. Reshmin S.A. Properties of the time-optimal control for Lagrangian single-degree-of-freedom systems. IEEE Transactions on Automatic Control. 2015. vol. 60. no. 12. pp. 350–355.
53. Katz I.Ya., Krasovsky N.N. [About stability of systems with casual parameters]. Prikladnaja matematika i mehanika – Journal of Applied Mathematics and Mechanics. 1960. Issue 24. vol. 5. pp. 809–823. (In Russ.).
54. Poltavskiy A.V., Burba A.A. [Modeling of unmanned aircrafts information managing systems tasks]. Dvojnye tehnologii – Doubled technologies. 2012. vol. 4. pp. 65–70. (In Russ.).
55. Goryanskij A.S., Prorok V.Y. [Technique of outer space optoelectronic monitoring devices application planning]. Vestnik MGTU im. N.E. Baumana. Seriya "Priborostroenie" – Bauman Moscow State Technical University (BMSTU). Series "Instrument Engineering". 2018. vol. 5. pp. 68–83. (In Russ.).
56. Borisenkov I.L., Kalinov M.I., Rodinov V.A. [Blighty space systems of earth surface radar and radio electronic monitoring]. Nauchno-tehnicheskie vedomosti Sankt-Peterburgskogo gosudarstvennogo politehnicheskogo universiteta – St. Petersburg State Polytechnic University Journal of Engineering Science and Technology. 2014. vol. 2(195). pp. 18–25. (In Russ.).
57. Ivanov D. et al. A dynamic model and an algorithm for short-term supply chain scheduling in the smart factory industry 4.0. International Journal of Production Research. 2016. vol. 54. no. 2. pp. 386–402.
58. Torkjazi M, Fazlollahtabar H. A Fuzzy Probabilistic Maximum Technique to Optimize an Unconstrained Utility Based Multi Objective Model. Industrial Engineering and Management. 2015. vol. 4. no. 147. pp. 2169–0316.
59. Arora N., Saini J.K.R. A Fuzzy Probabilistic Neural Network for Student’s Academic Performance Prediction. International Journal of Innovative Research in Science, Engineering and Technology. 2013. vol. 2. no. 9. pp. 4425–4432.
60. Laaksonen O., Peltoniemi M. The essence of dynamic capabilities and their measurement. International Journal of Management Reviews. 2018. vol. 20(2). рp. 184–205.
61. Pavlov A., Ivanov D., Dolgui A., Sokolov B. Hybrid Fuzzy-Probabilistic Approach to Supply Chain Resilience Assessment. IEEE Transactions on Engineering Management. 2017. vol. 65. no. 2. pp. 303–315.
62. Khuman A.S., Yang Y., John R. Quantification of R-fuzzy sets. Expert Systems with Applications. 2016. vol. 55. pp. 374–387.
63. Lertworaprachaya Y., Yang Y., John R. Interval-valued fuzzy decision trees with optimal neighbourhood perimeter. Applied Soft Computing. 2014. vol. 24. pp. 851–866.

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Robotics, Automation and Control Systems

Study of Plans Sustainability of Active Moving Objects Control Systems Application

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