Mvc Ivc

1 f>ieu khi€!n toi U'Utinh 11

1.1 Nh~p moo 111.1.1 The nEIOla bai toim dieu khien toi Lfutinh? 11

1.1.2 Phan lo~ibai toim toi Lfu 15Bai toim toi Lfutuyen tinh/phi tuyen 15Bai loan can toi Lfu(suboptimal) 16Bai loan toi Lfuco rang bUl?c/khongrang buc;Jc 18Nghiem toi Lfudia phLfong/toancuc 18

1.1.3 Gong c\1loan hoc: Tap lei va ham loi 19

1.2 Nhii'ngbili loan toi uu di€!nhinh 231.2.1 Bai loan toi Lfuloi 23

1.2.2 Bailoan toiLfuloan phLfong , 251.2.3 Bai loan toi Lfuhyperbol 27

1.3 Tim nghi~m biing phudng phap Iy thuyet 291.3.1 Moiquan he giiia bai loan toi Lfuva bai loan diem yen ngl,la 29

1.3.2 PhLfongphap Kuhn-Tucker 31

1.3.3 PhLfongphap Lagrange 34

1.4 Tim nghi~m biing phudng phap so 361.4.1 Bai loan toi Lfutuyen tinh va phLfongphap don hinh (simplex) 36

1.4.2 PhLfongphap tuyen tinh hoa Wng do~n 40

1.4.3 PhLfongphap Newton-Raphson 41

1.5 Tim nghi~m biing phudng phap huang den clfc tr! 44

1.5.1 Nguyen Iy chung 44

1.5.2 Xac dinh bLfCCtim toi Lfu 46

Xac dinh btJng phLfong phap giai tich 46

Xac dinh btJng phLfong phap so 47Thuat toarl nhat ci'\tvang """"""""""""""""""""""""""""""'" 47

1.5.3 PhLfongphap Gauss-Seidel 49

1.5.4 PhLfongphap gradient 51

1.5.5 Kythu$t ham ph~t va ham ch~n 53Kythu$t ham ph~t 53Kythuat ham chao 56

1.6 Mi?tso vi dy ung dyng 571.6.1 Xac dinh tham so toi Lfucho bc;Jdieu khien PID 57

1.6.2 Nh$n d~ng tham so mo hlnh doi tLfQnglien d!nh 60Nhan d~ng tham so mo hinh khong lien t(,Jc 60Nh$n d~ng tham so mohinhlient(,Jc 62

1.6.3 Ung dl;mgVaGdieu khien ben vCtngtrang kh6ng gian tri?ngthai " 63Phat bieu bai toan ,.. 63

Phlidng phap Roppenecker 65Phlidng phap Konigorski 68

1.6.4 Ung dl,mg VaGdieu khien thiGh nghi 73Muc dich cua dieu khien thiGh nghi 73Vai tra cua dieu khien toi U'UtTnhtrong dieu khien thiGh nghi 77

Cau hoi on t~p va bai t~p 78

2 Bieu khi':;ntoi U'udQng 81

2.1 Nh~pmon 812.1.1 The naG 103bar loan dieu khien toi U'Ud(mg? ;; 81

Bai loan toi U'Ud(mg lien tyc 81Bai loan dieu khien toi U'Ukh6ng lien tyc 83

2.1.2 Phan loi?i bar loan toi liu d(mg 84

2.2 Phltdng phap bien phan 86

2.2.1 Ham Hamilton, phlidng trinh Euler-Lagrange va dieu ki$n can " 86

2.2.2 Phlidng trinh vi phan Riccati va b6 dieu khien toi U'Ukh6ng dung cho doitlidng tuyen tinh (trlidng h<;Jpthdi gran hCtuhc:ln) : 91

Phat bieu bar loan va tim nghi$m nhd phlidng phap bien phan " 91Tim nghiem toi liu W phlidng trinh vi phan Riccati " 93Thiet ke b6 dieu khien toi U'U,phan hoi tri?ng thai, kh6ng dUng 95

2.2.3 Phlidng trinh d<?iso Riccati va b9 dieu khien toi U'UtTnh, phan hoi tr<?ngthaicho doi tlidng tuyen tinh (trlidng h<;Jpthdi gran v6 h<?n)- B6 dieu khien LOR 97

Phat bieu bar toan , 97

Ldi giai cua bar loan -B6 dieu khien toi U'ULOR phan hoi dlidng " 97B9 dieu khien toi U'ULOR phan hoi am 100

2.2.4 M9t so ket lu$n bo sung, rut ra dU'clcW phvdng phap bien phan " 101Phvdng trinh xac dinh tin hi$u dieu khien toi Vu 102Ban them ve ham Hamilton 103

2.3 Nguyen Iy cl!c d':li2.3.1 Dieu khien doi tvdng nlJa tuyen tinh, da breI trudc diem trang thai dau va

khoang thdi gran xay ra qua trinh tai U'U 104

2.3.2 Dieu khien toi U'Ulac d9ng nhanh doi tu<;Jngtuyen tinh 107Nguyen Iy clfc dai 107Xay dlfng quy d?o trang thai toi U'U 111DinhIyFeldbaumvesolan chuyendolgiatr!vaynghTaltngdyng , 117

2.3.3 Nguyen Iy clfc dai d?ng tong quat: Dieu ki$n can, dieu ki$n hoanh " 121Dieu kien can 122

Dieu ki$n hoanh (dieu kien trUcgiao) 124Bai loan toi U'Uco khoang thdi gran co d!nh va cho trlidc 129Bai loan toi Vuco doi tvdng kh6ng autonom 130

2.3.4 Ve y nghTavector bien dong tr?ng thai 131

103

2.4 Phltdng phap quy ho~ch dQng(Bellman) 1362.4.1 N1;>idung phLtcmgphap 137

Nguyen Iytoi Ltucua Bellman 137Hai vang tfnh cua phLtongphap: Vang ngLt9c(I<ythu$t nhung) va vang xuei 138

2.4.2 Mdr1;>ngcho trLtdngh9Pham ml,Jctieu khengd d?ng tong 1422.4.3 Md r1;>ngcho trLtdngh9P die;mcuoi kheng co dinh 1452.4.4 Md r1;>ngcho h~ lien tl,Jcva phLtongtrlnh Hamilton-jacobi-Bellman 146

Cilu hoi on t~p va ba; t~p 150

3 Dieu khi~n toi LtUng~u nhiim 153

3.1 MQtso khiii n;~m nh~p mon 1533.1.1 Qua trinh ngau nhien 153

f>inhnghia va me ta chung 153Quatrinhngau nhiendCtng " 155Qua trinh ngau nhien egodic 156Ham m$t d1;>pho va anh Laplace cua qua trlnh ngau nhien egodic 156

3.1.2 H~ ngau nhiim va me hinh toan h9Ctrong mien phuc 157Phep bien doi Fourier 157Xac d!nh me hlnh ham truyen d?t 158

3.1.3 Bai toan dieu khie;ntoi Ltungau nhien 159

3.2 £)ieukhi~n toi ltUng~u nhien tinh 1613.2.1 Nh$nd?ng tn!c tuyen tham so me hlnh kheng lien tl,Jc 161

3.2.2 Nh$nd?ngtn!c tuyen (on-line)me hlnhtuyentfnhlientl,Jc 163Nh$n d?ng tn!c tuyen me hlnh kheng tham so 163Nh$n d?ng tn!ctuyenthamso me hinhdoitLt9ngkhengco thanh phanviphiln 166Nh$n d?ng tn!c tuyen tham so me hlnh doi tLt9ngkheng co thanh phan tfchphiln 167

3.3 £)ieu khiii'n to; ltu ng~u nhien dQng 168

3.3.1 B1;>locWiener 168Ml,Jcdfch cua be 19C , 168Cac bLtdCthiet ke 169

3.3.2 B1;>quan satjrang thai Kalman (19c Kalman) 172Ml,Jcdich cua b1;>quansat 172Thiet ke b1;>quan sat tr?ng thai cho doi tLt9ngtuyen tfnh 174

3.3.3 B1;>dieu khie;n LQG (Linear Quadratic Gaussian) 177N1;>idung b1;>dieu khie;n LQG 177Nguyen Iy tach (separation principle) 180

Cilu hoi on t~p va bai t~p 182

4 Dieu khi~n toi LtURHoo(Dieu khi~n ben vli'ng) 183

4.1 Khong gian chufln Hardy 183

4.1.1 Kheng gian chu&n L2va H2(RH2) 183

Khenggran L2 183

Kheng gian H2va RH2""""""""""""""""""'"""""""""""""""""""""""""", 184Me,r(>ngcho ma tr~n ham phCtc(h$ MIMO) 186Cach tfnh chuan b~c hai 186

4.1.2 Kheng gran chuan H=va RH= 188

Khaini$mkhenggian H=va RH= 188Tfnhchuanve clAng 189

4.2 Tham so h6a be?dh!u khi~n 1924.2.1 He c6 cac khauSISO 192

Truong ht;)pdai tut;)ng113on d!nh 192Truong ht;)pdai tut;)ngkheng on d!nh 194Thu~t loan tlm nghi$m phuong trinh Bezout , 196Tong ket: Thu~t loan xac d!nh t~p cac b9 dieu khien on d!nh 202

4.2.2 H$ c6 cac khau ..MIMO 204Khaini$mhai ma tr~n nguyento clAngnhau 204Phantfch ma tr~ntruyend?t thanh ~p cac ma tr~n nguyento cung nhau 206Xac d!nh t~pcac b9 dieu khienlamon d!nhh$ thong 209Thu~t loan tim nghi$mh$ phuongtrinh Bezout 211Tong ket: Thu~t loan tham so h6a b9 dieu khienon d!nh 215

4.2.3 Llngdungtrangdieu khienon dinhn9i 217Khai ni$m on d!nh n9i 217Tinh ond!nhn9idut;)c(internalstabilizable) 219B9 dieu khien on d!nh n9i 222

4.3 E>ieukhi~n toi lIU RH~ 223

4.3.1 Nhiing bar loan dieu khien RH= dien hinh , 223

Bai toan can b~ng me hlnh 223Bai toan cuc lieu d9 nhay voi sai lech me hinh 224

Bai loan tai L1URH= mau (standard) 225Bai loan on d!nh ben viing voi sai I$ch me hinh 229

4.3.2 Trinh tuthljc hi$n bar loan tai L1URH= 231

Buoc 1: Chuyen thanh bar loan can b~ng me hinh """""""""""""""""""""""""" 231Buoc 2: Tim nghi$m bar loan can b~ng me hinh I '231

4.3.3 Kha nang ton t?i nghi$m cua bar loan can b~ng me hinh 231

4.3.4 Phuong phap 1: Tim nghi$m bar loan can b~ng me hlnh nho loan ti'JHankelva dinh Iy Nehari 235

Phan tfch ham trong va ham ngoai 235Toan III Hankel 237

£)!nhIy Nehariva nghi$mcua bai loan (4.70) 239Thuat loan xac dinh nghi$m bar loan can b~ng me hinh 240

4.3.5 Phuong phap 2: Tim nghi$m bar loan can b~ng me hinh nho phep n9i suyNevannlinna-Pick 242

N9i suy Nevannlinna-Pick 243Tim gia tr! chan duoi Ion nhat 246

Tong ket: Thu~t loan tlm nghi$m bar loan can b~ng me hinh 248

4.3.6 Nghi$m c$n toi l1U(suboptimal) 250

Cau hoi on t~p va bai t~p 253

5 Bieu khi.y;nthich nghi va ben vii'ng 255

5.1 Ly thuyet Lyapunov 255

5.1.1 Tieu chw3n on d!nh lyapunov va d!nh Iy LaSalle 255TLftLfdng chung 258Tieu chuan lyapunov va ham lyapunov 259D!nh Iy laSalle 262

Ap dl.mg cho h$ tuyen tinh va phLfdng trinh lyapunov 266

5.1.2 Thiet ke b9 dieu khi~n GAS nhd ham dieu khi~n lyapunov (ClF) 270Khai ni$m ham dieu khi~n lyapunov 270Thiet ke ham dieu khi~n lyapunov cho h$ affine 272Thiet ke cuon chieu (backstepping) ham ClF cho h$ truyen ngLf<;jc 275Thiet ke cuon chieu (backstepping) ham ClF eho h$ tam giae 277Thiet ke ham ClF cho h$ truyen ngLf<;:Jcch~t nhd phep doi bien vi phoi 281Thiet ke ham ClF cho h$ affine-truyen ngLf<;:Jcnhd phep doi bien vi phoi 286Dieu khi~n tuyen tinh h6a chinh xac gan di~m et,tccho h$ tam giae 289

5.2 E)jeukhi~n thich nghi tl! chinh (5TR) 2925.2.1 Tong quat ve cd cau nhim dc~mgtham so mo hinh, phLfdng philp blnh phLfdng

nhe nhat va mo hlnh hoi quy """"""""""""""""""""""""""""""""""""""""'" 293PhLfdng philp blnh phLfdng nhe nhat 293Nh$n d~ng tham so mo hlnh khong lien tl,lc 295Nh$n d~ng tham so mo hinh lien tl,lc 296

5.2.2 Cd cau xac d!nh tham so b9 dieu khi~n tlJ mo hlnh doi tLf<;:Jng 296Xac d!nh tham so b9 dieu khi~n PI thee phLfdng philp toi l1Ud9 Idn 297Xac d!nh tham so b9 dieu khi~n PID thee phLfdng philp toi l1Udoi xCtng 297Xae d!nh tham so b9 dieu khi~n toi l1Uthee nhi~u 298Thiet ke b9 dieu khi~n phlm hoi, tinh, thee nguyen tiile eho trLfdc di~m ct,te 299Thiet ke b9 dieu khi~n d9ng, phan hoi tin hi$u ra cOdi~m et,teeho trLfdc 301Thiet ke b9 dieu khi~n vdi mo hlnh mau (model following) 303Xac d!nh tham so b9 dieu khi~n khong lien tl,lC 310

5.2.3 sa dl,lng mo hinh mau nhLfm9t thiet b! thee d6i: Dieu khi~n thiGh nghi tt,tchinh trt,tc tiep 312

Xac d!nh tr9'c tiep tham so b9 dieu khi~n khong lien tl,lc 312Xac d!nh trt,tctiep tham so b9 dieu khi~n lien tl,lC 315

5.3 f>ieu khii!n thich nghi co mo hinh thee doi (MRAC) 316

5.3.1 Hi$u chinh tham so b9 dieu khi~n thee lu$t MIL 318N9i dung phLfdng philp 318Danh gia chat ILf<;:Jngcd cau chinh d!nh 323

5.3.2 Hi$u chinh tham so b9 dieu khi~n nhd ct,teti~u h6a ham ml,lc lieu h<;:Jpthue(xac d!nh dLfdng) 325

5.4 f>ieukhii!n&ndjnh 155 va dieu khii!n bat dinh, thich nghi khang nhi~u 336

5.4.1 D~t van de """"""""""""""""""""""""""""""""""""""""""""'" 336

5.4.2 Dieu khi~n thieh nghi doi tLf<;:Jngphi tuyen e6 tham so h~ng bat d!nh 338

Phvc:lng philp gia dinh ra (certainty equivalence) 338

Thiet ke cuon chieu (backstepping) b9 dieu khien thiGh nghi gia d!nh ra chodoi tvqng truyen ngvqc 344Thiet kecuon chieu (backstepping) b9 dieu khien bam thiGh nghi cho doitvqng tam giac co tham so h<'Jngbat d!nh 349

5.4.3 Dieu khien thiGh nghi doi tvqng phi tuyen co tham so bat dinh ph(,Jthu9C thdigian """""""""""""""""""""""""""'" 352

Phvdng philp nemmien hap dan (damping) 353

Khai ni$m on d!nh ISS, ham ISS-Lyapunov va ham ISS-CLF 356Phvdng philp dieu khien ISS thiGh nghi khang nhieu 363Thiet ke cuon chieu (backstepping) ham ISS-CLF 369

5.5 si't dL.Jngphuong phap dieu khii!n truc;lt 373

5.5.1 XII~t phat diem cua phvdng philp dieu khien trvqt ~ 373

5.5.2 Thiet ke b9 dieu khien trvqt on d!nh ben vCtng 376

5.5.3 Thiet ke be dieu khien trvqt bam ben vCtng 381

5.6 Dieu khii!n thich nghi bu bat d!nh 382

5.6.1 Dieu khien thiGhnghi bu bat d!nh doi tvqng tuyen tfnh 382Bu bat d!nh b<'Jngphan hoi tin hi$u ra 382Bu bat d!nhb<'Jngphan hoi tr<;1ng thai 386

5.6.2 Dieu khien thiGh nghi bu bat d!nhdoi tvqngphituyen 387Dieu khien tuyen tfnh hoa chinh xac h$ co m9tdau vao 387Dieu khien tuyen tfnh hoa chinh xac h$ co nhieudau vao 395Dieu khien thiGh nghi bu bat d!nh doi tvqng phi tuyen affine 410

Cau hili on t~p va bai t~p 415

6 Mi?t so khai ni~m cd ban cua dieu khi€!nva nhftng van de be) sung 419

6.1 Nhiing khai ni~m co ban 419

6.1.1 Cau trucd<;1iso 419Nhom 419Vanh 420

Trvdng 421Kheng gran vector 421Da tap tuyen tfnh 423D<;1iso 424Ideale 425

6.1.2 D<;1iso ma tr$n va me hinh h$ tuyen tfnh 425Cac phep tfnh vdi ma tr$n 426H<;1ngcua ma tr$n 427Dinh thuGcua ma tr$n 428Ma tr$n nghich dao 429Vet cua ma tr$n 430Ma tr$n la m9t anh x<;1 tuyentfnh 431Phep bien doi tvdng dvdng 431Gia tr! ri€mg va vector ri€mg 432Me hinh tr<;1ngthai h$ tuyen tfnh """""""""""""""""""""""""""""""""""""""'" 434

6.1.3 Kh6ng gian ham so va m6 hinh h$ phi tuyen 437Kh6ng gian metric 437Kh6ng gian du 438Kh6nggiancompact , 439Kh6ng gian chuan 439Kh6ng gian Banach 441Kh6ng gian Hilbert 441Kh6ng gian cac anh xi? lien tI,jc 443M6 hinhtri?ngthai h$ phi tuyen , 445

6.2 Ly thuyet ham bien phuc 4486.2.1 Binh nghi'a, khai ni$m ham lien tI,JC,ham giai tfch 448

6.2.2 Ham baa giac (conform) ".. 450

6.2.3 Tich phan phLtcva nguyen Iy cl,J'cdi?i modulus 452

6.3 Toantii Fourier khong lien tl,lc 455

6.3.1 Nhi$m vl,l cua toim tLtFourier kh6ng lien tl,lc 455

6.3.2 Hai sai so cua anh Fourier kh6ng lien tl,lCva ky thu$t giam thieu 456Ham md rc?ngdirac va ham trich mau 456Trich mau trong mien thdi gian va hi$u (Jngtrung pho (aliasing) 458HiJu hi?n h6a mien xac dinh cua tin hi$u va hi$u (Jng ra r1(leakage) 460

6.4 Ly thuyet e)n dinh Kharitonov 462

6.4.1 Ne;>idungdinh Iy Kharitonov " 4626.4.2 Thiet ke be;>dieu khien on dinh ben vCtngcho doi tL19ngtuyen tfnh co tham so

bat dinh 465

6.5 O'ngdl,lng hinh h,?cvi phiin vao dieu khie'n 469

6.5.1 H$ affine 469

6.5.2 Cac phep tfnh Cdban " 471Bao ham cua ham v6 hL1ang(di?o ham Lie) 471

Phep nhan Lie, hay di?o ham cua vector ham 472Ham md re;>ng(distribution) 473

6.5.3 Phepdoi bienvi ph6itach h$ affine " 476

Hi li~u tham khao 482