DOI: https://doi.org/10.15588/1607-3274-2018-1-17

OPTIMAL CONTROLLING PATH DETERMINATION WITH THE HELP OF HYBRID OPTIONAL FUNCTIONS DISTRIBUTIONS

A. V. Goncharenko

Abstract


Context. The problem of the determination of the optimal value of the augmentation coefficient of a proportional governor included
into an inertness-less linear object control system on the basis of a synthesized model is solved. The object of the presented study is the
optimal control process.
Objective. The goal of the work is a creation of a method for a problematic situation of the optimum definition, evaluation, and
determination solving at the control system.
Method. A rough model of the phenomenon, and simplified dependence of optimal controlling trajectory upon the cost, of control in
an inertness-less linear controlling system equipped with a proportional governor are proposed. The accuracy of the behavior of the
investigated linear object of control has been chosen in the given consideration as an initial target value which needs to be minimized. The method of the model building with regards to an expenditures principle is offered. It provides taking into account the cost of controlling
process. It allows finding the optimal controlling value on the multi-optional basis. There applied a certain analogue to the subjective
entropy maximum principle of the subjective analysis in order to obtain a specific optimal distributions for the objective value in the view
of the composed functional. The method of the uncertainty degree of the options extremization is improved by a continuous optional value
introduction that allows forming the value distribution density. The optional synthesized model of the control process is built.
Results. The developed theoretical models allow obtaining, and have been implemented in, finding the hybrid optional density as an
optimal solution of a variational problem with two independent variables, which maximal value is the sought optimal controlling path
delivering minimum to the integrated expenses pertaining with the process.
Conclusions. The numerical experiments on the proposed methods studying in the problem of optimization are conducted. The
discovered dependencies are substantiated as a result of these experiments. Their use in practice makes it possible, and is recommended, to carryout optimal control in the described systems. The prospects for further research may include creations of models for the optimal control trajectories findings on conditions involving rates of the considered values varying and in probabilistic, stochastic, undetermined
problem settings.

Keywords


hybrid function; multi-optional control; distribution density; optimal path; variational principle; optimal controlling surface; optional functions entropy.

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GOST Style Citations


1. Subbotin S. O. Programni zasoby syntezu diagnostychnyh i
rozpiznaval’nyh modelej za precedentamy, Suchasni problemy i dosjagnennja v galuzi radiotehniky, telekomunikacij ta
informacijnyh tehnologij : VI Mizhnarodna naukovo-praktychna
konferencija, Zaporizhzhja, 19–21 veres-nja 2012 r. : tezy
dopovidej. Zaporizhzhja, ZNTU, 2012, pp. 21–22.
2. Boguslaev A. V., Olejnik Al. A., Olejnik An. A., Pavlenko D. V., Subbotin S. A. ; pod red. D. V. Pavlenko, S. A. Subbotina
Progressivnye texnologii modelirovaniya, optimizacii i
intellektual’noj avtomatizacii e’tapov zhiznennogo cikla
aviacionnyx dvigatelej : monografiya. Zaporozh’e, OAO “Motor
Sich”, 2009, 468 p.
3. Dmitriev S., Burlakov V., Popov O., Popov D. Technological
processes and quality control in aircraft engine maintenance,
Aviation, 2015, Vol. 19, No. 3, pp. 133–137.
4. Kulyk M., Dmitriev S., Yakushenko O., Popov O. Method of
formulating input parameters of neural network for diagnosing
gas-turbine engines, Aviation, 2013, Vol. 17, No. 2, pp. 52–56.
5. Sushchenko O., Goncharenko A. Design of Robust Systems for Stabilization of Unmanned Aerial Vehicle Equipment,
International Journal of Aerospace Engineering [Electronic
resource]. Access mode: http://ix.doi.org/10.1155/2016/6054081.
6. Zaporozhets O., Tokarev V., Attenborough K. Aircraft Noise.
Assessment, prediction and control. Glyph International, Tailor
and Francis, 2011, 480 p.
7. Solomentsev O., Zaliskyi M., Zuiev O. Estimation of Quality
Parameters in the Radio Flight Support Operational System,
Aviation, 2016, Vol. 20, No. 3, pp. 123–128.
8. Silberberg E., Suen W. The structure of economics. A mathematical analysis. New York, McGraw-Hill Higher Education, 2001, 668 p.
9. Kolstad Ch. D. Environmental Economics. New York, USA,
Oxford. Univ. Press, 2000, 400 p.
10.Intriligator M. Matematicheskie metody optimizatsiji i
ekonomicheskaja teorija. Moscow, Ajris-press, 2002, 576 p.
11. Subbotin S. O., Olijnyk A. O. (Ukrai’na) Pat. 18294 Ukrai’na, MPK2006 G06F 19/00. Sposib vidboru informatyvnyh oznak dlja diagnostyky vyrobiv ; zajavnyk Zaporiz’kyj nacional’nyj tehnichnyj universytet. № u200603087; Zajavl. 22.03.06; Opubl.15.11.06, Bjul. №11, 4 p.
12. Kasianov V. Subjective entropy of preferences. Subjective analysis: monograph. Warsaw, Poland, Institute of aviation, 2013, 644 p.
13. Kas’janov V. A., Goncharenko A. V. Variatsionnyje printsipy
subjectivnogo analiza. Modifitsirovannyj variatsionnyj printsyp
Ejlera-Lagranzha. Entropijnyj podkhod: monografiya. Kiev, DP
NVTS “Pryoritety”, 2015, 112 p.
14. Kas’janov V. A., Goncharenko A. V. Svet i ten’. Proportsii tenevoj ekonomiki. Entropijnyj podkhod: monografiya. Kiev, Kafedra, 2013, 86 p.
15. Kasyanov V., Szafran K. Some hybrid models of subjective analysis in the theory of active systems, Transactions of the Institute of Aviation, 2015, No. 3, pp. 27–31. (ISSN: 0509-6669 240)
16. Goncharenko A. V. Optimal managerial and control values for active operation, Electronics and control systems, 2016,
No. 3(49), pp. 112–115. (ISSN: 1990-5548)
17. Goncharenko A. V. Ekspluatatsija aktyvnykh transportnych
system v umovakh bagatoal’ternatyvnosti ta nevyznachenosti :dis. … dokt. tekhn. nauk : 05.22.20. Kyiv, Natsional’nyj
aviatsijnyj universytet, 2016, 328 p. http://er.nau.edu.ua:8080/handle/NAU/22359
18. Goncharenko A. V. Ekspluatatsija aktyvnykh transportnych
system v umovakh bagatoal’ternatyvnosti ta nevyznachenosti :avtoref. … dokt. tekhn. nauk : 05.22.20. Kyiv, Natsional’nyj
aviatsijnyj universytet, 2016, 39 p. http://er.nau.edu.ua:8080/
handle/NAU/22359; http://er.nau.edu.ua:8080/handle/NAU/22627                                                                     19. Goncharenko A. V. Several Models of Artificial Intelligence
Elements for Aircraft Control, Methods and Systems of Navigation and Motion Control (MSNMC) : 4th International Conference, Kyiv, 18–20 October 2016 : proceedings. Kyiv, National Aviation University (NAU), IEEE, 2016, pp. 224–227.
20. Goncharenko A. V. Applicable Aspects of Alternative UAV
Operation, Actual Problems of Unmanned Air Vehicles
Developments : 3rd International Conference, Kyiv, 13–15
October 2015 : proceedings. Kyiv, NAU, IEEE, 2015, pp. 316–
319.
21. Goncharenko A. V. Navigational alternatives, their control and subjective entropy of individual preferences, Methods and Systems of Navigation and Motion Control (MSNMC) : 3rd International Conference, Kyiv, 14–17 October 2014 : proceedings. Kyiv, NAU, IEEE, 2014, pp. 99–103.
22. Goncharenko A. V. Expediency of unmanned air vehicles
application in the framework of subjective analysis, Actual
Problems of Unmanned Air Vehicles Developments : 2nd
International Conference, Kyiv, 15–17 October 2013 :
proceedings. Kyiv, NAU, IEEE, 2013, pp. 129–133.
23.Gnoenskiy L. S., Kamenskiy G. A., El’sgol’ts L. E.
Matematicheskije osnovy teorii upravl’ajemykh sistem. Moscow, Nauka, 1969, 512 p.
24. Gel’fand I. M., Fomin S. V. Variatsionnoe ischislenie. Moscow, Gosudarstvennoe izdatel’stvo fiziko-matematicheskoj literatury, 1961, 228 p.
25. Kuntsevich V. M. Upravlenie v uslovijakh neopredelennosti:
garantirovannye rezul’taty v zadachakh upravlenija i identifikatsii: monografiya. Kyiv, Naukova dumka, 2006, 264 p.
26. Gnedenko B. V., Kovalenko I. N. Vvedenie v teoriju massovogo obsluzhivaniya : izd. 6. Moscow, URSS, 2013, 400 p.
27.Ventsel’ E. S. Teoriya verojatnostej: uchebnik. Moscow, Nauka, 1969, 576 p.






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