Control Systems and Computers

DOI: https://doi.org/10.15407/usim.2016.02.022

Upr. sist. maš., 2016, Issue 2 (262), pp. 22-27.

UDC 519.6

V.V. Komyak, PhD (Eng.), National University of Civil Protection of Ukraine (Kharkiv), E-mail: vlad1m1r@list.ru,

V.M. Komyak, Doctor (Eng.), National University of Civil Protection of Ukraine (Kharkiv), E-mail: vkomyak@ukr.net, 

A.V. Pankratov,  Doctor (Eng.), Institute of Mechanical Engineering of A.M. Podgorny NAS Ukraine (Kharkiv), E-mail: impankratov@mail.ru,

A.Yu. Prikhodko, adjunct, National University of Civil Protection of Ukraine (Kharkiv), E-mail: akhir21@mail.ru

Obtaining the Local Extremum in the Problem of Covering the Fields by the Circles of Variable Radius

The problem of covering the area of the variable radius circle is considered. The mathematical model of the coating is built. A new coverage criterion is offered, based on which the range of permissible solutions of the problem is analytically described. Based on the analysis of the model properties, it is shown that the solution of the problem can be reduced to the nonlinear programming sequence solution of problems.

Download full text (On English)!

Keywords: circle of variable radius coverage, coverage criteria, optimization, nonlinear programming.

1. Stoyan, Yu.G., 1983. Osnovnaya zadacha geometricheskogo proyektirovaniya. Kharkov, 36 p. In-t problem mashinostroyeniya AN USSR (In Russian).
2. Yakovlev, C.V., Gil’, N.I., Komyak V.M. et. al., 1995. Elementy teorii geometricheskogo proyektirovaniya.K.: Nauk. dumka, 241 p. (In Russian).
3. Stoyan, Yu.G., Yakovlev, S.V., 1986. Matematicheskiye modeli i optimizatsionnyye metody geometricheskogo proyektirovaniya. K.: Nauk. dumka, 265 p. (In Russian).
4. Romanova, T.Ye., Pankratov, A.V., Patsuk V.N. et. al., 2005. “Metod pokrytiya pryamougol’nika kongruentnymi krugami s uchotom dopolnitel’nykh ogranicheniy”. Radioelektronika i informatika, 1, pp. 48–51. (In Russian).
5. Antoshkin, A.A., Pankratov, A.V., Patsuk, V.N. et. al., 2001. “Zadacha pokrytiya pryamougol’noy oblasti krugami zadannogo radiusa”. Radioelektronika i informatika, 3, pp. 38–41. (In Russian).
6. Pankratov, A.V., Patsuk, V.N., Romanova T.Ye. et. al., 2002. “Metod regulyarnogo pokrytiya pryamougol’noy oblasti krugami zadannogo radiusa”. Radioelektronika i informatika, 1, pp. 50–52. (In Russian).
7. Zlotnik, M.V., Krivulya, A.V., Pankratov A.V. et. al., 2007. “Strategiya resheniya zadachi pokrytiya mnogosvyaznoy mnogougol’noy oblasti”. Bionika intellekta, 2(67), pp. 51–55. (In Russian).
8. Feyyesh, Tot L., 1958. Raspolozheniya na ploskosti, na sfere i v prostranstve. M.: Fizmatgiz, 363 p. (In Russian).
9. Fejes, Tot G., 1979. “Multiple packing and covering of spheres”. Acta Math. Acad. Sci. Hungar, 34, 1–2, pp. 165–176.
10. Konvey, Dzh., Sloyen, N., 1990. Upakovka sharov, reshetki i gruppy. M.: Mir, T. 1–2. (In Russian).
11. Drezer, Z., 1984. “The p-centre problem – heuristic and optimal
    algorithms”. J.OR Soc., 35, pp. 741–748.
12. Komyak, V.M., Sobol, O.M., Kosse, A.H. et. al., 2010. “Osoblyvosti metodu vyznachennya ratsionalʹnoyi kilʹkosti ta mistsʹ roztashuvannya operatyvnykh pidrozdiliv dlya zakhystu obʺyektiv zaliznytsi”. Problemy nadzvychaynykh sytuatsiy: Zb. nauk. pr. NUTSZ Ukrayiny. Kharkiv: NUTSZU, 11, pp. 74–79. (In Ukrainian).
13. Komyak, V.M., Pankratov, A.V., Prikhodko A.Yu. et. al., 2014. “Optimizatsiya razmeshcheniya punktov nablyudeniya nazemnikh sistem video-monitoringa lesnykh pozharov”. Problemy pozharnoy bezopasnosti: Sb. nauch. tr. NUGZ Ukrainy. Kharkov: NUGZU, 36. pp. 117–126. (In Russian).
14. Stoyan, Yu.G., Romanova, T.Ye., Chernov N.I. et. al., 2010. “Polnyy klass F-funktsiy dlya bazovykh obyektov”. Dop. NAN Ukrainy, 12, pp. 25–30. (In Russian).

Received  15.01.2016