1. Trang chủ
  2. » Giáo Dục - Đào Tạo

LUẬN văn THẠC sĩ HAY bài toán đuổi bắt trong trò chơi tuyến tính với hạn chế tích phân trên thang thời gian

50 1 0

Đang tải... (xem toàn văn)

Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống

THÔNG TIN TÀI LIỆU

Thông tin cơ bản

Định dạng
Số trang 50
Dung lượng 637,52 KB

Nội dung

ĐẠI HỌC THÁI NGUYÊN TRƯỜNG ĐẠI HỌC KHOA HỌC  - LÊ VĂN QUÝ BÀI TOÁN ĐUỔI BẮT TRONG TRỊ CHƠI TUYẾN TÍNH VỚI HẠN CHẾ TÍCH PHÂN TRÊN THANG THỜI GIAN LUẬN VĂN THẠC SĨ TOÁN HỌC THÁI NGUYÊN - 2017 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ĐẠI HỌC THÁI NGUYÊN TRƯỜNG ĐẠI HỌC KHOA HỌC  - LÊ VĂN Q BÀI TỐN ĐUỔI BẮT TRONG TRỊ CHƠI TUYẾN TÍNH VỚI HẠN CHẾ TÍCH PHÂN TRÊN THANG THỜI GIAN LUẬN VĂN THẠC SĨ TỐN HỌC Chun ngành: Tốn ứng dụng Mã số : 60 46 01 12 NGƯỜI HƯỚNG DẪN KHOA HỌC: PGS.TS Tạ Duy Phượng THÁI NGUYÊN - 2017 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ▼ö❝ ❧ư❝ ▼ð ✤➛✉ ✶ ❑❤→✐ ♥✐➺♠ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✶ ✹ ✶✳✶ ❚❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✷ ❚ỉ ♣ỉ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✸ ❈→❝ ✤à♥❤ ♥❣❤➽❛ ❝ì ❜↔♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✹ P❤➨♣ t➼♥❤ ✈✐ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✺ ✹ ✶✳✹✳✶ ✣↕♦ ❤➔♠ ❍✐❧❣❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✹✳✷ ❚➼♥❤ ❝❤➜t ❝õ❛ ✤↕♦ ❤➔♠ ❍✐❧❣❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ P❤➨♣ t➼♥❤ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✺✳✶ ❍➔♠ t✐➲♥ ❦❤↔ ✈✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✺✳✷ P❤➨♣ t➼♥❤ t➼❝❤ ♣❤➙♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ q✉② tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✼ ❍➔♠ ♠ơ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸ ✷ ❚rá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✷✻ ✷✳✶ ❍➺ ✤ë♥❣ ❧ü❝ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✶✳✶ P❤÷ì♥❣ tr➻♥❤ ✈➔ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ ✤ë♥❣ ❧ü❝ t✉②➳♥ t➼♥❤ ❜➟❝ ♥❤➜t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✶✳✷ ❈æ♥❣ t❤ù❝ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ ✈➔ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ ✤ë♥❣ ❧ü❝ t✉②➳♥ t➼♥❤ ❜➟❝ ♥❤➜t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✶✳✸ ❍➺ ✤ë♥❣ ❧ü❝ t✉②➳♥ t➼♥❤ ❝â ❤❛✐ t❤❛♠ sè ✤✐➲✉ ❦✐➸♥ ✳ ✳ ✳ ✸✶ ✐ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✐✐ ✷✳✷ ❚rá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✸ ❚rá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ t❤æ♥❣ t✐♥ ❝❤➟♠ ✈➔ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ❑➳t ❧✉➟♥ ❚➔✐ ❧✐➺✉ tr➼❝❤ ❞➝♥ ✹✹ ✹✺ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ▼ð ✤➛✉ ◆❤➡♠ t❤è♥❣ ♥❤➜t ♥❣❤✐➯♥ ❝ù✉ ❝→❝ ❤➺ ✤ë♥❣ ❧ü❝ ❧✐➯♥ tö❝ ✭❤➺ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥✮ ✈➔ ❤➺ ✤ë♥❣ ❧ü❝ rí✐ r↕❝ ✭❤➺ ♣❤÷ì♥❣ tr➻♥❤ s❛✐ ♣❤➙♥✮✱ ❙t❡❢❛♥ ❍✐❧❣❡r ♥➠♠ ✶✾✽✽✱ tr♦♥❣ ❧✉➟♥ →♥ ❚✐➳♥ s➽ ❝õ❛ ♠➻♥❤✱ ✤➣ ✤÷❛ r❛ ❦❤→✐ ♥✐➺♠ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✭t✐♠❡ s❝❛❧❡✮✳ ❚ø ✤â ✤➳♥ ♥❛② ✤➣ ❝â ♠ët sè q✉②➸♥ s→❝❤✱ ❤➔♥❣ ❝❤ö❝ ❧✉➟♥ →♥ t✐➳♥ s➽ ✈➔ ❤➔♥❣ ♥❣➔♥ ❜➔✐ ❜→♦ ♥❣❤✐➯♥ ❝ù✉ ✈➲ ❣✐↔✐ t➼❝❤ ✭♣❤➨♣ t♦→♥ ✈✐ ♣❤➙♥✱ t➼❝❤ ♣❤➙♥✮ ✈➔ ❤➺ ✤ë♥❣ ❧ü❝ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ❚❤❛♥❣ t❤í✐ ❣✐❛♥ ❝â þ ♥❣❤➽❛ tr✐➳t ❤å❝ s➙✉ s➢❝✿ ❚❤❛♥❣ t❤í✐ ❣✐❛♥ ❝❤♦ ♣❤➨♣ ♥❣❤✐➯♥ ❝ù✉ ❤❛✐ ♠➦t ❜↔♥ ❝❤➜t ❝õ❛ t❤ü❝ t➳✱ ✤â ❧➔ t➼♥❤ ❧✐➯♥ tư❝ ✈➔ t➼♥❤ rí✐ r↕❝✳ ❚r♦♥❣ t♦→♥ ❤å❝✱ t❤❛♥❣ t❤í✐ ❣✐❛♥ ❝❤♦ ♣❤➨♣ ♥❣❤✐➯♥ ❝ù✉ t❤è♥❣ t ổ ữợ ũ ởt ♥✐➺♠ ✈➔ ❝ỉ♥❣ ❝ư✳ ●✐↔✐ t➼❝❤ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈➔ ❤➺ ✤ë♥❣ ❧ü❝ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✤❛♥❣ ✤÷đ❝ õ t tr ữợ q✉❛♥ t➙♠✳ ✣➣ ❝â ♠ët sè ❜➔✐ ✈✐➳t ✈➲ ù♥❣ ❞ư♥❣ ❝õ❛ t❤❛♥❣ t❤í✐ ❣✐❛♥ tr♦♥❣ ♥❣❤✐➯♥ ❝ù✉ ❦✐♥❤ t➳ ✈➽ ♠ỉ✱ ❤➺ s✐♥❤ t❤→✐✱ ❜➔✐ t♦→♥ tè✐ ÷✉✳ ❇➔✐ t♦→♥ ✤✉ê✐ ❜➢t ❧➔ ♠ët tr♦♥❣ ♥❤ú♥❣ ❝→❝ ❜➔✐ t♦→♥ ỡ ỵ tt trỏ ỡ r t t t ữớ ợ ❝õ❛ ♠➻♥❤✮ ❧✉æ♥ ❝è ❣➢♥❣ ❝❤↕② ❝➔♥❣ ♥❤❛♥❤✱ ❝➔♥❣ ①❛ ♥❣÷í✐ ✤✉ê✐ ❝➔♥❣ tèt✳ ❈á♥ ♥❣÷í✐ ✤✉ê✐ t❤➻ ❝è ❣➢♥❣ ✧♣❤→t r❛ ✧ ♥❤ú♥❣ ✤✐➲✉ ❦✐➸♥ ✤➸ t✐➳♥ ✤➳♥ ♥❣÷í✐ ❝❤↕② ❝➔♥❣ ❣➛♥ ❝➔♥❣ tèt✳ ◆❤÷♥❣ ✤➸ trá ❝❤ì✐ ❦➳t t❤ó❝ t❤➻ t❛ ♣❤↔✐ ✤➦t ❣✐↔ t❤✐➳t ❧➔ ♥❣÷í✐ ✤✉ê✐ ♣❤↔✐ ❝â ❧đ✐ t❤➳ ❤ì♥ ♥❣÷í✐ ❝❤↕② ♥❤÷ ❧➔ ❤↕♥ ❝❤➳ ✈➲ ♥➠♥❣ ❧÷đ♥❣✱ ♥❣÷í✐ ✤✉ê✐ ❧✉ỉ♥ ❜✐➳t ✤÷đ❝ t❤ỉ♥❣ t✐♥ ✈➲ ❜✐➳♥ ✤✐➲✉ ❦✐➸♥ ❝õ❛ ♥❣÷í✐ ❝❤↕②✳✳✳❚r♦♥❣ ❧✉➟♥ ✈➠♥ ♥➔② ❝❤ó♥❣ tỉ✐ ♥❣❤✐➯♥ ❝ù✉ ✈➲ ✤✐➲✉ ❦✐➺♥ ✤õ ✤➸ ❦➳t t❤ó❝ trá ❝❤ì✐ ♥❤÷ ✈➟②✳ ✶ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✷ ◆ë✐ ❞✉♥❣ ❝❤➼♥❤ ❝õ❛ ❧✉➟♥ ✈➠♥ ❧➔ ♥❣❤✐➯♥ ❝ù✉ ❜➔✐ t♦→♥ ✤✉ê✐ ❜➢t tr♦♥❣ trá ❝❤ì✐ t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ✣÷❛ r❛ ✤✐➲✉ ❦✐➺♥ ✤➸ ❜➔✐ t♦→♥ ❦➳t t❤ó❝ ✈ỵ✐ ❝→❝ ❜✐➳♥ ✤✐➲✉ ❦❤✐➸♥ t❤ä❛ ♠➣♥ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ ✭❤↕♥ ❝❤➳ ♥➠♥❣ ❧÷đ♥❣✮✳ ◆ë✐ ❞✉♥❣ ❝õ❛ ỗ ữỡ ữỡ tr ♥✐➺♠ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ❉ü❛ t❤❡♦ ❬✺❪✱ ❬✻❪✱ ❬✽❪ ✈➔ ♠ët sè t➔✐ ❧✐➺✉ ❦❤→❝✱ ❝→❝ ❦❤→✐ ♥✐➺♠✱ t➼♥❤ ❝❤➜t ❝ì ❜↔♥ ✈➲ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈➔ ❝→❝ ✈➜♥ ✤➲ ✈➲ ❣✐↔✐ t➼❝❤ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✤÷đ❝ tr➻♥❤ ❜➔② ♥❣➢♥ ❣å♥✱ t↕♦ ✤✐➲✉ ❦✐➺♥ ✤➸ ♥❣❤✐➯♥ ❝ù✉ ❜➔✐ t♦→♥ trá ❝❤ì✐ ✤ê✐ ❜➢t t✉②➳♥ t➼♥❤ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ tr♦♥❣ ❈❤÷ì♥❣ ✷✳ ❈❤÷ì♥❣ ✷ tr➻♥❤ ❜➔② ❝ỉ♥❣ t❤ù❝ ♥❣❤✐➺♠ ❝õ❛ ❤➺ ✤ë♥❣ ❧ü❝ ✈➔ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥✱ ❜➔✐ t♦→♥ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ ✈➔ tổ t tr t tớ ỵ tr♦♥❣ ❝❤÷ì♥❣ ♥➔② ❧➔ ❝→❝ ❦➳t q✉↔ ❝❤✉♥❣ ❝õ❛ ❜❛ t→❝ ❣✐↔ ❱✐ ❉✐➺✉ ▼✐♥❤✱ ▲➯ ❚❤à ❚❤ó② ◆❣➔ ✈➔ ✤÷đ❝ tr➻♥❤ ❜➔② tr♦♥❣ ❬✸❪✳ ❚→❝ ❣✐↔ ①✐♥ ✤÷đ❝ ❣û✐ ❧í✐ ❝↔♠ ì♥ s➙✉ s➢❝ tỵ✐ P●❙✳ ❚❙✳ ❚↕ ❉✉② Pữủ ữớ t tớ ữợ t t➻♥❤ ❝❤➾ ❜↔♦✱ t↕♦ ✤✐➲✉ ❦✐➺♥ ✈➔ ❣✐ó♣ ✤ï tr♦♥❣ tr❛♥❣ ❜à ❦✐➳♥ t❤ù❝✱ tr♦♥❣ ♥❣❤✐➯♥ ❝ù✉ ✈➔ tê♥❣ ❤ñ♣ t➔✐ ❧✐➺✉ ✤➸ ❤♦➔♥ t❤➔♥❤ ❧✉➟♥ ✈➠♥✳ ❚→❝ ❣✐↔ ❝ô♥❣ ①✐♥ ❣û✐ ❧í✐ ❝↔♠ ì♥ ❝❤➙♥ t❤➔♥❤ tỵ✐ ❇❛♥ ❣✐→♠ ❤✐➺✉✱ P❤á♥❣ ❙❛✉ ✤↕✐ ❤å❝✱ P❤á♥❣ ✣➔♦ t↕♦✱ ❑❤♦❛ ❚♦→♥✲❚✐♥ ✈➔ ❝→❝ t❤➛② ❝ỉ tr♦♥❣ tr÷í♥❣ ✣↕✐ ❤å❝ ❑❤♦❛ ❤å❝ ✕ ✣↕✐ ❤å❝ ❚❤→✐ ◆❣✉②➯♥ ✤➣ t↕♦ ✤✐➲✉ ❦✐➺♥ t❤✉➟♥ ❧đ✐ tr♦♥❣ s✉èt q✉→ tr➻♥❤ ❤å❝ t➟♣ t↕✐ tr÷í♥❣✳ ❳✐♥ ✤÷đ❝ ❝↔♠ ì♥ ❇❛♥ ❣✐→♠ ❤✐➺✉✱ ❇❛♥ ❝❤✉②➯♥ ♠ỉ♥ ❝ị♥❣ ỗ tr rữớ tr tổ ữ ❨➯♥✱ t➾♥❤ ❍÷♥❣ ❨➯♥✱ ♥ì✐ tỉ✐ ❝ỉ♥❣ t→❝✱ ✤➣ t↕♦ ♠å✐ ✤✐➲✉ ❦✐➺♥ ✤➸ tỉ✐ ❤♦➔♥ t❤➔♥❤ ♥❤✐➺♠ ✈ư ❤å❝ t➟♣✳ ❳✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ì♥ ❚❤↕❝ s➽ ❱✐ ❉✐➺✉ ▼✐♥❤✱ ❣✐↔♥❣ ✈✐➯♥ ♠ỉ♥ ❚♦→♥✱ tr÷í♥❣ ✣↕✐ ❤å❝ ◆ỉ♥❣ ▲➙♠✱ ✣↕✐ ❤å❝ ❚❤→✐ ◆❣✉②➯♥ ✤➣ ❝ị♥❣ ❝ë♥❣ t→❝ ✈➔ ❣✐ó♣ ✤ï tæ✐ ✈➲ ❝❤✉②➯♥ ♠æ♥ tr♦♥❣ s✉èt q✉→ tr➻♥❤ ❧➔♠ ❧✉➟♥ ✈➠♥✳ ❈✉è✐ ❝ị♥❣ t→❝ ❣✐↔ ①✐♥ ❣û✐ ❧í✐ ❝↔♠ ì♥ ✤➦❝ ❜✐➺t ✤➳♥ ♥❤ú♥❣ ♥❣÷í✐ t❤➙♥✱ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ỗ ✈➔ ♥❤ú♥❣ ♥❣÷í✐ ❜↕♥ ✤➣ t↕♦ ♠å✐ ✤✐➲✉ ❦✐➺♥ t❤✉➟♥ ❧đ✐✱ ✤ë♥❣ ✈✐➯♥✱ ❣✐ó♣ ✤ï tỉ✐ tr♦♥❣ s✉èt q✉→ tr➻♥❤ ❤å❝ t➟♣ ✈➔ ❤♦➔♥ t❤✐➺♥ ❧✉➟♥ ✈➠♥✳ ❚❤→✐ ◆❣✉②➯♥✱ ♥❣➔② t ỵ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❈❤÷ì♥❣ ✶ ❑❤→✐ ♥✐➺♠ t❤❛♥❣ t❤í✐ ❣✐❛♥ ❈❤÷ì♥❣ ♥➔② tr➻♥❤ ❜➔② ❦❤→✐ ♥✐➺♠ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ❉ü❛ t❤❡♦ ❬✺❪✱ ❬✻❪✱ ❬✽❪ ✈➔ ♠ët sè t➔✐ ❧✐➺✉ ❦❤→❝✱ ❝→❝ ❦❤→✐ ♥✐➺♠✱ t➼♥❤ ❝❤➜t ❝ì ❜↔♥ ✈➲ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈➔ ❝→❝ ✈➜♥ ✤➲ ✈➲ ❣✐↔✐ t➼❝❤ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✤÷đ❝ tr➻♥❤ ❜➔②✳ ✶✳✶ ❚❤❛♥❣ t❤í✐ ❣✐❛♥ ✣à♥❤ ♥❣❤➽❛ ✶✳✶ ❚❤❛♥❣ t❤í✐ ❣✐❛♥ t s t õ tũ ỵ rộ tr♦♥❣ t➟♣ sè t❤ü❝ R ❚❤❛♥❣ t❤í✐ ❣✐❛♥ t❤÷í♥❣ ✤÷đ❝ ỵ T t R, Z, N, [0; 1] ∪ [2; 3] ❧➔ ❝→❝ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈➻ ❝❤ó♥❣ ❧➔ ♥❤ú♥❣ t➟♣ ✤â♥❣ tr♦♥❣ R✳ ✷✮ ❈→❝ t➟♣ Q, R\Q; [0, 1) ❦❤æ♥❣ ♣❤↔✐ ❧➔ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈➻ ❝❤ó♥❣ ❦❤ỉ♥❣ ♣❤↔✐ ❧➔ t➟♣ ✤â♥❣ tr♦♥❣ R ❚➟♣ ❝→❝ sè ❤ú✉ t➾ Q✱ t➟♣ ❝→❝ sè ✈ỉ t➾ R\Q ❦❤ỉ♥❣ ♣❤↔✐ ❧➔ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈➻ ❝❤ó♥❣ t✉② ♥➡♠ tr♦♥❣ R ♥❤÷♥❣ ❦❤ỉ♥❣ ✤â♥❣ tr♦♥❣ R✳ ❚❤➟t ✈➟②✱ tr➯♥ Q ①➨t ❞➣② sè {xn }✿ ✶❀ ✶✱✹❀ ✶✱✹✶❀ ✶✱✹✶✹❀ ✳ ✳ ✳ ❚❛ t❤➜② xn ∈Q✱ √ ♥❤÷♥❣ lim xn = ∈ / Q ♥➯♥ Q ❦❤æ♥❣ ♣❤↔✐ ❧➔ t➟♣ ❝♦♥ ✤â♥❣ tr➯♥ R ❱➻ n→∞ ✈➟② Q ❦❤ỉ♥❣ ♣❤↔✐ ❧➔ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ❚r➯♥ R\Q ①➨t ❞➣② sè {xn } : √ √ √ √ 3 3; ; ; ; ; n ✹ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✺ ❚❛ t❤➜② xn ∈ R\Q ♥❤÷♥❣ lim xn = ∈ / R\Q ♥➯♥ R\Q ❦❤æ♥❣ ♣❤↔✐ ❧➔ t➟♣ x→∞ ❝♦♥ ✤â♥❣ tr♦♥❣ R ❙✉② r❛ R\Q ❦❤ỉ♥❣ ♣❤↔✐ ❧➔ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ❚➟♣ ❬✵❀✶✮ ❧➔ ❦❤♦↔♥❣ ♠ð tr♦♥❣ R ♥➯♥ ❦❤æ♥❣ ♣❤↔✐ ❧➔ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ✸✮ ▼➦t ♣❤➥♥❣ ♣❤ù❝ C ❦❤ỉ♥❣ ♣❤↔✐ ❧➔ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈➻ C ❦❤ỉ♥❣ ♥➡♠ tr♦♥❣ R, ♠➦❝ ❞ị ♥â ❧➔ t➟♣ ✤â♥❣✳ ✶✳✷ ❚ỉ ♣ỉ tr➯♥ t❤❛♥❣ tớ rữợ t t ởt t❤ù❝ ❝õ❛ tæ♣æ✳ ●✐↔ sû (X, τ ) ❧➔ ♠ët ❦❤æ♥❣ ❣✐❛♥ tæ♣æ✱ M ⊂ X ❧➔ ♠ët t➟♣ ❝♦♥ ♥➔♦ ✤â✳ ❚æ♣æ ❝↔♠ s✐♥❤ τM tr➯♥ M tø τ ✤÷đ❝ ✤à♥❤ ♥❣❤➽❛ ♥❤÷ s❛✉✳ ❚➟♣ ♠ð tr♦♥❣ τM ❧➔ t➜t ❝↔ ❝→❝ t➟♣ ❝â ❞↕♥❣ σM = M ∩ U tr♦♥❣ ✤â σ ∈ τ ✳ ❑❤✐ ➜② τM = {UM : UM = M ∩ U, U ∈ τ } ❧➔ ♠ët tæ♣æ tr➯♥ M ✳ ❚❤➟t ✈➟② t❛ ❝â ✶✮ ❱➻ ∅ ✈➔ X ✤➲✉ t❤✉ë❝ τ ♥➯♥ ❞➵ t❤➜② ∅ = ∅ ∩ M, M = M ∩ M s✉② r❛ ∅ ✈➔ M ✤➲✉ t❤✉ë❝ τM ✷✮ ●✐↔ sû V1 , V2 ∈ τM t ủ t tự tỗ t U1 , U2 ∈ τ s❛♦ ❝❤♦ V1 = M ∩ U1 ✈➔ V2 = M ∩ U2 ✳ ❚❛ ❝â V1 ∩ V2 = (M ∩ U1 ) ∩ (M ∩ U2 ) = M ∩ (U1 ∩ U2 )✳ ❱➻ U1 ∩ U2 ∈ τ ♥➯♥ s✉② r❛ V1 ∩ V2 ∈ τM ✭t❤❡♦ ✤à♥❤ ♥❣❤➽❛ t➟♣ τM ✮✳ ✸✮ ●✐↔ sû {Vα }α∈I ❧➔ ♠ët ❤å ❜➜t ❦➻ ❝→❝ t➟♣ t❤✉ë❝ τM ✳ ❑❤✐ ✤â t❛ ❝â Uα ✈ỵ✐ Uα ∈ τ ∀α ∈ I ✳ ❱➻ (M ∩ Uα ) = M ∩ α∈I α∈I V α ∈ τM ✳ α∈I Vα = α∈I Uα ∈ τ ♥➯♥ s✉② r❛ α∈I ❚ø ✶✮✱ ✷✮✱ ✸✮ s✉② r❛ τM ❧➔ ♠ët tæ♣æ ✈➔ ❣å✐ ❧➔ tæ♣æ ❝↔♠ s✐♥❤ tø τ tr➯♥ M ✳ ❈➦♣ (M, τM ) ✤÷đ❝ ❣å✐ ❧➔ ❦❤ỉ♥❣ ❣✐❛♥ tỉ♣ỉ ❝↔♠ s✐♥❤ ❝õ❛ ❦❤ỉ♥❣ ❣✐❛♥ tæ♣æ (X, τ ) ❚r♦♥❣ ❧✉➟♥ ✈➠♥ ♥➔② t❛ ❧✉ỉ♥ ❣✐↔ t❤✉②➳t r➡♥❣ t❤❛♥❣ t❤í✐ ❣✐❛♥ T ✤÷đ❝ tr❛♥❣ ❜à ♠ët tỉ♣ỉ ❝↔♠ s✐♥❤ tø tỉ♣ỉ t❤ỉ♥❣ t❤÷í♥❣ ❝õ❛ t➟♣ sè t❤ü❝ ✭tỉ♣ỉ t❤ỉ♥❣ t❤÷í♥❣ tr➯♥ t➟♣ sè t❤ü❝ R ❧➔ tỉ♣ỉ t↕♦ ❜ð✐ ❝→❝ ❦❤♦↔♥❣ ♠ð ❝ị♥❣ ✈ỵ✐ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✻ ❣✐❛♦ ❤ú✉ ❤↕♥ ✈➔ ❤đ♣ ❜➜t ❦➻ ❝õ❛ ❝❤ó♥❣✮✱ ♥❣❤➽❛ ❧➔ ❝→❝ t➟♣ ♠ð ❝õ❛ T ❧➔ ❣✐❛♦ ❝õ❛ ❝→❝ t➟♣ ♠ð tr♦♥❣ R ✈ỵ✐ T ❈→❝ ❦❤→✐ ♥✐➺♠ ❧➙♥ ợ tửữủ ợ ❤↕♥✱ ❧✐➯♥ tư❝✳✳✳ tr♦♥❣ tỉ♣ỉ ❝↔♠ s✐♥❤✳ ✶✳✸ ❈→❝ ✤à♥❤ ♥❣❤➽❛ ❝ì ❜↔♥ ✣à♥❤ ♥❣❤➽❛ ✶✳✷ ❈❤♦ T ❧➔ t❤❛♥❣ t❤í✐ ❣✐❛♥✳ ❚♦→♥ tû ♥❤↔② t✐➳♥ ✭❢♦r✇❛r❞ ❥✉♠♣✮ ❧➔ t♦→♥ tû σ:T→T ✤÷đ❝ ①→❝ ✤à♥❤ ❜ð✐ ❝ỉ♥❣ t❤ù❝ σ(t) := inf{s ∈ T : s > t} ❚♦→♥ tû ♥❤↔② ❧ị✐ ✭❜❛❝❦✇❛r❞ ❥✉♠♣✮ ❧➔ t♦→♥ tû ρ:T→T ✤÷đ❝ ①→❝ ✤à♥❤ ❜ð✐ ❝æ♥❣ t❤ù❝ ρ(t) := sup{s ∈ T : s < t} ữợ inf = sup T, sup ∅ = inf T ❙✉② r❛ σ(M ) = M ♥➳✉ M ❧➔ ♣❤➛♥ tû ❧ỵ♥ ♥❤➜t ✭♥➳✉ ❝â✮ ❝õ❛ T; ρ(m) = m ♥➳✉ m ❧➔ ♣❤➛♥ tû ♥❤ä ♥❤➜t ✭♥➳✉ ❝â✮ ❝õ❛ T ❱➼ ❞ư ✶✳✷ ✶✮ ❱ỵ✐ t❤❛♥❣ t❤í✐ ❣✐❛♥ T = Z ✭t❤❛♥❣ t❤í✐ ❣✐❛♥ rí✐ r↕❝✮ t❤➻ σ(t) = t + ✈➔ ρ(t) = t − ✈ỵ✐ ♠å✐ t ∈ T ❳❡♠ ❍➻♥❤ ✶✳✶✭❜✮✳ ✷✮ ❱ỵ✐ t❤❛♥❣ t❤í✐ ❣✐❛♥ T = R ✭t❤❛♥❣ t❤í✐ ❣✐❛♥ ❧✐➯♥ tư❝✮ t❤➻ σ(t) = ρ(t) = t ✈ỵ✐ ♠å✐ t ∈ T ❳❡♠ ❍➻♥❤ ✶✳✶✭❛✮✳ ❍➻♥❤ ✶✳✶ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✷ ❚❛ ❝â z = z σ − µ(t)z ∆ ❚❤❛② ✈➔♦ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ tr➯♥✱ t❛ ❝â z ∆ (t) = A[z σ (t) − µ(t)z ∆ ] − Bu(t) + Cv(t) ⇔ (I + Aµ(t))z ∆ (t) = Az σ (t) − Bu(t) + Cv(t) A AB AC ⇔ z ∆ (t) = z σ (t) − u(t) + u(t) I + Aµ(t) I + Aµ(t) I + Aµ(t) = −( A)z σ (t) − AB I+Aµ(t) u(t) + AC I+Aà(t) u(t) ỵ ( ( A)) = A ✱ t❛ ❝â ♥❣❤✐➺♠ ❝õ❛ ❤➺ ✭✷✳✶✳✶✸✮ ❧➔ t z(t) = eA (t, t0 )z0 − eA (t, τ ) t0 t eA (t, τ ) + t0 Bu(τ ) ∆τ I + Aµ(τ ) Cv(τ ) ∆τ I + Aµ(τ ) (∗∗) ❍ì♥ ♥ú❛✱ t❤❡♦ ✣à♥❤ ỵ t õ eA (t, τ ) eA (t, τ ) eA (t, τ ) = = = eA (t, σ(τ )) I + Aµ(τ ) eA (σ(τ ), t0 ).eA (t0 , τ ) eA (σ(τ ), τ ) ❚❤❛② ✈➔♦ ✭✯✯✮✱ t❛ ❝â ♥❣❤✐➺♠ ❝õ❛ ✭✷✳✶✳✶✸✮ ❝â ❞↕♥❣ t z(t) = eA (t, t0 )z0 − t eA (t, σ(τ ))Bu(τ )∆τ + t0 eA (t, ( ))Cv( ) t0 ỵ ❝❤ù♥❣ ♠✐♥❤✳ ✷✳✷ ❚rá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ●✐↔ sû ❝❤✉②➸♥ ✤ë♥❣ ❝õ❛ ❤❛✐ ✤è✐ t÷đ♥❣ x(t) ∈ Rn ✭✤÷đ❝ ❣å✐ ❧➔ ♥❣÷í✐ ✤✉ê✐✮ ✈➔ y(t) ∈ Rn ✭✤÷đ❝ ❣å✐ ữớ ợ t tr t tớ T ✤÷đ❝ ♠ỉ t↔ t÷ì♥❣ ù♥❣ ❜ð✐ ❝→❝ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ x∆ (t) = f (x(t), u(t), t) (2.2.1) y ∆ (t) = f (y(t), v(t), t) (2.2.2) ✈➔ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✸ tr♦♥❣ ✤â u(t) ∈ Rp ✱ v(t) ∈ Rq ❧➔ ❝→❝ ❤➔♠ ✤♦ ✤÷đ❝ ✈➔ r❞✲❧✐➯♥ tư❝ tr➯♥ T✳ ✣➦t T = s✉♣{t, t ∈ T} ❈→❝ ✤✐➲✉ ❦❤✐➸♥ u(t), v(t) t❤ä❛ ♠➣♥ ❝→❝ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ ✭❤↕♥ ❝❤➳ ♥➠♥❣ ❧÷đ♥❣✮ ❞↕♥❣ T T 2 v(s) ∆s ≤ σ u(s) ∆s ≤ ρ , t0 (2.2.3) t0 tr♦♥❣ õ , số trữợ ✤♦ ✤÷đ❝ u(t) ✈➔ v(t) t❤ä❛ ♠➣♥ ✭✷✳✷✳✸✮ ✤÷đ❝ ❣å✐ t÷ì♥❣ ù♥❣ ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ ❝õ❛ ♥❣÷í✐ ữớ ợ x(0) = x0 trữợ ✈➔ u(t) ✤÷đ❝ ❝❤å♥✱ t❤❛② ✈➔♦ ✭✷✳✷✳✶✮✱ ❤➺ ✤ë♥❣ ❧ü❝ ✭✷✳✷✳✶✮ s➩ ①→❝ ✤à♥❤ ♠ët q✉ÿ ✤↕♦ x(t) ❧➔ ♥❣❤✐➺♠ ❝õ❛ ✭✷✳✷✳✶✮✱ ①✉➜t ♣❤→t tø ✤✐➸♠ ❜❛♥ ✤➛✉ x0 t÷ì♥❣ ự ợ u(t), t T ữỡ tỹ ợ y(0) = y0 trữợ v(t) ữủ t❤❛② ✈➔♦ ✭✷✳✳✷✳✷✮✱ ♣❤÷ì♥❣ tr➻♥❤ ✭✷✳✷✳✷✮ s➩ ①→❝ ✤à♥❤ ♠ët q✉ÿ ✤↕♦ y(t), t ∈ T ❧➔ ♥❣❤✐➺♠ ❝õ❛ ✭✷✳✷✳✷✮✱ t t tứ y0 tữỡ ự ợ ✤✐➲✉ ❦❤✐➸♥ v(t) ❚❛ ♥â✐ trá ❝❤ì✐ ❦➳t t❤ó❝ s❛✉ t❤í✐ ❣✐❛♥ K ♥➳✉ ✈ỵ✐ ♠é✐ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ v(t) ❝õ❛ ♥❣÷í✐ ❝❤↕②✱ ♥❣÷í✐ ✤✉ê✐ ❝â t❤➸ ①➙② ❞ü♥❣ ✤÷đ❝ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ u(t) ❝õ❛ ♠➻♥❤ s❛♦ ❝❤♦ ♥❣❤✐➺♠ t÷ì♥❣ ù♥❣ ❝õ❛ ✭✷✳✷✳✶✮ ✈➔ ✭✷✳✷✳✷✮ t❤ä❛ x(K) = y(K) (2.2.4) ữ ợ z(t) = F (z(t), u(t), v(t)) = x(t) y(t) f (x(t), u(t), t) g(y(t), v(t), t) ❑❤✐ ➜② ❤➺ ữỡ tr õ t t ữợ z (t) = F (z(t), u(t), v(t), t) (2.2.5) LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✹ ❍➺ t❤ù❝ ✭✷✳✷✳✹✮ s➩ ①→❝ ✤à♥❤ tr♦♥❣ ❦❤æ♥❣ ❣✐❛♥ R2n ♠ët ❦❤æ♥❣ ❣✐❛♥ ❝♦♥✱ tù❝ ❧➔ t➟♣ ❤ñ♣ ♥❤ú♥❣ ✤✐➸♠ z(K) t❤ä❛ ♠➣♥ ✭✷✳✷✳✹✮ ❝â ❞↕♥❣ M := {z = x y , x ∈ Rn , y ∈ Rn , x = y} ◆❤÷ ✈➟②✱ ❝â t❤➸ ♣❤→t ❜✐➸✉ ❧↕✐ ❜➔✐ t♦→♥ trỏ ỡ ởt tờ qt ữ s trữợ ❦❤ỉ♥❣ ❣✐❛♥ ❝♦♥ M ⊂ RN ✈ỵ✐ ❞✐♠ M < N − ❚❛ ♥â✐ r➡♥❣ q✉→ tr➻♥❤ ✤✉ê✐ ❜➢t ổ t ữỡ tr ợ z RN ✱ ①✉➜t ♣❤→t tø ✤✐➸♠ z0 ∈ / M s➩ ❦➳t t❤ó❝ s❛✉ t❤í✐ ❣✐❛♥ K ✱ ♥➳✉ ✈ỵ✐ ♠é✐ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ v(t) ❝õ❛ ♥❣÷í✐ ❝❤↕②✱ ♥❣÷í✐ ✤✉ê✐ ❝â t❤➸ ①➙② ❞ü♥❣ ✤÷đ❝ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ u(t) s❛♦ ❝❤♦ ♥❣❤✐➺♠ ❝õ❛ ❤➺ ✭✷✳✷✳✺✮ t❤ä❛ ♠➣♥ z(K) M õ q ữợ t❤ỉ♥❣ t✐♥ ♥❤÷ s❛✉✿ ❚↕✐ ♠é✐ t❤í✐ ✤✐➸♠ t, ✤➸ ①➙② ❞ü♥❣ ❞➣② ✤✐➲✉ ❦❤✐➸♥ u(t) ♥❣÷í✐ ✤✉ê✐ ✤÷đ❝ ❜✐➳t tr↕♥❣ t❤→✐ ❝õ❛ ❤➺ ✭♣❤÷ì♥❣ tr➻♥❤ ✭✷✳✷✳✺✮✮✱ ❝→❝ ❤↕♥ ❝❤➳ ✭✷✳✷✳✸✮ ✈➔ ✤➦❝ ❜✐➺t✱ ✤✐➲✉ ❦❤✐➸♥ v(t) ❝õ❛ ♥❣÷í✐ ❝❤↕②✳ ❳➨t ❜➔✐ t♦→♥ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ❞↕♥❣ z ∆ (t) = Az(t) − Bu(t) + Cv(t), t ≥ t0 (2.2.6) ◆❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ ✭✷✳✷✳✻✮ ✤÷đ❝ ♠æ t↔ ❜ð✐ ❝æ♥❣ t❤ù❝ s❛✉ t t z(t) = eA (t, t0 )z0 − eA (t, σ(τ ))Cv(τ )∆τ eA (t, σ(τ ))Bu(τ )∆τ + t0 t0 ❑➼ ❤✐➺✉ L ❧➔ ♣❤➛♥ ❜ị trü❝ ❣✐❛♦ ❝õ❛ ❦❤ỉ♥❣ ❣✐❛♥ ❝♦♥ M tr♦♥❣ Rn , tù❝ ❧➔ Rn = M ⊕ L✱ ❤❛② M + L = Rn ✈➔ M ∩ L = {0}✳ ❑❤✐ ➜② ✈ỵ✐ ♠é✐ z ∈ Rn tỗ t t z1 M z2 L s❛♦ ❝❤♦ z = z1 + z2 ❑➼ ❤✐➺✉ π ❧➔ ♣❤➨♣ ❝❤✐➳✉ trü❝ ❣✐❛♦ tø Rn ①✉è♥❣ L✳ ❑❤✐ ➜② ✤✐➲✉ ❦✐➺♥ ❦➳t t❤ó❝ z(K) ∈ M tữỡ ữỡ ợ z(K) = ỵ sû ❝→❝ ❣✐↔ t❤✐➳t s❛✉ ✤÷đ❝ t❤ä❛ ♠➣♥✿ ●✐↔ t❤✐➳t ỗ t t tỷ t t tử F (τ ) : Rq → Rp t❤ä❛ ♠➣♥ πeA (t, τ )BF (τ ) = πeA (t, τ )C ✈ỵ✐ ♠å✐ τ ≥ t0 , τ ∈ T, LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✺ tr♦♥❣ ✤â π ❧➔ ♣❤➨♣ ❝❤✐➳✉ trü❝ ❣✐❛♦ tø Rn ❧➯♥ L ●✐↔ t❤✐➳t ✷ ●✐↔ sû K ❧➔ sè ♥❤ä ♥❤➜t tr♦♥❣ sè ❝→❝ sè t❤ü❝ t ≥ t0 s❛♦ ❝❤♦ χ(K) ≤ ρ✱ tr♦♥❣ ✤â t χ (t) = F (τ )v(τ ) ∆τ sup t t0 v(τ ) ∆τ ≤σ t0 ●✐↔ t❤✐➳t ✸ πeA (K, t0 )z0 ∈ G(K)✱ tr♦♥❣ ✤â K G(K) := K w(τ ) ∆τ ≤ (ρ − χ(K))2 πeA (K, σ(τ ))Bw(τ )∆τ : t0 t0 ❑❤✐ ➜② trá ❝❤ì✐ ❦➳t t❤ó❝ s❛✉ t❤í✐ ❣✐❛♥ K ✳ ❈❤ù♥❣ ♠✐♥❤ ứ tt s r tỗ t ởt sè w(s) s❛♦ ❝❤♦ K πeA (K, σ(τ ))Bw(τ )∆τ, πeA (K, t0 )z0 = (2.2.7) t0 tr♦♥❣ ✤â K t0 w(τ ) ∆τ ≤ (ρ − χ(K))2 ●✐↔ sû v(τ ) ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ ❜➜t ❦➻ ❝õ❛ ♥❣÷í✐ ❝❤↕②✱ tù❝ ❧➔ K v(τ ) ∆τ ≤ σ t0 ❳➙② ❞ü♥❣ ✤✐➲✉ ❦❤✐➸♥ ❝õ❛ ♥❣÷í✐ ✤✉ê✐ ♥❤÷ s❛✉ u(τ ) = F (τ )v(τ ) + w(τ ), ≤ τ ≤ K ❚❤❡♦ ❜➜t ✤➥♥❣ t❤ù❝ ❈❛✉❝❤②✲❇✉♥❤✐❛❝♦♣①❦✐ t❛ ❝â K K u(τ ) ∆τ F (τ )v(τ ) + w(τ ) ∆τ = t0 t0 K ≤ K F (τ )v(τ ) t0 ∆τ w(τ ) ∆τ ≤ χ(K) + (ρ − χ(K)) = ρ + t0 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✻ ❈❤ù♥❣ tä u(τ ) ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝✳ ❚❤❡♦ ❝ỉ♥❣ t❤ù❝ ♥❣❤✐➺♠ ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ ✤ë♥❣ ❧ü❝ t❛ ❝â K πz(K) = π eA (K, t0 )z0 − eA (K, σ(τ ))Bu(τ )∆τ t0 K eA (K, σ(τ ))Cv(τ )∆τ + t0 K = πeA (K, t0 )z0 − πeA (K, σ(τ ))Bu(τ )∆τ t0 K + πeA (K, σ(τ ))Cv(τ )∆τ t0 K = πeA (K, t0 )z0 − πeA (K, σ(τ ))B(F (τ )v(τ ) + w(τ ))∆τ t0 K πeA (K, τ )Cv(τ )∆τ + t0 K = πeA (K, t0 )z0 − πeA (K, σ(τ ))BF (τ )v(τ )∆τ t0 K − K πeA (K, σ(τ ))Bw(τ )∆τ + t0 πeA (K, σ(τ ))Cv(τ )∆τ t0 ❚ø ●✐↔ t❤✐➳t ✶ ✈➔ ✭✷✳✷✳✼✮ t❛ s✉② r❛ K πz(K) = πeA (K, t0 )z0 − πeA (K, σ(τ ))Bw(τ )∆τ = t0 ◆❤÷ ✈➟②✱ t❛ ✤➣ ①➙② ❞ü♥❣ ✤÷đ❝ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ u(t) t❤❡♦ t❤ỉ♥❣ t✐♥ v(t) s❛♦ ❝❤♦ trá ❝❤ì✐ ❦➳t t❤ó❝ s❛✉ tớ K ỵ ữủ ự ♠✐♥❤✳ ◆❤➟♥ ①➨t ✷✳✷ ❚r♦♥❣ tr÷í♥❣ ❤đ♣ T = R ❝→❝ ❤➺ ✤ë♥❣ ❧ü❝ ✭✷✳✷✳✶✮✱ ✭✷✳✷✳✷✮ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ ✭✷✳✷✳✸✮ trð t❤➔♥❤ x(t) ˙ = A(t)x − B(t)u + C(t)v, t≥0 ✈ỵ✐ ❝→❝ ❤↕♥ ❝❤➳ +∞ +∞ 2 v(s) ds ≤ σ u(s) ds ≤ ρ , 0 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com õ ỵ s trữớ ủ t ỵ ❦❤✐ T = R ❍➺ q✉↔ ✶ ✭◆✐❦♦❧s❦✐✐✱ ①❡♠ ❬✶✶❪✮ ●✐↔ sû ❝→❝ ❣✐↔ t❤✐➳t s❛✉ ✤➙② ✤÷đ❝ t❤ä❛ ♠➣♥ tt ỗ t t tỷ t t ❧✐➯♥ tö❝ F (s) : Rq → Rp t❤ä❛ πesA BF (s) = πesA C ✈ỵ✐ ♠å✐ s ≥ 0, tr♦♥❣ ✤â π ❧➔ ♣❤➨♣ ❝❤✐➳✉ trü❝ ❣✐❛♦ tø Rn ❧➯♥ L ●✐↔ t❤✐➳t ✷ ❈❤♦ ❚ ❧➔ sè ♥❤ä ♥❤➜t tr♦♥❣ sè ❝→❝ sè t❤ü❝ t ≥ s❛♦ ❝❤♦ χ(T ) ≤ ρ ❚r♦♥❣ ✤â t χ (t) = F (s)v(s) ds sup t 0 v(s) ds≤σ ●✐↔ t❤✐➳t ✸ πeT Az0 ∈ G(T )✱ tr♦♥❣ ✤â T T A(T −s) G(T ) := πe w(s) ds ≤ (ρ − χ(T ))2 Bw(s)ds : 0 ❑❤✐ ➜② trá ❝❤ì✐ ❦➳t t❤ó❝ s❛✉ t❤í✐ ❣✐❛♥ T ✳ ◆❤➟♥ ①➨t ✷✳✸ tr÷í♥❣ ❤đ♣ T = Z ❝→❝ ❤➺ ✤ë♥❣ ❧ü❝ ✭✷✳✷✳✷✮ ✈ỵ✐ ❤↕♥ ❝❤➳ ♥➠♥❣ ❧÷đ♥❣ ✭✷✳✷✳✸✮ trð t❤➔♥❤ z(k + 1) = A(k)z(k) − B(k)u(k) + C(k)v(k), k = 0, 1, ợ ữủ u(i) i=0 2 ≤ρ , v(i) ≤ σ2 (2.2.8) i=0 ❍➺ q✉↔ s❛✉ ✤➙② ❧➔ tr÷í♥❣ ❤đ♣ ✤➦❝ ❜✐➺t ❝õ❛ ỵ T = Z q ✭◆✳ ❨✉✳ ❙❛t✐♠♦✈✱ ①❡♠❬✶✵❪✮ ●✐↔ sû K ❧➔ sè ♥❤ä ♥❤➜t tr♦♥❣ sè ❝→❝ sè tü ♥❤✐➯♥ k1 s❛♦ ❝❤♦ ❝→❝ ❣✐↔ t❤✐➳t s❛✉ ✤➙② ✤÷đ❝ t❤ä❛ ♠➣♥ ●✐↔ t❤✐➳t ỗ t tr F (k) p × q t❤ä❛ ♠➣♥ πAK−1−k BF (k) = πAK−1−k C, ∀k = 0, 1, , K − 1, LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✽ tr♦♥❣ ✤â π ❧➔ ♣❤➨♣ ❝❤✐➳✉ trü❝ ❣✐❛♦ tø Rn ❧➯♥ L ●✐↔ t❤✐➳t ✷ χ(T ) ≤ ρ✱ tr♦♥❣ ✤â K−1 χ (t) = F (k)v(k) sup K−1 v(i) ≤σ k=0 i=0 ●✐↔ t❤✐➳t ✸ πeT Az0 ∈ G(K)✱ tr♦♥❣ ✤â K−1 K K−1−i πA G(K) = p Bw(k) : w(k) ∈ R , k=0 w(k) ≤ (ρ − χ(T ))2 k=0 ❑❤✐ ➜② trá ỡ t tú s K ữợ rỏ ỡ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ t❤ỉ♥❣ t✐♥ ❝❤➟♠ ✈➔ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ❳➨t ❜➔✐ t♦→♥ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ❞↕♥❣ z ∆ (t) = Az(t) − Bu(t) + Cv(t), t ≥ t0 ; t, t0 ∈ T, z(t0 ) = z0 (2.3.1) Ð ✤➙② z ∈ Rn , ❝→❝ ❤➔♠ u(.), u : T → Rp ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝õ❛ ♥❣÷í✐ ✤✉ê✐✱ ✈➔ v(.), v : T → Rq ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝õ❛ ♥❣÷í✐ ❝❤↕②✳ ❈→❝ ♠❛ tr➟♥ A, B ✈➔ C ❝â sè tữỡ ự n ì n, n ì p ✈➔ n × q ❈→❝ ✤✐➲✉ ❦❤✐➸♥ t❤ä❛ ♠➣♥ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ s❛✉ T T u(s) ∆s ≤ ρ2 ; t0 v(s) ∆s ≤ σ (2.3.2) t0 ❈→❝ ❤➔♠ ❦❤↔ t➼❝❤ u(.) ✈➔ v(.) t❤ä❛ ♠➣♥ ✭✷✳✸✳✷✮ ✤÷đ❝ ❣å✐ ❧➔ ❝→❝ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ữủ r trữợ t t ự ♠✐♥❤ ✤à♥❤ ❧➼ ✈➲ ✤✐➲✉ ❦✐➺♥ ✤õ ❦➳t t❤ó❝ trá ❝❤ì✐ tr♦♥❣ tr÷í♥❣ ❤đ♣ ❣✐↔ t❤✐➳t t❤ỉ♥❣ t✐♥ ❧➔✿ ◆❣÷í✐ ✤✉ê✐ ①➙② ❞ü♥❣ t❤æ♥❣ t✐♥ u (t) = u (v (t)) tự t ộ ữợ t ỹ ❝❤✐➳♥ ❧÷đ❝ ❝õ❛ ♠➻♥❤✱ ♥❣÷í✐ ✤✉ê✐ ✤÷đ❝ ❜✐➳t t❤ỉ♥❣ t✐♥ ✈➲ ✤✐➲✉ ❦❤✐➸♥ v(t) ❝õ❛ ♥❣÷í✐ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✸✾ ❝❤↕②✳ ❚✉② ♥❤✐➯♥✱ tr♦♥❣ t❤ü❝ t➳ t❤ỉ♥❣ t✐♥ ♠➔ ♥❣÷í✐ ✤✉ê✐ t❤÷í♥❣ ❜à ❝❤➟♠ ❜ð✐ ♠ët ❦❤♦↔♥❣ t❤í✐ ❣✐❛♥ ♥➔♦ ✤â✳ ❱➻ ✈➟②✱ tr♦♥❣ ♠ư❝ ♥➔② t❛ s➩ ♣❤→t ❜✐➸✉ ✤✐➲✉ ❦✐➺♥ ❦➳t t❤ó❝ trá ❝❤ì✐ ✈ỵ✐ t❤ỉ♥❣ t✐♥ ❝❤➟♠✳ ✣➸ ①➙② ❞ü♥❣ t❤ỉ♥❣ t✐♥ t ữ tt s sỷ tỗ t↕✐ ♠ët sè ν ∈ T, ν ≥ ✈➔ ♠ët ❤➔♠ r : Tν → T ❦❤æ♥❣ ❣✐↔♠✱ ❞❡❧t❛✲❦❤↔ ✈✐ tr➯♥ T t❤ä❛ ♠➣♥ ❝→❝ t➼♥❤ ❝❤➜t s❛✉ r(t) ≤ t ✈ỵ✐ ♠å✐ t ∈ Tν , tr♦♥❣ ✤â Tν := T ∩ [ν, +∞) ✣➸ ①➙② ❞ü♥❣ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ u(.), ♥❣÷í✐ ✤✉ê✐ ✤÷đ❝ ❜✐➳t t❤ỉ♥❣ t✐♥ ✈➲ ❤➺ ✭✷✳✸✳✶✮✱ t➟♣ ❦➳t t❤ó❝ trá ❝❤ì✐ M, ✈➔ ✤➦❝ ❜✐➺t✱ ♥❣÷í✐ ✤✉ê✐ ✤÷đ❝ ❜✐➳t t❤ỉ♥❣ t✐♥ ✈➲ ✤✐➲✉ ❦❤✐➸♥ ❝õ❛ ♥❣÷í✐ ❝❤↕② t↕✐ t❤í✐ ✤✐➸♠ r(t), tù❝ ❧➔ u(t) = u (v(r(t))) ●✐↔ sû u∗ (t) ❧➔ ♠ët ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ ♥➔♦ ✤â ❝õ❛ ♥❣÷í✐ ✤✉ê✐✱ tù❝ ❧➔ T u (s) ∆s ≤ ρ , ❑➼ ❤✐➺✉ ρ := ρ − ∗ 2 t0 T u∗ (s) ∆s t0 π ❧➔ ♣❤➨♣ ❝❤✐➳✉ trü❝ ❣✐❛♦ tø R ①✉è♥❣ ❦❤æ♥❣ ❣✐❛♥ ✈✉ỉ♥❣ ❣â❝ ✈ỵ✐ M, M = M1 + M2 ⊆ RN , tr♦♥❣ ✤â M1 ⊂ RN ⊆ RN , M2 ⊆ RN ✱ RN ❧➔ ❝→❝ ❦❤æ♥❣ n ❣✐❛♥ ❝♦♥ ❝õ❛ RN ✈➔ RN = RN ⊕ RN ❑❤✐ ✤â✱ ✤✐➲✉ ❦✐➺♥ ❦➳t t❤ó❝ trá ❝❤ì✐ s➩ ❧➔ z(K) ∈ M t÷ì♥❣ ữỡ ợ z(K) M2 tr ❦✐➺♥ ❦➳t t❤ó❝ trá ❝❤ì✐ t❛ ✤÷❛ ✈➔♦ ❦❤→✐ ♥✐➺♠ ❤✐➺✉ ❤➻♥❤ ❤å❝ P♦♥t✐❛❣✐♥ ♥❤÷ s❛✉ A∗B := {z ∈ Rn , z + B A} ỵ ●✐↔ sû K ∈ T ❧➔ sè ♥❤ä ♥❤➜t s❛♦ ❝❤♦ ❝→❝ ❣✐↔ t❤✐➳t s❛✉ ✤➙② ✤÷đ❝ t❤ä❛ ♠➣♥✳ ●✐↔ tt ỗ t ởt tr r tử F (t) : Rq → Rp s❛♦ ❝❤♦ πeA (K, σ(t))BF (t) = πeA (K, σ (r(t))) C ✈ỵ✐ ♠å✐ t ∈ T, t ≥ υ (2.3.3) ●✐↔ t❤✐➳t ✷ K χ2 (K) = sup K F (t)v(r(t))r∆ (t) ∆t ≤ ρ2 (2.3.4) v(s) ∆s≤σ υ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✵ ●✐↔ t❤✐➳t ✸ υ πeA (K, σ(s))Bu∗ (s)∆s ∈ G(K) + (M2 ∗H(K)) , (2.3.5) πeA (K, 0)z0 − tr♦♥❣ ✤â K K G(K) = w(s) ∆τ ≤ (ρ − χ(K))2 , πeA (K, σ(s))Bw(s)∆s : ν ν r(ν) πeA (K, σ(s))Cv(s)∆s H(K) = K K πeA (K, σ(s))Cv(s)∆s : + r(K) v(s) ≤ θ2 ❑❤✐ ➜② trá ❝❤ì✐ ✤✉ê✐ ❜➢t ✭✷✳✸✳✶✮✲✭✷✳✸✳✷✮ ❦➳t t❤ó❝ s❛✉ tớ K ự tỗ t ởt ✈❡❝tì m ∈ M2∗H(K) ✈➔ ♠ët ❤➔♠ K ❦❤↔ t➼❝❤ w(s) tr➯♥ [υ, K] ∩ T ✈ỵ✐ w(s) ∆s ≤ (ρ − χ(K))2 s❛♦ ❝❤♦ υ υ K πeA (K, σ(s))Bu∗ (s)∆s = πeA (K, 0)z0 − πeA (K, σ(s))Bw(s)∆s + m υ ❱➻ m ∈ M2 ∗H(K) ♥➯♥ m + H(K) ⊆ M2 ●✐↔ sû v(.) ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ ❜➜t ❦➻ ❝õ❛ ♥❣÷í✐ ✤✉ê✐✱ ❦❤✐ ➜② K r(ν) πeA (K, σ(s))Cv(s)∆s ∈ H(K) eA (K, (s))Cv(s)s + r(K) õ tỗ t ♠ët ✈❡❝tì m2 ∈ M2 s❛♦ ❝❤♦ r(ν) m+ K πeA (K, σ(s))Cv(s)∆s + πeA (K, σ(s))Cv(s)∆s = m2 r(K) ❈❤ù♥❣ tä υ πeA (K, 0)z0 − πeA (K, σ(s))Bu∗ (s)∆s = r(ν) K πeA (K, σ(s))Cv(s)∆s − πeA (K, σ(s))Bw(s)∆s + m2 υ − K πeA (K, σ(s))Cv(s)∆s (2.3.6) r(K) LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✶ ❱ỵ✐ v(.) ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ ❜➜t ❦➻ ❝õ❛ ♥❣÷í✐ ❝❤↕②✱ t❛ ①➙② ❞ü♥❣ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ ❝õ❛ ♥❣÷í✐ ✤✉ê✐ ♥❤÷ s❛✉  u∗ (t) ♥➳✉ t ∈ [0; υ]T ; u(t) := F (t)v(r(t))r∆ (t) + w(t) ♥➳✉ t ∈ [υ; K] T ❑❤✐ ➜② t❤❡♦ ❜➜t ✤➥♥❣ t❤ù❝ ▼✐♥❦♦✈s❦✐ t❛ ❝â K K F (t)v(r(t))r∆ (t) + w(t) ∆s u(s) ∆s = υ υ K K F (t)v(r(t))r∆ (t) ∆s + ≤ w(t) ∆s υ υ ≤ (ρ − χ(K)) + χ(K) = ρ ❱➟② K υ u(s) ∆s = u(s) ∆s u(s) ∆s + 0 υ K υ u∗ (s) ∆s + = K F (t)v(r(t))r∆ (t) + w(t) ∆s υ υ u∗ (s) ∆s + ρ2 = ρ2 − ρ2 + ρ2 = ρ2 ≤ ❈❤ù♥❣ tä u(.) ❧➔ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝✳ ❚❤❡♦ ❝ỉ♥❣ t❤ù❝ ♥❣❤✐➺♠ ❝õ❛ ❤➺ ✤ë♥❣ ❧ü❝ K πz(K) = πeA (K, 0)z0 − πeA (K, σ(τ ))Bu(τ )∆τ K + πeA (K, σ(τ ))Cv(τ )∆τ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✷ υ πeA (t, σ(τ ))Bu∗ (τ )∆τ = πeA (K, 0)z0 − K πeA (K, σ(τ ))B[F (τ )v(r(τ ))r∆ (τ ) + w(τ )]∆τ − ν K πeA (K, σ(τ ))Cv(τ )∆τ + (2.3.7) ❙û ❞ö♥❣ ●✐↔ t❤✐➳t ✶ πeA (K, σ(t))BF (t) = πeA (K, σ (r(t))) C ❚❛ ❝â K πeA (K, σ(τ ))B[F (τ )v(r(τ ))r∆ (τ ) + w(τ )]∆τ ν K K ∆ = πeA (K, σ(τ ))BF (τ )v(r(τ ))r (τ )∆τ + πeA (K, σ(τ ))Bw(τ )∆τ ν ν K πeA (K, σ(r(τ )))Cv(r(τ ))r∆ (τ )∆τ = ν K + πeA (K, σ(τ ))Bw(τ )∆τ (2.3.8) ν ❚❤ü❝ ❤✐➺♥ ♣❤➨♣ ✤ê✐ ❜✐➳♥ ϑ := r(τ ) t❛ ❝â ∆ϑ = r∆ (τ )∆τ t❛ ✤✐ ✤➳♥ r(K) K πeA (K, σ(r(τ )))Cv (r (τ )) r∆ (τ )∆τ = υ πeA (K, σ(ϑ))Cv (ϑ) ∆ϑ r(υ) ❚❤❛② ✈➔♦ ✭✷✳✸✳✽✮ t❛ ✤÷đ❝ K K πeA (K, σ(r(τ )))Cv (r (τ )) r∆ (τ )∆τ + = υ υ r(K) = K πeA (K, σ(ϑ))Cv (ϑ) ∆ϑ + r(υ) πeA (K, σ(τ ))Bw(τ )∆τ πeA (K, σ(τ ))Bw(τ )∆τ υ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✸ ❚❤❛② ✈➔♦ ✭✷✳✸✳✼✮ t❛ ✤÷đ❝ K πz(K) = πeA (K, 0)z0 − πeA (K, σ(τ ))Bu(τ )∆τ K πeA (K, σ(τ ))Cv(τ )∆τ + ν πeA (K, σ(τ ))Bu∗ (τ )∆τ = πeA (K, 0)z0 − r(K) − πeA (K, σ(ϑ))Cv(ϑ)∆ϑ r(ν) K − r(ν) πeA (K, σ(τ ))Bw(τ )∆τ + ν πeA (K, σ(τ ))Cv(τ )∆τ r(K) + K πeA (K, σ(τ ))Cv(τ )∆τ + r(ν) πeA (K, σ(τ ))Cv(τ )∆τ r(K) ν πeA (K, σ(τ ))Bu∗ (τ )∆τ = πeA (K, 0)z0 − K − πeA (K, σ(τ ))Bw(τ )∆τ ν K r(ν) πeA (K, σ(τ ))Cv(τ )∆τ πeA (K, σ(τ ))Cv(τ )∆τ + + r(K) ❙û ❞ö♥❣ ✭✷✳✸✳✻✮ t❛ ✤✐ ✤➳♥ ν πeA (K, σ(τ ))Bu∗ (τ )∆τ πz(K) = πeA (K, 0)z0 − K − πeA (K, σ(τ ))Bw(τ )∆τ ν r(ν) + K πeA (K, σ(τ ))Cv(τ )∆τ + πeA (K, σ(τ ))Cv(τ )∆τ r(K) = m2 ❱➟② πz(K) = m2 ∈ M2 ❤❛② trá ❝❤ì✐ ❦➳t t❤ó❝ s❛✉ tớ K ỵ ữủ ự t r(t) t t ỵ ỵ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❑➳t ❧✉➟♥ ▲✉➟♥ ✈➠♥ ✤➣ tr➻♥❤ ❜➔② ♠ët sè ✤à♥❤ ♥❣❤➽❛ ✈➔ ❝→❝ ❦❤→✐ ♥✐➺♠✱ t➼♥❤ ❝❤➜t ❝ì ❜↔♥ ✈➲ ❣✐↔✐ t➼❝❤ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✭❈❤÷ì♥❣ ✶✮✱ ❇➔✐ t♦→♥ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥✱ ❜➔✐ t♦→♥ trá ❝❤ì✐ ✤✉ê✐ ❜➢t ✈ỵ✐ t❤æ♥❣ t✐♥ ❝❤➟♠ ✈➔ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ tr♦♥❣ ❈❤÷ì♥❣ ✷✳ ❚r♦♥❣ ❧✉➟♥ ✈➠♥ ♥➔② t→❝ ❣✐↔ ✤➣ ♣❤→t ❜✐➸✉ ✈➔ ❝❤ù♥❣ ♠✐♥❤ ✤✐➲✉ ❦✐➺♥ ❦➳t t❤ó❝ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈ỵ✐ ❤↕♥ ❝❤➳ t➼❝❤ ♣❤➙♥✳ ❈❤♦ ♣❤➨♣ ❤đ♣ ♥❤➜t ♠ët sè ❦➳t q✉↔ ✤➣ ❜✐➳t tr♦♥❣ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ ♠ỉ t↔ ❜ð✐ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ ữỡ tr s ợ r t ✳ ✹✹ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ❚✐➳♥❣ ❱✐➺t ❬✶❪ P❤❛♥ ❍✉② ❑❤↔✐ ởt số t ỵ tt trỏ ỡ ✈✐ ♣❤➙♥ ✈➔ s❛✐ ♣❤➙♥✱ ●✐→♦ tr➻♥❤ ❈❛♦ ❤å❝✱ ❱✐➺♥ ❚♦→♥ ❤å❝✳ ❬✷❪ ❱✐ ❉✐➺✉ ▼✐♥❤ ✭✷✵✶✼✮✱ ❱➲ trá ❝❤ì✐ ✤✉ê✐ ❜➢t t✉②➳♥ t➼♥❤ tr➯♥ t❤❛♥❣ t❤í✐ ❣✐❛♥✱ tr❛♥❣ ✶✲✻✳ ❬✸❪ ❱✐ ❉✐➺✉ ▼✐♥❤✱ ▲➯ ❚❤à ❚❤ó② ◆❣➔✱ ▲➯ ❱➠♥ ỵ trỏ ỡ t t t tr t❤❛♥❣ t❤í✐ ❣✐❛♥ ✈ỵ✐ t❤ỉ♥❣ t✐♥ ❝❤➟♠✱ ❇→♦ ❝→♦ t↕✐ ❤ë✐ ♥❣❤à t♦→♥ ❤å❝ ♠✐➲♥ ❚r✉♥❣✲❚➙② ◆❣✉②➯♥✱ t❤→♥❣ ✶✷✲✷✵✶✼✭✤➣ ❣û✐ t♦➔♥ ✈➠♥✮✳ ❚✐➳♥❣ ❆♥❤ ❬✹❪ ❘❛✈✐ ❆❣❛r✇❛❧✱ ▼❛rt✐♥ ❇♦❤♥❡r✱ ❉♦♥❛❧ ♦✬❘❡❣❛♥ ❆❧❧❛♥ P❡t❡rs♦♥ ✭✷✵✵✷✮✱ ✏❉②♥❛♠✐❝ ❡q✉❛t✐♦♥s ♦♥ t✐♠❡ s❝❛❧❡s✿ ❛ s✉r✈❡②✑✱ ❏♦✉r♥❛❧ ♦❢ ❈♦♠♣✉t❛✲ t✐♦♥❛❧ ❛♥❞ ❆♣♣❧✐❡❞ ▼❛t❤❡♠❛t✐❝s✱ ✶✹✶ ✭✶✲✷✮✱ ♣♣✳ ✶✲✷✻✳ ❬✺❪ ▼✳ ❇♦❤♥❡r ❛♥❞ ❆✳ P❡t❡rs♦♥ ✭✷✵✵✶✮✱ ❉②♥❛♠✐❝ ❊q✉❛t✐♦♥s ♦♥ ❚✐♠❡ ❙❝❛❧❡s✿ ❆♥ ■♥tr♦❞✉❝t✐♦♥ ✇✐t❤ ❆♣♣❧✐❝❛t✐♦♥s✱ ❇✐r❦❤☎❛✉s❡r✱ ❇♦st♦♥✳ ❬✻❪ ▼✳ ❇♦❤♥❡r ❛♥❞ ❆✳ P❡t❡rs♦♥ ✭✷✵✵✸✮✱ ❆❞✈❛♥❝❡s ✐♥ ❉②♥❛♠✐❝ ❊q✉❛t✐♦♥s ♦♥ ❚✐♠❡ ❙❝❛❧❡s✱ ❇✐r❦❤☎❛✉s❡r✱ ❇♦st♦♥✳ ❬✼❪ ❍✐❧❣❡r ✭✶✾✽✽✮✱ ❊✐♥ ▼❛ß❦❡tt❡♥❦❛❧❦☎ ✉❧ ♠✐t ❛♥✇❡♥❞✉♥❣ ❛✉❢ ❩❡♥tr✉♠s♠❛♥♥✐♥❣✲❢❛❧t✐❦❡✐t❡♥✱ P❤✳❉✳ ❚❤❡s✐s✱ ❯♥✐✈❡rs✐t☎❛t ❲☎ ✉r③❜✉r❣✳ ✹✺ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ✹✻ ❬✽❪ ❏✳ ❏✳ ❉❛❈✉♥❤❛ ✭✷✵✵✹✮✱ ▲②❛♣✉♥♦✈ ❙t❛❜✐❧✐t② ❛♥❞ ❋❧♦q✉❡t ❚❤❡♦r② ❢♦r ◆♦❛✉t♦♥♦♠♦✉s ▲✐♥❡❛r ❉②♥❛♠✐❝ ❙②st❡♠s ♦♥ ❚✐♠❡ ❙❝❛❧❡s✱ P❤✳ ❉✳ ❚❤❡✲ s✐s✱ ❇❛②❧♦r ❯♥✐✈❡rs✐t②✳ ❬✾❪ ❇✳ ❏✳ ❏❛❝s♦♥ ✭✷✵✵✼✮✱ ❆ ●❡♥❡r❛❧ ▲✐♥❡❛r ❙②st❡♠s ❚❤❡♦r② ♦♥ ❚✐♠❡ ❙❝❛❧❡s✿ ❚r❛♥s❢♦r♠s✱ ❙t❛❜✐❧✐t②✱ ❛♥❞ ❈♦♥tr♦❧✱ P❤✳ ❉✳ ❚❤❡s✐s✱ ❇❛②❧♦r ❯♥✐✈❡rs✐t②✳ ❬✶✵❪ P❤❛♥ ❍✉② ❑❤❛✐ ✭✶✾✽✸✮✱ ❖♥ t❤❡ P✉rs✉✐t Pr♦❝❡ss ✐♥ ❉✐❢❢❡r❡♥t✐❛❧ ●❛♠❡s✱ ✽ ❆❝t❛ ▼❛t❤❡♠❛t✐❝❛ ❱✐❡t♥❛♠✐❝❛✱ ✭✶✮✱ ♣♣✳ ✹✶✲✺✼✳ ❬✶✶❪ P❤❛♥ ❍✉② ❑❤❛✐ ✭✶✾✽✺✮✱ ❖♥ ❛♥ ❊❢❢❡❝t✐✈❡ ▼❡t❤♦❞ ♦❢ P✉rs✉✐t ✐♥ ▲✐♥❡❛r ❉✐s❝r❡t❡ ●❛♠❡s ✇✐t❤ ❉✐❢❢❡r❡♥t ❚②♣❡s ♦❢ ❈♦♥str❛✐♥ts ♦♥ ❈♦♥tr♦❧s✱ ❆❝t❛ ▼❛t❤❡♠❛t✐❝❛ ❱✐❡t♥❛♠✐❝❛✱ ✶✵✭✷✮✱ ♣♣✳ ✷✽✷✲✷✾✺✳ LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ... TRƯỜNG ĐẠI HỌC KHOA HỌC  - LÊ VĂN QUÝ BÀI TOÁN ĐUỔI BẮT TRONG TRỊ CHƠI TUYẾN TÍNH VỚI HẠN CHẾ TÍCH PHÂN TRÊN THANG THỜI GIAN LUẬN VĂN THẠC SĨ TỐN HỌC Chun ngành: Tốn ứng dụng Mã số... (k(a + b); k(a + b) + a) ✤➲✉ ❧➔ ✤✐➸♠ trò ♠➟t✳ ✰✮ ◆➳✉ t = k(a + b) t❤➻ σ(t) = t, ρ(t) = t − b, ✈➔ µ (t) = ❉➝♥ ✤➳♥ σ(t) = t, ρ(t) < t ♥➯♥ t = k(a + b) ❧➔ ✤✐➸♠ trò t ỗ tớ ổ tr ◆➳✉ t = k(a + b)... sè f : T → R ✤÷đ❝ ❣å✐ ❧➔ ❝❤➼♥❤ q✉② rt ợ õ tỗ t ỳ ❤↕♥✮ t↕✐ ♠å✐ ✤✐➸♠ trò ♠➟t ♣❤↔✐ tr♦♥❣ T ✈➔ ợ tr õ tỗ t ỳ t ♠å✐ ✤✐➸♠ trò ♠➟t tr→✐ ❝õ❛ T✳ ✣à♥❤ ♥❣❤➽❛ ✶✳✶✶ ❍➔♠ f : T → R ✤÷đ❝ ❣å✐ ❧➔ r❞✲❧✐➯♥

Ngày đăng: 19/12/2022, 18:24

TÀI LIỆU CÙNG NGƯỜI DÙNG

TÀI LIỆU LIÊN QUAN