close

Вход

Забыли?

вход по аккаунту

?

Показатель устойчивости функционирования комплекса средств передачи информации автоматизированной системы управления воздушным движением.

код для вставкиСкачать
2015
ɇȺɍɑɇɕɃ ȼȿɋɌɇɂɄ ɆȽɌɍ ȽȺ
ʋ 222
ɍȾɄ 351.814.334
ɉɈɄȺɁȺɌȿɅɖ ɍɋɌɈɃɑɂȼɈɋɌɂ
ɎɍɇɄɐɂɈɇɂɊɈȼȺɇɂə ɄɈɆɉɅȿɄɋȺ
ɋɊȿȾɋɌȼ ɉȿɊȿȾȺɑɂ ɂɇɎɈɊɆȺɐɂɂ
ȺȼɌɈɆȺɌɂɁɂɊɈȼȺɇɇɈɃ ɋɂɋɌȿɆɕ ɍɉɊȺȼɅȿɇɂə
ȼɈɁȾɍɒɇɕɆ ȾȼɂɀȿɇɂȿɆ
ɗ.Ⱥ. ȻɈɅȿɅɈȼ, Ʉ.ɇ. ɆȺɌɘɏɂɇ, ɇ.ɇ. ɆȺɃɅɈȼ
ȼ ɫɬɚɬɶɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɩɨɧɹɬɢɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ ɤɨɦɩɥɟɤɫɚ ɫɪɟɞɫɬɜ ɩɟɪɟɞɚɱɢ
ɢɧɮɨɪɦɚɰɢɢ, ɜɯɨɞɹɳɟɝɨ ɜ ɫɨɫɬɚɜ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ, ɚ ɬɚɤɠɟ ɞɚɟɬɫɹ
ɨɩɪɟɞɟɥɟɧɢɟ ɭɫɬɨɣɱɢɜɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɤɨɦɩɥɟɤɫɚ ɢ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɫɩɨɫɨɛ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɨɤɚɡɚɬɟɥɹ
ɭɫɬɨɣɱɢɜɨɫɬɢ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɨɟ ɫɨɫɬɨɹɧɢɟ, ɤɨɦɩɥɟɤɫ ɫɪɟɞɫɬɜ ɩɟɪɟɞɚɱɢ ɢɧɮɨɪɦɚɰɢɢ, ɩɨɤɚɡɚɬɟɥɶ ɭɫɬɨɣɱɢɜɨɫɬɢ.
ȼȼȿȾȿɇɂȿ
ɋɨɜɪɟɦɟɧɧɚɹ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɚɹ ɫɢɫɬɟɦɚ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ (Ⱥɋ ɍȼȾ)
ɹɜɥɹɟɬɫɹ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɫɢɫɬɟɦɨɣ ɫɟɬɟɜɨɝɨ ɬɢɩɚ ɢ ɩɪɟɞɧɚɡɧɚɱɟɧɚ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ, ɩɨɜɵɲɟɧɢɹ ɷɤɨɧɨɦɢɱɧɨɫɬɢ ɢ ɪɟɝɭɥɹɪɧɨɫɬɢ ɩɨɥɟɬɨɜ ɚɜɢɚɰɢɢ ɪɚɡɥɢɱɧɵɯ
ɜɟɞɨɦɫɬɜ ɜ ɪɚɣɨɧɟ ɚɷɪɨɞɪɨɦɚ, ɧɚ ɜɨɡɞɭɲɧɵɯ ɬɪɚɫɫɚɯ ɢ ɜɨ ɜɧɟɬɪɚɫɫɨɜɨɦ ɜɨɡɞɭɲɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ ɩɭɬɟɦ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɨɜ ɬɟɤɭɳɟɝɨ ɩɥɚɧɢɪɨɜɚɧɢɹ, ɫɛɨɪɚ, ɨɛɪɚɛɨɬɤɢ ɢ ɨɬɨɛɪɚɠɟɧɢɹ
ɪɚɞɢɨɥɨɤɚɰɢɨɧɧɨɣ ɢɧɮɨɪɦɚɰɢɢ, ɢɧɮɨɪɦɚɰɢɢ, ɩɨɥɭɱɟɧɧɨɣ ɩɨ ɤɚɧɚɥɚɦ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɡɚɜɢɫɢɦɨɝɨ ɧɚɛɥɸɞɟɧɢɹ ɢ ɦɟɬɟɨɢɧɮɨɪɦɚɰɢɢ [1].
Ɉɞɧɨɣ ɢɡ ɯɚɪɚɤɬɟɪɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɫɨɜɪɟɦɟɧɧɵɯ Ⱥɋ ɍȼȾ ɹɜɥɹɟɬɫɹ ɬɟɪɪɢɬɨɪɢɚɥɶɧɚɹ
ɪɚɫɩɪɟɞɟɥɟɧɧɨɫɬɶ ɤɨɦɩɨɧɟɧɬɨɜ ɫɢɫɬɟɦɵ, ɱɬɨ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɬɪɟɛɭɟɬ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɪɚɡɧɨɬɢɩɧɵɯ ɤɚɧɚɥɨɜ ɫɜɹɡɢ. Ʉɨɦɩɥɟɤɫ ɫɪɟɞɫɬɜ ɫɜɹɡɢ ɢ ɩɟɪɟɞɚɱɢ ɢɧɮɨɪɦɚɰɢɢ (Ʉɋɉɂ), ɜɯɨɞɹɳɢɣ ɜ ɫɨɫɬɚɜ
Ⱥɋ ɍȼȾ, ɢɫɩɨɥɶɡɭɟɬ ɦɚɝɢɫɬɪɚɥɶɧɵɟ ɤɚɧɚɥɵ ɫɜɹɡɢ, ɩɪɨɜɨɞɧɵɟ ɢ ɛɟɫɩɪɨɜɨɞɧɵɟ ɥɢɧɢɢ ɫɜɹɡɢ.
Ɉɫɧɨɜɧɵɦɢ ɡɚɞɚɱɚɦɢ, ɪɟɲɚɟɦɵɦɢ Ʉɋɉɂ, ɹɜɥɹɸɬɫɹ:
- ɫɛɨɪ ɞɚɧɧɵɯ ɨɬ ɢɫɬɨɱɧɢɤɨɜ ɢɧɮɨɪɦɚɰɢɢ (ɬɪɚɫɫɨɜɵɟ ɢ ɚɷɪɨɞɪɨɦɧɵɟ ɪɚɞɢɨɥɨɤɚɬɨɪɵ, ɚɜɬɨɦɚɬɢɱɟɫɤɢɟ ɩɟɥɟɧɝɚɬɨɪɵ, ɤɨɦɩɥɟɤɫɵ ɪɚɞɢɨɥɨɤɚɰɢɨɧɧɨɣ ɫɢɫɬɟɦɵ ɩɨɫɚɞɤɢ (Ɋɋɉ), ɬɪɚɧɫɩɨɧɞɟɪɵ ɫɢɫɬɟɦɵ ɚɜɬɨɦɚɬɢɱɟɫɤɨɝɨ ɡɚɜɢɫɢɦɨɝɨ ɧɚɛɥɸɞɟɧɢɹ (ȺɁɇ) ɢ ɞɪ.);
- ɨɛɪɚɛɨɬɤɭ ɢɧɮɨɪɦɚɰɢɢ, ɟɟ ɤɨɞɢɪɨɜɚɧɢɟ ɢ ɞɟɤɨɞɢɪɨɜɚɧɢɟ;
- ɫɨɩɪɹɠɟɧɢɟ ɫ ɤɚɧɚɥɚɦɢ ɫɜɹɡɢ;
- ɩɟɪɟɞɚɱɭ ɢɧɮɨɪɦɚɰɢɢ ɩɨ ɤɚɧɚɥɚɦ ɫɜɹɡɢ;
- ɜɵɞɚɱɭ ɢɧɮɨɪɦɚɰɢɢ ɩɨɬɪɟɛɢɬɟɥɹɦ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɥɸɛɨɦ ɢɡ ɜɚɪɢɚɧɬɨɜ ɢɫɩɨɥɧɟɧɢɹ Ⱥɋ ɍȼȾ ɨɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɷɥɟɦɟɧɬɨɜ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ Ʉɋɉɂ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɚɞɟɠɧɨɫɬɢ ɜ ɤɨɦɩɥɟɤɬ Ʉɋɉɂ ɜɯɨɞɹɬ ɩɨ ɞɜɟ
ɫɬɚɧɰɢɢ ɩɪɢɟɦɚ/ɩɟɪɟɞɚɱɢ ɢɧɮɨɪɦɚɰɢɢ: ɨɫɧɨɜɧɚɹ ɢ ɪɟɡɟɪɜɧɚɹ. Ʉɋɉɂ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɫɪɟɞɫɬɜɚɦɢ ɤɨɧɬɪɨɥɹ, ɞɢɚɝɧɨɫɬɢɪɨɜɚɧɢɹ ɢ ɭɩɪɚɜɥɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɦ ɫɨɫɬɨɹɧɢɟɦ, ɚ ɬɚɤɠɟ ɩɪɨɝɪɚɦɦɧɨɚɩɩɚɪɚɬɧɵɦɢ ɫɪɟɞɫɬɜɚɦɢ ɡɚɳɢɬɵ ɨɬ ɧɟɫɚɧɤɰɢɨɧɢɪɨɜɚɧɧɨɝɨ ɞɨɫɬɭɩɚ. Ʉɋɉɂ ɫɨɜɪɟɦɟɧɧɨɣ Ⱥɋ
ɍȼȾ ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɨɣ ɬɟɯɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɨɣ. Ⱦɥɹ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ Ʉɋɉɂ ɢɫɩɨɥɶɡɭɸɬɫɹ
ɪɹɞ ɱɚɫɬɧɵɯ ɩɨɤɚɡɚɬɟɥɟɣ ɷɮɮɟɤɬɢɜɧɨɫɬɢ (ɰɟɥɟɜɵɯ, ɧɚɞɟɠɧɨɫɬɧɵɯ, ɜɪɟɦɟɧɧɵɯ) [1], ɨɬɥɢɱɢɬɟɥɶɧɨɣ ɨɫɨɛɟɧɧɨɫɬɶɸ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɨɩɪɟɞɟɥɟɧɧɚɹ ɫɬɟɩɟɧɶ ɞɭɛɥɢɪɨɜɚɧɢɹ ɭɱɢɬɵɜɚɟɦɵɯ ɫɜɨɣɫɬɜ
ɤɨɦɩɥɟɤɫɚ, ɱɬɨ ɜ ɤɨɧɟɱɧɨɦ ɢɬɨɝɟ ɡɚɬɪɭɞɧɹɟɬ ɪɟɚɥɶɧɭɸ ɨɰɟɧɤɭ ɷɮɮɟɤɬɢɜɧɨɫɬɢ Ʉɋɉɂ.
ȼɦɟɫɬɟ ɫ ɬɟɦ, ɞɥɹ ɷɮɮɟɤɬɢɜɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ ɧɚɢɛɨɥɟɟ ɜɚɠɧɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɭɫɬɨɣɱɢɜɨɟ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ Ʉɋɉɂ. ɉɨɞ ɭɫɬɨɣɱɢɜɨɫɬɶɸ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ
ɉɨɤɚɡɚɬɟɥɶ ɭɫɬɨɣɱɢɜɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ…
183
Ʉɋɉɂ ɩɨɧɢɦɚɸɬ ɫɩɨɫɨɛɧɨɫɬɶ ɫɢɫɬɟɦɵ ɜɵɩɨɥɧɹɬɶ ɭɫɬɚɧɨɜɥɟɧɧɵɣ ɨɛɴɟɦ ɫɜɨɢɯ ɮɭɧɤɰɢɣ ɩɪɢ
ɜɧɟɲɧɢɯ ɢ ɜɧɭɬɪɟɧɧɢɯ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɯ ɜɨɡɞɟɣɫɬɜɢɹɯ, ɧɟ ɩɪɟɞɭɫɦɨɬɪɟɧɧɵɯ ɭɫɥɨɜɢɹɦɢ ɧɨɪɦɚɥɶɧɨɝɨ ɩɪɢɦɟɧɟɧɢɹ, ɚ ɬɚɤɠɟ ɫɩɨɫɨɛɧɨɫɬɶ ɩɪɨɬɢɜɨɫɬɨɹɬɶ ɬɚɤɢɦ ɜɨɡɞɟɣɫɬɜɢɹɦ (ɜɵɛɨɪ ɧɚɢɥɭɱɲɟɝɨ ɪɟɠɢɦɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ, ɩɟɪɟɫɬɪɨɣɤɚ ɫɬɪɭɤɬɭɪɵ, ɢɡɦɟɧɟɧɢɟ ɮɭɧɤɰɢɣ ɩɨɞɫɢɫɬɟɦ).
Ʉɚɤ ɜɫɹɤɚɹ ɫɥɨɠɧɚɹ ɬɟɯɧɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ Ʉɋɉɂ ɨɛɥɚɞɚɟɬ ɢɡɛɵɬɨɱɧɨɫɬɶɸ, ɩɪɟɠɞɟ ɜɫɟɝɨ
ɫɬɪɭɤɬɭɪɧɨɣ (ɧɚɥɢɱɢɟ ɪɟɡɟɪɜɧɵɯ ɭɫɬɪɨɣɫɬɜ ɜ ɫɨɫɬɚɜɟ ɤɨɦɩɥɟɤɫɚ) ɢ ɮɭɧɤɰɢɨɧɚɥɶɧɨɣ (ɧɚɥɢɱɢɟ
ɪɚɡɧɨɬɢɩɧɵɯ ɤɚɧɚɥɨɜ ɫɜɹɡɢ). ɋɬɪɭɤɬɭɪɧɚɹ ɢ ɮɭɧɤɰɢɨɧɚɥɶɧɚɹ ɢɡɛɵɬɨɱɧɨɫɬɶ ɜɥɢɹɟɬ ɧɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ Ʉɋɉɂ ɢ ɨɩɪɟɞɟɥɹɬɫɹ ɫɬɪɭɤɬɭɪɨɣ ɤɨɦɩɥɟɤɫɚ. ɇɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ Ʉɋɉɂ ɨɤɚɡɵɜɚɸɬ ɜɥɢɹɧɢɟ ɬɚɤɠɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɩɨɞɫɢɫɬɟɦ
(ɩɨɞɫɢɫɬɟɦɚ ɤɨɧɬɪɨɥɹ, ɞɢɚɝɧɨɫɬɢɤɢ ɢ ɭɩɪɚɜɥɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɦ ɫɨɫɬɨɹɧɢɟɦ, ɩɨɞɫɢɫɬɟɦɚ ɡɚɳɢɬɵ
ɢɧɮɨɪɦɚɰɢɢ), ɪɚɡɥɢɱɧɵɟ ɜɧɟɲɧɢɟ ɢ ɜɧɭɬɪɟɧɧɢɟ ɢɧɮɨɪɦɚɰɢɨɧɧɵɟ ɢ ɮɢɡɢɱɟɫɤɢɟ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɟ ɜɨɡɞɟɣɫɬɜɢɹ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɤɚɡɚɬɟɥɶ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɭɫɬɨɣɱɢɜɨɫɬɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ Ʉɋɉɂ
ɞɨɥɠɟɧ ɡɚɜɢɫɟɬɶ ɨɬ ɫɬɪɭɤɬɭɪɵ ɢ ɜɵɯɨɞɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɢɫɬɟɦɵ, ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɩɨɞɫɢɫɬɟɦ, ɜɧɟɲɧɢɯ ɢ ɜɧɭɬɪɟɧɧɢɯ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɢ ɮɢɡɢɱɟɫɤɢɯ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɯ
ɜɨɡɞɟɣɫɬɜɢɣ.
ɐɟɥɶɸ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ ɹɜɥɹɟɬɫɹ ɮɨɪɦɭɥɢɪɨɜɤɚ ɩɨɤɚɡɚɬɟɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ Ʉɋɉɂ, ɜ ɤɨɬɨɪɨɣ ɛɵɥɢ ɛɵ ɭɱɬɟɧɵ ɷɬɢ ɮɚɤɬɨɪɵ.
ɉɨɞ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɢɦ ɫɨɫɬɨɹɧɢɟɦ (ɂɌɋ) Ʉɋɉɂ ɛɭɞɟɦ ɩɨɧɢɦɚɬɶ ɫɨɜɨɤɭɩɧɨɫɬɶ ɫɜɨɣɫɬɜ ɢ ɩɪɢɡɧɚɤɨɜ ɤɚɤ ɬɟɯɧɢɱɟɫɤɨɝɨ, ɬɚɤ ɢ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɯɚɪɚɤɬɟɪɚ, ɩɪɢɫɭɳɢɯ ɫɢɫɬɟɦɟ ɜ ɨɩɪɟɞɟɥɟɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ [4].
1. ɆɈȾȿɅɖ ɂɇɎɈɊɆȺɐɂɈɇɇɈ-ɌȿɏɇɂɑȿɋɄɈȽɈ ɋɈɋɌɈəɇɂə Ʉɋɉɂ
ȼ ɨɛɳɟɦ ɜɢɞɟ ɦɨɞɟɥɶ ɂɌɋ Ʉɋɉɂ ɦɨɠɟɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜɟɤɬɨɪɨɦ:
S (t ) = {S ɢ (t ), S ɬ (t )},
(1)
ɝɞɟ S ɢ (t ) - ɜɟɤɬɨɪ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ Ʉɋɉɂ; S ɬ (t ) - ɜɟɤɬɨɪ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ Ʉɋɉɂ.
Ʉɋɉɂ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜɵɲɟ, ɫɨɫɬɨɢɬ ɢɡ ɩɨɞɫɢɫɬɟɦ, ɭɫɬɪɨɣɫɬɜ, ɥɢɧɢɣ ɫɜɹɡɢ ɢ ɬ.ɞ., ɤɨɬɨɪɵɟ
ɜ ɞɚɥɶɧɟɣɲɟɦ ɞɥɹ ɩɪɨɫɬɨɬɵ ɛɭɞɟɦ ɧɚɡɵɜɚɬɶ ɷɥɟɦɟɧɬɚɦɢ ɫɢɫɬɟɦɵ. Ɍɨɝɞɚ ɦɨɞɟɥɶ ɂɌɋ Ʉɋɉɂ
ɦɨɠɟɬ ɛɵɬɶ ɫɮɨɪɦɢɪɨɜɚɧɚ ɧɚ ɨɫɧɨɜɟ ɦɨɞɟɥɟɣ ɂɌɋ ɫɨɫɬɚɜɥɹɸɳɢɯ ɟɟ ɷɥɟɦɟɧɬɨɜ. ɉɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɷɥɟɦɟɧɬɭ Ʉɋɉɂ ɞɨɫɬɚɬɨɱɧɨ ɩɨɥɧɨɣ ɦɨɞɟɥɶɸ ɂɌɋ ɹɜɥɹɟɬɫɹ ɦɨɞɟɥɶ [2], [4]:
- ɫ ɬɪɟɦɹ ɧɟɫɨɜɦɟɫɬɧɵɦɢ ɬɟɯɧɢɱɟɫɤɢɦɢ ɫɨɫɬɨɹɧɢɹɦɢ s ɬj , ~sɬj , sɬj , ɝɞɟ s ɬj – ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɟ
ɫɨɫɬɨɹɧɢɟ j -ɝɨ ɷɥɟɦɟɧɬɚ, ~s - ɫɨɫɬɨɹɧɢɟ ɜɪɟɦɟɧɧɨɝɨ ɨɬɤɚɡɚ j -ɝɨ ɷɥɟɦɟɧɬɚ, s - ɫɨɫɬɨɹɧɢɟ ɩɨɥɬj
ɬj
ɧɨɝɨ ɭɫɬɨɣɱɢɜɨɝɨ ɨɬɤɚɡɚ j -ɝɨ ɷɥɟɦɟɧɬɚ;
- ɫ ɬɪɟɦɹ ɧɟɫɨɜɦɟɫɬɧɵɦɢ ɢɧɮɨɪɦɚɰɢɨɧɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ: sɢj , ~sɢj , sɢj , ɝɞɟ s ɢj - ɛɟɡɨɩɚɫɧɨɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɟ ɫɨɫɬɨɹɧɢɟ, ~s - ɩɨɬɟɧɰɢɚɥɶɧɨ ɨɩɚɫɧɨɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɟ ɫɨɫɬɨɹɧɢɟ, s –
ɢj
ɢj
ɨɩɚɫɧɨɟ ɢɥɢ ɤɪɢɬɢɱɟɫɤɨɟ ɢɧɮɨɪɦɚɰɢɨɧɧɨɟ ɫɨɫɬɨɹɧɢɟ.
ɍɱɢɬɵɜɚɹ ɷɬɨ, ɜɟɤɬɨɪ ɂɌɋ j -ɝɨ ɷɥɟɦɟɧɬɚ Ʉɋɉɂ ɢɦɟɟɬ ɜɢɞ:
S j (t ) = S ɬj (t ) ⊗ S ɢj (t ) ,
[
]
(2)
ɝɞɟ S ɬj (t ) = s ɬj (t ), ~sɬj (t ), s ɬj (t ) ɬ - ɜɟɤɬɨɪ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ j -ɝɨ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ;
ɬ
S ɢj (t ) = s ɢj (t ), ~sɢj (t ), sɢj (t ) - ɜɟɤɬɨɪ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ j -ɝɨ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ; ⊗ ɫɢɦɜɨɥ ɩɪɹɦɨɝɨ ɩɪɨɢɡɜɟɞɟɧɢɹ ɦɚɬɪɢɰ.
[
]
184
ɗ.Ⱥ. Ȼɨɥɟɥɨɜ, Ʉ.ɇ. Ɇɚɬɸɯɢɧ, ɇ.ɇ. Ɇɚɣɥɨɜ
Ɍɨɝɞɚ, ɞɥɹ j -ɝɨ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ ɦɨɞɟɥɶ ɂɌɋ ɛɭɞɟɬ ɜɤɥɸɱɚɬɶ ɞɟɜɹɬɶ ɧɟɫɨɜɦɟɫɬɧɵɯ ɫɨɫɬɨɹɧɢɣ:
ªs ɢj (t )s ɬj (t )º
«
~ »
«s ɢj (t )sɬj (t )»
« ( ) ( )»
«s ɢj t s ɬj t »
«~sɢj (t )s ɬj (t )»
«
»
S j (t ) = «~sɢj (t )~sɬj (t )» ,
»
«~
« sɢj (t )s ɬj (t )»
« s (t )s (t )»
« ɢj ɬj »
« sɢj (t )~sɬj (t )»
»
«
«¬ sɢj (t )s ɬj (t )»¼
(3)
ɉɟɪɜɨɟ ɂɌɋ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ s ɬj (t )s ɢj (t ) ɹɜɥɹɟɬɫɹ ɫɨɫɬɨɹɧɢɟɦ, ɩɪɢ ɤɨɬɨɪɨɦ ɷɥɟɦɟɧɬ
Ʉɋɉɂ ɧɚɯɨɞɢɬɫɹ ɜ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɦ ɬɟɯɧɢɱɟɫɤɨɦ ɫɨɫɬɨɹɧɢɢ ɢ ɛɟɡɨɩɚɫɧɨɦ ɢɧɮɨɪɦɚɰɢɨɧɧɨɦ
ɫɨɫɬɨɹɧɢɢ, ɬ.ɟ. ɢɦɟɟɬ ɦɟɫɬɨ ɟɝɨ ɲɬɚɬɧɨɟ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ. ɉɨɫɥɟɞɧɟɟ ɂɌɋ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ
s ɬj (t )sɢj (t ) ɹɜɥɹɟɬɫɹ ɫɨɫɬɨɹɧɢɟɦ, ɩɪɢ ɤɨɬɨɪɨɦ ɷɥɟɦɟɧɬ Ʉɋɉɂ ɩɨɥɧɨɫɬɶɸ ɧɟɪɚɛɨɬɨɫɩɨɫɨɛɟɧ ɢ
ɧɚɯɨɞɢɬɶɫɹ ɜ ɨɩɚɫɧɨɦ ɢɧɮɨɪɦɚɰɢɨɧɧɨɦ ɫɨɫɬɨɹɧɢɢ. Ɉɫɬɚɥɶɧɵɟ ɂɌɋ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ – ɷɬɨ
ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɯɚɪɚɤɬɟɪɢɡɭɟɦɵɟ ɪɚɡɥɢɱɧɨɣ ɫɬɟɩɟɧɶɸ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ ɢ ɛɟɡɨɩɚɫɧɨɫɬɢ ɷɥɟɦɟɧɬɚ Ʉɋɉɂ.
Ɉɛɳɟɟ ɱɢɫɥɨ ɂɌɋ Ʉɋɉɂ ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɢɫɥɨɦ ɷɥɟɦɟɧɬɨɜ ɫɢɫɬɟɦɵ:
J
N
N = ∏qj j ,
(4)
j =1
ɝɞɟ q j - ɱɢɫɥɨ ɂɌɋ j -ɝɨ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ; N j - ɱɢɫɥɨ ɷɥɟɦɟɧɬɨɜ ɫɢɫɬɟɦɵ, ɢɦɟɸɳɢɯ q j
ɂɌɋ; J - ɤɨɥɢɱɟɫɬɜɨ ɝɪɭɩɩ ɷɥɟɦɟɧɬɨɜ Ʉɋɉɂ.
ȼɵɪɚɠɟɧɢɟ (4) ɭɱɢɬɵɜɚɟɬ ɬɨɬ ɮɚɤɬ, ɱɬɨ ɷɥɟɦɟɧɬɵ Ʉɋɉɂ ɦɨɝɭɬ ɢɦɟɬɶ ɪɚɡɥɢɱɧɨɟ ɱɢɫɥɨ
ɂɌɋ. ɇɚɩɪɢɦɟɪ, ( j + 1) -ɣ ɷɥɟɦɟɧɬ ɫɢɫɬɟɦɵ ɦɨɠɟɬ ɢɦɟɬɶ ɞɜɚ ɧɟɫɨɜɦɟɫɬɧɵɯ ɬɟɯɧɢɱɟɫɤɢɯ s ɬj +1 (t ) ,
s (t ) ɫɨɫɬɨɹɧɢɹ ɢ ɬɪɢ ɧɟɫɨɜɦɟɫɬɧɵɯ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ s (t ), ~s (t ), s (t ) ɫɨɫɬɨɹɧɢɹ. Ɍɨɝɞɚ
ɬj +1
ɢj +1
ɢj +1
ɢj +1
ɨɛɳɟɟ ɱɢɫɥɨ ɂɌɋ ( j + 1) -ɝɨ ɷɥɟɦɟɧɬɚ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (2), ɛɭɞɟɬ ɪɚɜɧɨ ɲɟɫɬɢ. Ʉ ɬɨɦɭ ɠɟ, ɜ
Ʉɋɉɂ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɪɹɞ ɷɥɟɦɟɧɬɨɜ, ɢɦɟɸɳɢɯ ɬɨɥɶɤɨ ɬɟɯɧɢɱɟɫɤɭɸ ɢɥɢ ɬɨɥɶɤɨ ɢɧɮɨɪɦɚɰɢɨɧɧɭɸ ɤɨɦɩɨɧɟɧɬɭ ɦɨɞɟɥɢ ɂɌɋ.
ȼɜɟɞɟɦ ɤɨɧɟɱɧɨɟ ɦɧɨɠɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɫɨɫɬɨɹɧɢɣ Ω , ɤɨɬɨɪɨɟ ɫɨɞɟɪɠɢɬ ɷɥɟɦɟɧɬɵ ɬɪɟɯ ɬɢɩɨɜ. ɗɥɟɦɟɧɬɵ ɩɟɪɜɨɝɨ ɬɢɩɚ ɩɪɢɧɚɞɥɟɠɚɬ ɩɨɞɦɧɨɠɟɫɬɜɭ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɂɌɋ Ω1 , ɷɥɟɦɟɧɬɵ ɜɬɨɪɨɝɨ ɬɢɩɚ ɩɪɢɧɚɞɥɟɠɚɬ ɩɨɞɦɧɨɠɟɫɬɜɭ ɱɚɫɬɢɱɧɨ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ
ɂɌɋ Ω 2 , ɷɥɟɦɟɧɬɵ ɬɪɟɬɶɟɝɨ ɬɢɩɚ ɩɪɢɧɚɞɥɟɠɚɬ ɩɨɞɦɧɨɠɟɫɬɜɭ ɩɨɥɧɨɫɬɶɸ ɧɟɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ
ɂɌɋ Ω3 .
ɉɨɞɦɧɨɠɟɫɬɜɨ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɂɌɋ Ω1 ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɬɟɦ, ɱɬɨ ɡɧɚɱɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɯ ɢ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɫɨɯɪɚɧɹɸɬɫɹ ɧɚ ɭɪɨɜɧɟ, ɤɨɬɨɪɵɣ ɨɛɟɫɩɟɱɢɜɚɟɬ ɜɵɩɨɥɧɟɧɢɟ ɡɚɞɚɧɧɵɯ Ʉɋɉɂ ɮɭɧɤɰɢɣ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɟɞɴɹɜɥɹɟɦɵɦɢ ɤ ɧɟɣ ɬɪɟɛɨɜɚɧɢɹɦɢ (ɜɤɥɸɱɚɹ
ɬɪɟɛɨɜɚɧɢɹ ɩɨ ɢɧɮɨɪɦɚɰɢɨɧɧɨɣ ɛɟɡɨɩɚɫɧɨɫɬɢ):
ɉɨɤɚɡɚɬɟɥɶ ɭɫɬɨɣɱɢɜɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ…
Ω1 = Ω ɬɪ ∩ Ω ɢ ɛ ,
185
(5)
ɝɞɟ Ω ɬɪ - ɦɧɨɠɟɫɬɜɨ ɬɟɯɧɢɱɟɫɤɢɯ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɫɨɫɬɨɹɧɢɣ; Ω ɢ ɛ - ɦɧɨɠɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɛɟɡɨɩɚɫɧɵɯ ɫɨɫɬɨɹɧɢɣ.
ɉɨɞɦɧɨɠɟɫɬɜɨ ɱɚɫɬɢɱɧɨ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɂɌɋ Ω 2 ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɬɟɦ, ɱɬɨ Ʉɋɉɂ ɜɵɩɨɥɧɹɟɬ ɜɫɟ ɠɢɡɧɟɧɧɨ ɜɚɠɧɵɟ ɮɭɧɤɰɢɢ ɢ ɧɟ ɜɵɩɨɥɧɹɟɬ ɧɟɤɨɬɨɪɭɸ ɞɨɩɭɫɬɢɦɭɸ ɱɚɫɬɶ ɢɧɵɯ
ɮɭɧɤɰɢɣ ɢɥɢ ɜɵɩɨɥɧɹɟɬ ɮɭɧɤɰɢɢ ɫ ɯɭɞɲɢɦ ɤɚɱɟɫɬɜɨɦ:
Ω 2 = Ω ɬɱɪ ∪ Ω ɢ ɱɛ ,
(6)
ɝɞɟ Ω ɬɱɪ - ɦɧɨɠɟɫɬɜɨ ɬɟɯɧɢɱɟɫɤɢɯ ɱɚɫɬɢɱɧɨ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɫɨɫɬɨɹɧɢɣ; Ω ɢ ɱɛ - ɦɧɨɠɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɱɚɫɬɢɱɧɨ ɛɟɡɨɩɚɫɧɵɯ ɫɨɫɬɨɹɧɢɣ.
ɉɨɞɦɧɨɠɟɫɬɜɨ ɩɨɥɧɨɫɬɶɸ ɧɟɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɂɌɋ Ω3 , ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɚɤ:
- ɦɧɨɠɟɫɬɜɨ ɬɟɯɧɢɱɟɫɤɢ ɧɟɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ, ɧɨ ɛɟɡɨɩɚɫɧɵɯ ɫɨɫɬɨɹɧɢɣ Ω ɬɧɪ ;
- ɦɧɨɠɟɫɬɜɨ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɢɥɢ ɱɚɫɬɢɱɧɨ ɪɚɛɨɬɨɫɩɨɫɨɛɧɵɯ ɬɟɯɧɢɱɟɫɤɢɯ ɫɨɫɬɨɹɧɢɣ,
ɧɨ ɤɪɢɬɢɱɟɫɤɢɯ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɫɨɫɬɨɹɧɢɣ Ωɢɤɪ .
Ɍɨɝɞɚ:
Ω 3 = Ω ɬɧɪ ∪ Ω ɢ ɤɪ .
(7)
Ⱦɥɹ j -ɝɨ ɷɥɟɦɟɧɬɚ ɫɢɫɬɟɦɵ (3) ɩɨɞɦɧɨɠɟɫɬɜɨ Ω1 ɢɦɟɟɬ ɦɨɳɧɨɫɬɶ, ɪɚɜɧɭɸ ɟɞɢɧɢɰɟ,
ɬ.ɟ. ɜɤɥɸɱɚɟɬ ɬɨɥɶɤɨ ɨɞɢɧ ɷɥɟɦɟɧɬ - s ɬj (t )s ɢj (t ) . ɉɨɞɦɧɨɠɟɫɬɜɨ Ω 2 ɫɨɫɬɨɢɬ ɢɡ ɬɪɟɯ
ɷɥɟɦɟɧɬɨɜ - s ɬj (t )~sɢj (t ) , ~sɬj (t )s ɢj (t ) , ~sɬj (t )~sɢj (t ) . Ɉɫɬɚɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɩɪɢɧɚɞɥɟɠɚɬ ɩɨɞɦɧɨɠɟɫɬɜɭ Ω3 .
ɉɪɨɰɟɫɫ ɩɟɪɟɯɨɞɚ Ʉɋɉɂ ɢɡ ɨɞɧɨɝɨ ɂɌɋ ɜ ɞɪɭɝɨɟ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɦ. ɋɥɨɠɧɨɫɬɶ ɷɬɚ ɨɛɭɫɥɨɜɥɟɧɚ, ɩɪɟɠɞɟ ɜɫɟɝɨ ɫɩɟɰɢɮɢɤɨɣ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ Ʉɋɉɂ, ɨɬɤɚɡɚɦɢ ɢ ɫɛɨɹɦɢ
ɜ ɪɚɛɨɬɟ Ʉɋɉɂ, ɤɨɬɨɪɵɟ ɩɪɢɜɨɞɹɬ ɤ ɩɨɥɧɨɣ ɢɥɢ ɱɚɫɬɢɱɧɨɣ ɩɨɬɟɪɟ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ ɫɢɫɬɟɦɵ,
ɚ ɬɚɤɠɟ ɤ ɧɚɪɭɲɟɧɢɹɦ ɢɧɮɨɪɦɚɰɢɨɧɧɨɝɨ ɨɛɦɟɧɚ ɦɟɠɞɭ ɷɥɟɦɟɧɬɚɦɢ ɫɢɫɬɟɦɵ ɢ ɩɨɬɟɪɟ ɯɪɚɧɢɦɨɣ ɜ ɫɢɫɬɟɦɟ ɢɧɮɨɪɦɚɰɢɢ, ɜɧɟɲɧɢɦɢ ɢɧɮɨɪɦɚɰɢɨɧɧɵɦɢ ɭɝɪɨɡɚɦɢ, ɱɟɥɨɜɟɱɟɫɤɢɦ ɮɚɤɬɨɪɨɦ
(ɨɲɢɛɤɢ ɩɟɪɫɨɧɚɥɚ, ɷɤɫɩɥɭɚɬɢɪɭɸɳɟɝɨ Ʉɋɉɂ).
ɋɥɭɱɚɣɧɵɣ ɩɪɨɰɟɫɫ S (t ) , ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɣ ɫɦɟɧɭ ɂɌɋ Ʉɋɉɂ, ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶ ɜ ɥɸɛɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɬɨɥɶɤɨ ɤɚɤɨɟ-ɥɢɛɨ ɨɞɧɨ ɡɧɚɱɟɧɢɟ ɢɡ ɤɨɧɟɱɧɨɝɨ ɦɧɨɠɟɫɬɜɚ Ω ɢ ɩɨɷɬɨɦɭ
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɞɢɫɤɪɟɬɧɵɣ ɫɥɭɱɚɣɧɵɣ ɩɪɨɰɟɫɫ, ɫɦɟɧɚ ɫɨɫɬɨɹɧɢɣ ɤɨɬɨɪɨɝɨ ɩɪɨɢɫɯɨɞɢɬ ɜ
ɫɥɭɱɚɣɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ:
S(t ) = F(S, Ȅ ɜɧɲ , Ȅ ɜɧɬ , t ) ,
[
(8)
]
ɝɞɟ Ȅɜɧɲ = Ȅɜɧɲ.ɢɧɮ ,Ȅɜɧɲ.ɮɢɡ - ɜɟɤɬɨɪ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɯ ɜɧɟɲɧɢɯ ɜɨɡɞɟɣɫɬɜɢɣ, ɜɤɥɸɱɚɸɳɢɣ ɜ ɫɟɛɹ ɜɟɤɬɨɪ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɯ ɜɧɟɲɧɢɯ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɜɨɡɞɟɣɫɬɜɢɣ Ξ ɜɧɲ.ɢɧɮ ɢ
ɜɟɤɬɨɪ ɞɟɫɬɚɛɢɥɢɡɢɪɭɸɳɢɯ ɜɧɟɲɧɢɯ ɮɢɡɢɱɟɫɤɢɯ ɜɨɡɞɟɣɫɬɜɢɣ Ȅɜɧɲ.ɮɢɡ ; Ȅɜɧɬ - ɜɟɤɬɨɪ ɞɟɫɬɚɛɢ-
ɥɢɡɢɪɭɸɳɢɯ ɜɧɭɬɪɟɧɧɢɯ ɜɨɡɞɟɣɫɬɜɢɣ; F(⋅) - ɨɩɟɪɚɬɨɪ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ.
ȼ ɜɵɪɚɠɟɧɢɢ (8) Ȅɜɧɲ ɢ Ȅɜɧɬ ɹɜɥɹɸɬɫɹ ɧɟɡɚɜɢɫɢɦɵɦɢ ɩɨ ɦɨɦɟɧɬɭ ɜɪɟɦɟɧɢ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɜɨɡɞɟɣɫɬɜɢɣ. ɗɬɨ ɞɨɩɭɳɟɧɢɟ ɨɛɴɹɫɧɹɟɬɫɹ ɪɚɡɥɢɱɧɨɣ ɩɪɢɪɨɞɨɣ ɷɬɢɯ ɜɨɡɞɟɣɫɬɜɢɣ. ɉɪɢ
ɛɨɥɟɟ ɞɟɬɚɥɶɧɨɦ ɪɚɫɫɦɨɬɪɟɧɢɢ ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɨ ɧɟɤɨɬɨɪɨɣ ɤɨɪɪɟɥɹɰɢɢ ɦɟɠɞɭ ɜɧɭɬɪɟɧɧɢɦɢ
186
ɗ.Ⱥ. Ȼɨɥɟɥɨɜ, Ʉ.ɇ. Ɇɚɬɸɯɢɧ, ɇ.ɇ. Ɇɚɣɥɨɜ
ɜɨɡɞɟɣɫɬɜɢɹɦɢ ɢ ɜɧɟɲɧɢɦɢ ɢɧɮɨɪɦɚɰɢɨɧɧɵɦɢ ɜɨɡɞɟɣɫɬɜɢɹɦɢ, ɚ ɬɚɤɠɟ ɦɟɠɞɭ ɜɧɭɬɪɟɧɧɢɦɢ
ɜɨɡɞɟɣɫɬɜɢɹɦɢ ɢ ɜɧɟɲɧɢɦɢ ɮɢɡɢɱɟɫɤɢɦɢ ɜɨɡɞɟɣɫɬɜɢɹɦɢ.
ɉɟɪɟɯɨɞɵ ɦɟɠɞɭ ɫɨɫɬɨɹɧɢɹɦɢ ɦɨɝɭɬ ɛɵɬɶ ɨɩɢɫɚɧɵ ɦɚɬɪɢɰɟɣ ɜɟɪɨɹɬɧɨɫɬɟɣ ɩɟɪɟɯɨɞɨɜ
Ʉɋɉɂ ɢɡ ɨɞɧɨɝɨ ɂɌɋ ɜ ɞɪɭɝɨɟ:
[(
)]
PS (t ) = p t, si , s j ,
(9)
ɝɞɟ p (t , si , s j ) - ɜɟɪɨɹɬɧɨɫɬɶ ɩɟɪɟɯɨɞɚ ɢɡ i-ɝɨ ɫɨɫɬɨɹɧɢɹ ɜ j-ɟ ɫɨɫɬɨɹɧɢɟ.
2. ɉɈɄȺɁȺɌȿɅɖ ɍɋɌɈɃɑɂȼɈɋɌɂ Ʉɋɉɂ
ȼ ɤɚɱɟɫɬɜɟ ɩɨɤɚɡɚɬɟɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ Ʉɋɉɂ ɜɜɟɞɟɦ ɤɨɷɮɮɢɰɢɟɧɬ
ɭɫɬɨɣɱɢɜɨɫɬɢ CS (coefficient of stability) [3]. Ɂɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɬɨɣɱɢɜɨɫɬɢ CS ɡɚɜɢɫɢɬ
ɨɬ ɫɬɪɭɤɬɭɪɵ Ʉɋɉɂ STR ɢ ɩɚɪɚɦɟɬɪɨɜ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɯ ɟɝɨ ɤɚɱɟɫɬɜɨ z ɬi , z ɢj , i = 1, I ,
{
}
j = 1, J , ɝɞɟ z ɬi - ɬɟɯɧɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ, z ɢj - ɢɧɮɨɪɦɚɰɢɨɧɧɵɟ ɩɚɪɚɦɟɬɪɵ (ɫɤɨɪɨɫɬɶ ɩɟɪɟɞɚɱɢ
ɞɚɧɧɵɯ, ɨɛɴɟɦ ɫɨɨɛɳɟɧɢɣ, ɮɨɪɦɚɬ ɫɨɨɛɳɟɧɢɣ (ɬɢɩ ɞɚɧɧɵɯ, ɫɩɨɫɨɛ ɤɨɞɢɪɨɜɚɧɢɹ)). ɉɭɫɬɶ ɧɚ
ɤɚɠɞɵɣ ɩɚɪɚɦɟɬɪ ɡɚɞɚɧɚ ɧɟɤɨɬɨɪɚɹ ɨɛɥɚɫɬɶ ɢɯ ɞɨɩɭɫɬɢɦɵɯ ɡɧɚɱɟɧɢɣ d . Ɍɨɝɞɚ ɤɨɷɮɮɢɰɢɟɧɬ
ɭɫɬɨɣɱɢɜɨɫɬɢ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɮɭɧɤɰɢɨɧɚɥ ɜɢɞɚ:
§
··
§ I
· § J
CS = F¨ STR, ¨¨ z ɬi ∈ d ɬi ¸¸ ¨ z ɢj ∈ d ɢj ¸ ¸ .
¨
¸¸
¨
© i =1
¹ © j=1
¹¹
©
(10)
ȼ ɜɵɪɚɠɟɧɢɢ (4) ɩɚɪɚɦɟɬɪɵ ɤɨɦɩɥɟɤɫɚ ɪɚɡɞɟɥɟɧɵ ɧɚ ɬɟɯɧɢɱɟɫɤɢɟ ɢ ɢɧɮɨɪɦɚɰɢɨɧɧɵɟ,
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɍɫɥɨɜɢɟ
I
z ɬi ∈ d ɬi
ɨɩɪɟɞɟɥɹɟɬ ɮɚɤɬ ɨɞɧɨɜɪɟɦɟɧɧɨɝɨ ɜɵɩɨɥɧɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɯ
i =1
ɬɪɟɛɨɜɚɧɢɣ ɤ Ʉɋɉɂ, ɚ ɭɫɥɨɜɢɟ
J
zɢj ∈ d ɢj - ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ.
j =1
ɉɪɢɧɚɞɥɟɠɧɨɫɬɶ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɨɫɬɨɹɧɢɹ Ʉɋɉɂ ɩɨɞɦɧɨɠɟɫɬɜɭ Ω1
ɮɢɤɫɢɪɭɟɬɫɹ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ CS ≥ CSɬɪ , ɝɞɟ CSɬɪ - ɬɪɟɛɭɟɦɨɟ ɡɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɭɫɬɨɣɱɢɜɨɫɬɢ. ɉɪɢ ɷɬɨɦ ɞɥɹ ɞɜɭɯ ɪɚɡɥɢɱɧɵɯ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɫɨɫɬɨɹɧɢɣ k ɢ m
ɩɨɞɦɧɨɠɟɫɬɜɚ Ω1 ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ CSk ≥ CSm . Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɝɨɜɨɪɹ ɷɬɨ, ɨɡɧɚɱɚɟɬ ɱɬɨ
ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɢɟ ɫɨɫɬɨɹɧɢɹ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɫɬɨɣɱɢɜɨɫɬɢ ɹɜɥɹɸɬɫɹ ɥɢɧɟɣɧɨ ɭɩɨɪɹɞɨɱɟɧɧɵɦɢ. Ⱦɥɹ ɥɢɧɟɣɧɵɯ ɫɬɪɭɤɬɭɪ ɫɭɳɟɫɬɜɭɟɬ ɜɟɪɯɧɹɹ ɢ ɧɢɠɧɹɹ ɝɪɚɧɢɰɵ ɦɧɨɠɟɫɬɜɚ ɷɥɟɦɟɧɬɨɜ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɮɭɧɤɰɢɨɧɚɥ (10) ɹɜɥɹɟɬɫɹ ɜɟɳɟɫɬɜɟɧɧɨɣ ɮɭɧɤɰɢɟɣ, ɜɟɪɯɧɹɹ ɢ ɧɢɠɧɹɹ ɝɪɚɧɢɰɵ ɨɩɪɟɞɟɥɹɸɬɫɹ ɦɚɤɫɢɦɚɥɶɧɵɦ ɢ ɦɢɧɢɦɚɥɶɧɵɦ ɡɧɚɱɟɧɢɹɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɬɨɣɱɢɜɨɫɬɢ
maxCS ɢ minCS . ɗɬɢ ɡɧɚɱɟɧɢɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɪɚɡɥɢɱɧɨɣ ɫɬɪɭɤɬɭɪɨɣ Ʉɋɉɂ. ɉɪɢ ɮɢɤɫɢɪɨɜɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɬɟɯɧɢɱɟɫɤɢɯ ɢ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɨɰɟɧɤɢ ɜɟɪɯɧɟɣ ɢ
ɧɢɠɧɟɣ ɝɪɚɧɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɬɨɣɱɢɜɨɫɬɢ ɜ ɜɢɞɟ:
§
··
§ I
· § J
CS∗ = max F¨ STR, ¨¨ z ɬi ∈ d ɬi ¸¸ ¨ z ɢj ∈ d ɢj ¸ ¸ ,
¨
¸¸
{STR } ¨
© i =1
¹ © j=1
¹¹
©
§
··
· § J
§ I
CS∗∗ = min F¨ STR, ¨¨ z ɬi ∈ d ɬi ¸¸ ¨ z ɢj ∈ d ɢj ¸ ¸ .
¸¸
¨
{STR } ¨
¹ © j=1
© i =1
¹¹
©
(11)
(12)
ɉɨɤɚɡɚɬɟɥɶ ɭɫɬɨɣɱɢɜɨɫɬɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ…
187
Ɂɧɚɱɟɧɢɹ ɜɟɪɯɧɢɯ ɢ ɧɢɠɧɢɯ ɨɰɟɧɨɤ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɢ ɧɚɢɥɭɱɲɟɦ ɡɧɚɱɟɧɢɢ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɤɨɦɩɥɟɤɫɚ ɢɦɟɸɬ ɜɢɞ:
CS∗ = max max F(STR, z ɬ , z ɢ ) ,
(13)
CS∗∗ = min max F(STR, z ɬ , z ɢ ) .
(14)
{STR }{z ɬ , z ɢ }
{STR }{z ɬ , z ɢ }
ɇɚɪɭɲɟɧɢɟ ɯɨɬɹ ɛɵ ɨɞɧɨɝɨ ɬɪɟɛɨɜɚɧɢɹ ɤ ɬɟɯɧɢɱɟɫɤɢɦ ɩɚɪɚɦɟɬɪɚɦ
I
z ɬi ∈ d ɬi
ɢɥɢ ɢɧ-
i =1
ɮɨɪɦɚɰɢɨɧɧɵɦ ɩɚɪɚɦɟɬɪɚɦ
J
z ɢj ∈ d ɢj
ɨɡɧɚɱɚɟɬ, ɱɬɨ ɢɧɮɨɪɦɚɰɢɨɧɧɨ-ɬɟɯɧɢɱɟɫɤɨɟ ɫɨɫɬɨɹɧɢɟ
j=1
Ʉɋɉɂ ɛɭɞɟɬ ɨɬɧɨɫɢɬɶɫɹ ɤ ɩɨɞɦɧɨɠɟɫɬɜɭ Ω 2 . Ɂɧɚɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɢ ɷɬɨɦ
ɛɭɞɟɬ ɦɟɧɶɲɟ ɜɟɥɢɱɢɧ, ɩɨɥɭɱɟɧɧɵɯ ɜ ɜɵɪɚɠɟɧɢɹɯ (13) ɢ (14).
ɉɨɞɫɢɫɬɟɦɚ ɡɚɳɢɬɵ ɢɧɮɨɪɦɚɰɢɢ ɢ ɩɨɞɫɢɫɬɟɦɚ ɤɨɧɬɪɨɥɹ, ɞɢɚɝɧɨɫɬɢɪɨɜɚɧɢɹ ɢ ɭɩɪɚɜɥɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɦ ɫɨɫɬɨɹɧɢɟɦ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɪɹɞɨɦ ɩɨɤɚɡɚɬɟɥɟɣ x n , n = 1, N ɢ ym , m = 1, M ,
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɇɚɩɪɢɦɟɪ, ɩɨɞɫɢɫɬɟɦɚ ɡɚɳɢɬɵ ɢɧɮɨɪɦɚɰɢɢ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɪɢɩɬɨɫɬɨɣɤɨɫɬɶɸ ɚɥɝɨɪɢɬɦɨɜ ɲɢɮɪɨɜɚɧɢɹ, ɜɟɪɨɹɬɧɨɫɬɶɸ ɨɛɧɚɪɭɠɟɧɢɹ ɭɝɪɨɡ, ɫɤɨɪɨɫɬɶɸ ɪɟɚɝɢɪɨɜɚɧɢɹ ɧɚ
ɭɝɪɨɡɭ ɢ ɬ.ɩ., ɩɨɞɫɢɫɬɟɦɚ ɤɨɧɬɪɨɥɹ, ɞɢɚɝɧɨɫɬɢɪɨɜɚɧɢɹ ɢ ɭɩɪɚɜɥɟɧɢɹ ɬɟɯɧɢɱɟɫɤɢɦ ɫɨɫɬɨɹɧɢɟɦ
ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɞɨɫɬɨɜɟɪɧɨɫɬɶɸ ɤɨɧɬɪɨɥɹ ɢ ɞɢɚɝɧɨɫɬɢɪɨɜɚɧɢɹ, ɩɨɥɧɨɬɨɣ ɤɨɧɬɪɨɥɹ, ɝɥɭɛɢɧɨɣ
ɞɢɚɝɧɨɫɬɢɪɨɜɚɧɢɹ.
ɍɱɢɬɵɜɚɹ ɩɨɤɚɡɚɬɟɥɢ ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɩɨɞɫɢɫɬɟɦ, ɜɵɪɚɠɟɧɢɹ (13) ɢ (14) ɩɪɢɦɭɬ ɜɢɞ:
CS∗ = max max F(x n , y m | STR, z ɬ , z ɢ ) ,
(15)
CS∗ = min max F(x n , y m | STR, z ɬ , z ɢ ) .
(16)
{STR }{z ɬ , z ɢ }
{STR }{z ɬ , z ɢ }
ɂɡ ɜɵɪɚɠɟɧɢɣ (15) ɢ (16) ɜɵɬɟɤɚɸɬ ɞɜɟ ɡɚɞɚɱɢ:
1) ɧɚɯɨɠɞɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɬɨɣɱɢɜɨɫɬɢ CS(x n , y m , STR ) ɨɬ ɩɨɤɚɡɚɬɟɥɟɣ
x n ɢ ym ;
2) ɨɰɟɧɤɚ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɭɫɬɨɣɱɢɜɨɫɬɢ CS(x n , y m , STR ) ɫ ɭɱɟɬɨɦ ɡɚɜɢɫɢɦɨɫɬɢ
ɨɬ ɩɨɤɚɡɚɬɟɥɟɣ x n ɢ ym .
ɉɟɪɜɚɹ ɡɚɞɚɱɚ ɹɜɥɹɟɬɫɹ ɡɚɞɚɱɟɣ ɩɨɫɬɪɨɟɧɢɹ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɭɫɬɨɣɱɢɜɨɫɬɢ Ʉɋɉɂ. ȼɬɨɪɚɹ ɡɚɞɚɱɚ ɫɜɨɞɢɬɫɹ ɤ ɩɨɥɭɱɟɧɢɸ ɨɰɟɧɤɢ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɭɫɬɨɣɱɢɜɨɫɬɢ ɩɪɢ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɩɚɪɚɦɟɬɪɨɜ z ɬi ɢ zɢj ɢ ɜɵɛɪɚɧɧɨɣ ɫɬɪɭɤɬɭɪɟ Ʉɋɉɂ.
ɅɂɌȿɊȺɌɍɊȺ
1. Ⱥɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɵɟ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ: ɇɨɜɵɟ ɢɧɮɨɪɦɚɰɢɨɧɧɵɟ ɬɟɯɧɨɥɨɝɢɢ ɜ ɚɜɢɚɰɢɢ: ɭɱɟɛ. ɩɨɫɨɛɢɟ / Ɋ.Ɇ. Ⱥɯɦɟɞɨɜ, Ⱥ.Ⱥ. Ȼɢɛɭɬɨɜ, Ⱥ.ȼ. ȼɚɫɢɥɶɟɜ ɢ
ɞɪ.; ɩɨɞ ɪɟɞ. ɋ.Ƚ. ɉɹɬɤɨ ɢ Ⱥ.ɂ. Ʉɪɚɫɨɜɚ. – ɋɉɛ.: ɉɨɥɢɬɟɯɧɢɤɚ, 2004.
2. əɪɥɵɤɨɜ Ɇ.ɋ., Ȼɨɝɚɱɟɜ Ⱥ.ɋ. Ⱥɜɢɚɰɢɨɧɧɵɟ ɪɚɞɢɨɷɥɟɤɬɪɨɧɧɵɟ ɤɨɦɩɥɟɤɫɵ. – Ɇ.:
ȼȼɂȺ ɢɦ. ɩɪɨɮ. ɇ.ȿ. ɀɭɤɨɜɫɤɨɝɨ, 2000.
3. ȼɨɫɤɨɛɨɟɜ ȼ.Ɏ., Ɋɟɣɯɨɜ ɘ.ɇ., Ʌɟɛɟɞɟɜ Ⱥ.ɘ. Ɉ ɜɵɛɨɪɟ ɩɨɤɚɡɚɬɟɥɹ ɭɫɬɨɣɱɢɜɨɫɬɢ
ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɨɛɴɟɤɬɚ ɌɗɄ // ȼɨɩɪɨɫɵ ɬɟɨɪɢɢ ɛɟɡɨɩɚɫɧɨɫɬɢ ɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɢɫɬɟɦ. – Ɇ.:
ȼɐ ɊȺɇ. 2005. ȼɵɩ. 7.
188
ɗ.Ⱥ. Ȼɨɥɟɥɨɜ, Ʉ.ɇ. Ɇɚɬɸɯɢɧ, ɇ.ɇ. Ɇɚɣɥɨɜ
4. Ȼɨɥɟɥɨɜ ɗ.Ⱥ., Ɇɚɬɸɯɢɧ Ʉ.ɇ., ɋɛɢɬɧɟɜ Ⱥ.ȼ., ɒɚɥɭɩɢɧ ɋ.ȼ. ɂɧɮɨɪɦɚɰɢɨɧɧɨɬɟɯɧɢɱɟɫɤɢɟ ɫɨɫɬɨɹɧɢɹ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɧɨɣ ɫɢɫɬɟɦɵ ɭɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɵɦ ɞɜɢɠɟɧɢɟɦ //
ɇɚɭɱɧɵɣ ɜɟɫɬɧɢɤ ɆȽɌɍ ȽȺ. 2015. ʋ 217.
THE INDICATOR OF STABILITY OF FUNCTIONING OF THE COMPLEX
MEDIA OF THE AUTOMATED SYSTEM OF AIR TRAFFIC CONTROL
Bolelov E.A., Matyukhin K.N., Mailov N.N.
The article discusses the concept of information and technical state media, which is part of the automated system
of air traffic control, as well as the definition of stability of functioning of the complex and a method of forming a resilience index.
Key words: information technology status, the complex transmission medium, the index of stability.
REFERENCES
1. Automated systems of air traffic control: New information technologies in aviation:
textbook. manual/ R.M. Akhmedov, A.A. Bebutov, A.V. Vasiliev and others; Under the ed. of
S.G. Pyatko and A.I. Krasova. – SPb.: University of technology, 2004.
2. Yarlykov M.S., Bogachev A.S. Aviation radio-electronic complexes. – M.: VVIA im. prof.
N.E. Zhukovsky, 2000.
3. Voskoboev V.F., Reich J.N., Lebedev A.Yu., On the choice of the indicator of stability of
functioning of the FEC object // Theory of security and stability of systems. Moscow: computing
centre of RAS. 2005. Vol. 7.
4. Bolelov E.A., Matyukhin, K.N., Sbitnev A.V., Chalopin S.V. Information and technical
state automated system of air traffic control // Scientific Bulletin of MSTUCA. 2015. No. 217.
ɋȼȿȾȿɇɂə ɈȻ ȺȼɌɈɊȺɏ
Ȼɨɥɟɥɨɜ ɗɞɭɚɪɞ Ⱥɧɚɬɨɥɶɟɜɢɱ (1967 ɝ.ɪ.), ɨɤɨɧɱɢɥ ȼɨɟɧɧɨ-ɜɨɡɞɭɲɧɭɸ ɢɧɠɟɧɟɪɧɭɸ
ɚɤɚɞɟɦɢɸ ɢɦ. ɇ.ȿ. ɀɭɤɨɜɫɤɨɝɨ (1997), ɞɨɰɟɧɬ, ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɡɚɜɟɞɭɸɳɢɣ
ɤɚɮɟɞɪɨɣ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɪɚɞɢɨɷɥɟɤɬɪɨɧɧɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɜɨɡɞɭɲɧɨɝɨ ɬɪɚɧɫɩɨɪɬɚ ɆȽɌɍ ȽȺ, ɚɜɬɨɪ 40 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɷɤɫɩɥɭɚɬɚɰɢɹ
ɫɥɨɠɧɵɯ ɬɟɯɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦ, ɨɛɪɚɛɨɬɤɚ ɢɧɮɨɪɦɚɰɢɢ ɜ ɧɚɜɢɝɚɰɢɨɧɧɵɯ ɤɨɦɩɥɟɤɫɚɯ. E-mail:
e.bolelov@mstuca.aero.
Ɇɚɬɸɯɢɧ Ʉɨɧɫɬɚɧɬɢɧ ɇɢɤɨɥɚɟɜɢɱ (1976 ɝ.ɪ.), ɨɤɨɧɱɢɥ ȼȼɂȺ ɢɦ. ɩɪɨɮ.
ɇ.ȿ. ɀɭɤɨɜɫɤɨɝɨ (2005), ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ ɨɫɧɨɜ ɪɚɞɢɨɬɟɯɧɢɤɢ ɢ
ɡɚɳɢɬɵ ɢɧɮɨɪɦɚɰɢɢ ɆȽɌɍ ȽȺ, ɚɜɬɨɪ 37 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɷɤɫɩɥɭɚɬɚɰɢɹ ɫɥɨɠɧɵɯ ɬɟɯɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦ. E-mail: k.matuhin@mstuca.aero.
Ɇɚɣɥɨɜ ɇɚɡɚɪ ɇɚɡɚɪɨɜɢɱ (1963 ɝ.ɪ.), ɨɤɨɧɱɢɥ ȼɨɟɧɧɵɣ ɢɧɠɟɧɟɪɧɵɣ ɤɪɚɫɧɨɡɧɚɦɟɧɧɵɣ
ɢɧɫɬɢɬɭɬ ɢɦ. Ⱥ.Ɏ. Ɇɨɠɚɣɫɤɨɝɨ (1985), ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɪɚɞɢɨɷɥɟɤɬɪɨɧɧɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɜɨɡɞɭɲɧɨɝɨ ɬɪɚɧɫɩɨɪɬɚ ɆȽɌɍ, ɚɜɬɨɪ 4 ɧɚɭɱɧɵɯ ɪɚɛɨɬ, ɨɛɥɚɫɬɶ ɧɚɭɱɧɵɯ ɢɧɬɟɪɟɫɨɜ – ɷɤɫɩɥɭɚɬɚɰɢɹ ɫɥɨɠɧɵɯ ɬɟɯɧɢɱɟɫɤɢɯ ɫɢɫɬɟɦ. E-mail: majlov@mail.ru.
1/--страниц
Пожаловаться на содержимое документа