Диссертация (1102653), страница 10
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3.183.22: íà ðèñ. 3.17,3.18 èçîáðàæåíà äèíàìèêà òðóáêè E (q(t), Q(t)), íà ðèñ. 3.19 èçîáðàæåíû ñîá-ñòâåííûå ÷èñëà òðóáêè âäîëü òðàåêòîðèè, è íà ðèñ. 3.203.22 èçîáðàæ¼í íàáîðäâèæåíèé êîíòåéíåðîâ â ðàçëè÷íûå ìîìåíòû âðåìåíè. Íà ýòèõ ðèñóíêàõ ñåðûìèçîáðàæåíû ïðåïÿòñòâèÿ, ïóíêòèðîì èçîáðàæåíî öåëåâîå ìíîæåñòâî, ñïëîøíîé÷åðíîé ëèíèåé èçîáðàæåíû ãðàíèöû êîíòåéíåðà, òîíêîé ëèíèåé îáîçíà÷åíûòðàåêòîðèè öåíòðîâ.90èñ. 3.18: Òðóáêè E (q1 (t), Q1(t)), E (q2 (t), Q2 (t)), èçîáðàæåííûå ñî ñïëîøíîéïîâåðõíîñòüþ.254.51.841.63EigenvaluesEigenvalues3.52.521.51.41.2110.80.50051015Time202530051015Time202530èñ.
3.19: Ñîáñòâåííûå ÷èñëà ìàòðèöû êîíèãóðàöèé êîíòåéíåðà Q1 (t) (ñëåâà)è Q2 (t) (ñïðàâà) âäîëü òðàåêòîðèè äâèæåíèÿ. Ïóíêòðèðíûìè ëèíèÿìè îòìå÷åíû âíóòðåííåå è âíåøíåå îãðàíè÷åíèå.9164422x22x600−2−2−4−4−6−6−8−6−4−202x4681012−8−6−4−2012x468101210121664422x2x2èñ. 3.20: Êîíòåéíåð â ìîìåíòû âðåìåíè t = 0, t = 6.12.00−2−2−4−4−6−6−8−6−4−202x4681012−8−6−4−2012x4681664422x2x2èñ. 3.21: Êîíòåéíåð â ìîìåíòû âðåìåíè t = 12.37, t = 18.62.00−2−2−4−4−6−6−8−6−4−202x4681012−81−6−4−202x4681èñ. 3.22: Êîíòåéíåð â ìîìåíòû âðåìåíè t = 24.87, t = 30.921012Çàêëþ÷åíèå çàêëþ÷åíèå êðàòêî ñîðìóëèðóåì îñíîâíûå ðåçóëüòàòû ðàáîòû.1. åøåíà çàäà÷à ñèíòåçà äëÿ ìàòðè÷íîé ëèíåéíî-êâàäðàòè÷íîé çàäà÷è ÷åðåç ñâåäåíèå å¼ ê âåêòîðíîé.
Ïîëó÷åíî ÿâíîå âûðàæåíèå äëÿ óíêöèèöåíû. Óêàçàí êëàññ ñèñòåì, â êîòîðîì ìåòîä ïîçâîëÿåò âåðíóòüñÿ ê èñõîäíûì ìàòðè÷íûì îáîçíà÷åíèÿì.2. Ïîñòðîåíà ñïåöèàëüíàÿ îðìà çàïèñè äåéñòâèÿ ìàòðè÷íûõ îïåðàòîðîââ òåðìèíàõ ïðåäñòàâëåíèé îïåðàòîðîâ, ïîçâîëÿþùàÿ ñîõðàíèòü ìàòðè÷íóþ îðìó ðåøåíèÿ. Âûâåäåí ðÿä ñâîéñòâ ïðåäñòàâëåíèé. Ïîêàçàíî, ÷òîèñïîëüçîâàíèå ïîäîáíîãî ïîäõîäà àëãîðèòìè÷åñêè áîëåå ýåêòèâíî, ÷åìðåøåíèå ÷åðåç âåêòîðèçàöèþ.3. Áûëà ðåøåíà ìàòðè÷íàÿ çàäà÷à ñèíòåçà ñ ãåîìåòðè÷åñêèì (¾æ¼ñòêèì¿)îãðàíè÷åíèåì íà óïðàâëåíèå. Ïðåäëîæåí ñïîñîá íàãëÿäíîé âèçóàëèçàöèèìíîæåñòâ â ïðîñòðàíñòâå ìàòðèö, åãî äåéñòâèå ïðîèëëþñòðèðîâàíî íà ðÿäå ïðèìåðîâ.
Ïðèâåäåíû îðìóëû äëÿ âíóòðåííèõ è âíåøíèõ îöåíîê ìíîæåñòâ äîñòèæèìîñòè è ðàçðåøèìîñòè â ïðîñòðàíñòâàõ ìàòðèö, íà îñíîâåêîòîðûõ ñòðîèòñÿ ïðèáëèæ¼ííîå ðåøåíèå çàäà÷è ñèíòåçà. Ïîëó÷åíûå ìåòîäû ïðèìåíåíû äëÿ ðåøåíèÿ çàäà÷è ðåêîíèãóðàöèè.åøåíèå çàäà÷ óïðàâëåíèÿ äëÿ ñèñòåì ñ ìàòðè÷íûìè àçîâûìè ïåðåìåííûìè ïðåäñòàâëÿåò áîëüøîé èíòåðåñ äëÿ ñîâðåìåííîé ìàòåìàòè÷åñêîé òåîðèè93óïðàâëåíèÿ.
Èçëîæåííûå â íàñòîÿùåé ðàáîòå ìåòîäû è ïîäõîäû ïðèìåíåíû êøèðîêîìó êðóãó ïîäîáíûõ çàäà÷. Îïåðàòîðíûé ìåòîä ðåøåíèÿ, èçëîæåííûéâî âòîðîé ãëàâå, ìîæåò áûòü èñïîëüçîâàí äëÿ çàäà÷ ñ âûñîêîé ðàçìåðíîñòüþàçîâîé ïåðåìåííîé. Ìåòîäû, èçëîæåííûå â òðåòüåé ãëàâå, ìîãóò ïðèìåíÿòüñÿäëÿ ìàòðè÷íûõ çàäà÷ äîñòèæèìîñòè è ñèíòåçà óïðàâëåíèé ïðè íàëè÷èè ãåîìåòðè÷åñêèõ îãðàíè÷åíèé íà óïðàâëåíèå. Çàäà÷è ðåêîíèãóðàöèè è ðàçáèåíèÿêîíòåéíåðà â òðåòüåé ãëàâå ïðîèñõîäÿò èç ãðóïïîâîãî óïðàâëåíèÿ è ÿâëÿþòñÿ ñîñòàâíûì ýòàïîì ðåøåíèÿ îáùåé çàäà÷è ñèíòåçà óïðàâëåíèé äëÿ ãðóïïûàãåíòîâ â óñëîâèÿõ ïðåïÿòñòâèé.åçóëüòàòû íàñòîÿùåé ðàáîòû äîïóñêàþò îáîáùåíèå è äàëüíåéøååå ðàçâèòèå â ðàìêàõ ýòèõ çàäà÷.94Ëèòåðàòóðà[1℄ A. B. Kurzhanski and I.
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