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1 SICE -- ( (pmal nl (ne hzn eedng hzn (mvng hzn Fg :, -V [9] (ne hzn (nne hzn ( Fg : ASA Fg : F-8 [].... (eedng hzn nl Fg : ( (, y ( h( ( M ( q q&& C( q, q& q& g( q τ X ( ( ( ( (, Fg. : ( U VV X 99 X V (, l( F( l( (sage s F( (emnal s l( >, l(,, F( > F( l( ( l( Q R Q, R > F( ( P ( 6
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4 ( ; V ( V ( l(, ( V (, ( l(, ( ( Q V (, : V ( V ( vale nn V ( > vale nn V ( ( ( ; ( ( ; ( ; ~ ( V ( ; ( ; ( ( ;, ( ( ; ( ( ;, ( ( ; X X ( ( ; ( ; ( ( ; 9 l( (nne hzn ( (eedng hzn nl V (, l( F( F( (emnal s F( ( A B y ( C V (, { ( Q ( R } [ F l](, (, A : X A P A P ( A Q A? ( P Q P A : A BK Q : Q K RK ( : K V (, { ( Q ( R } nl Lyapnv nn { ( Q ( R } ( P { ( Q ( R } { ( Q ( R } F( (nne hzn A. Jadbabae, J. Y and J. Hase, Unnsaned Reedng-Hzn Cnl nlnea Sysems, IEEE ans. Ama Cnl, Vl.6,., pp ,. l( V (, l( F( F( l( l( Hzn G. Gmm, M. J. Messna, S. E. na and A. R. eel, Mdel Pedve Cnl: F Wan a Lal Cnl Lyapnv Fnn, All s Ls, IEEE ans. Ama Cnl, Vl.,., pp.6-8,. A. Jadbabae and J. Hase, On he Sably Reedng Hzn Cnl Wh a Geneal emnal y Inse Cs, ehnlgy IEEE ans. Ama Cnl, Vl.,., pp ,. (,, w ( z h( ( w( w( W (, ( A : X X, X, X A : (, X A : (, (, w X, X, w W (, ( A : [ F l](, (, w, X, w W (, ( F( ( (bs nl Lyapnv nn [ V l](, (, w
5 mn-ma mn-ma ( mn-ma H V (, { l( l w ( w( } F( (game hey (nheen bsness.... (nvese pmaly (np--sae sably, ISS 6 Caleh ded an (Calna Inse ehnlgy Hve a ( Vsal Feedba Sysem ( Fg. : Caleh ded an Fg. : Hve Ca Fg. : Vsal Feedba Sysem 7 (Caleh ded an Caleh ded an Fg. : Caleh ded an ded an J I p m & FX F s θ snθ a X F b Zb m & z FZ F snθ sθ mg a X F b Zb e J && θ M a I pω& sθ FZ lτ b s [, z, θ, &, z&, & θ ] F, F [ ] Xb Zb hp:// Fg. : 8 (Caleh ded an U F X [] [] b F Zb -6. [] 6. [] X z [m]. [m] Fg.6 : J( q( τ, τ dτ V ( q(, e Qe e R e (sage s V ( e ( P e ( (emnal s e eq e eq Q >, R > eq [ md, zmd, θmd,,,] [ mg ] eq e, M. B. Mlam, R. Fanz, J. E. Hase and R. M. May, Reedng hzn nl veed hs lgh Epemen, IEE P.Cnl hey Appl., Vl.,., pp.-8,. 9 (Caleh ded an hp://
6 Hve a (Hve a Hve a, sn d sn s d s / L / L,, [ ] [ ],. Ohha and A. Kdama, Aman Cde Genean Sysem nlnea Reedng Hzn Cnl,, Vl.8,.7, pp Fg. : Hve Ca Fg.7 : Hve Ca hp://www-newn.meh.eng.saa-.a.jp/ ~hsa/pape/ccahp_hve.pd U ~ ma ma X ma ~ ma ( J ϕ L(, d (Hve a { } L ( p( Q( p( ϕ ( p( S ( p( Q > S > π p( [ ] α ( e (sage s (emnal s C/GMRES (Hve a hp://www-newn.meh.eng.saa-.a.jp/~hsa/eseah.hm (Vsal Feedba Cnl Vsal Feedba Cnl & ξ M ( q C( q, q& ξ M ( q s s & λ λ RwJbξ RwJbαJ b Rw R zw zw age Obje w Camea Plana Manpla Fg. : Vsal Feedba Sysem R& w J RHC (, l ( τ, τ dτ M ( l( τ, τ Q R (sage s M ( V ( (emnal s (Vsal Feedba Cnl (, ( (,, MPC Fg : P K 6 6
7 .... (nnlnea mdel pedve nl (bs mdel pedve nl (as sysems (hybd sysems 7,, (,,,,, 98.,,,,, vl. 6, n., 987. M 8 Fg.. Fg.. R,,,,,,,, O OFF, 9 I A hen B S X,U,ϕ ( X {,,,, } U { A, B, C} ϕ : X U X ( y( sysem d (, d y g(, n m R, R, y R p Peewse Ane Sysem Med Lgal Dynamal(MLD Peewse Ane( Lnea Cmplemenay(LC Eended Lnea Cmplemenay(ELC Ma-Mn-Pls-Salng(MMPS : X : X : X sa( [ ] sa X X / / ( X O sa( O 7
8 Peewse Ane Sysem (ppsnal als ( Peewse Ane Sysem A B y C D g P (ppsnal lg yle and Ma, Amaa 999 [] A hen B [ ( ] [ δ ] δ : - Snag, -AC 98 Jhanssn and Ranze, -AC 998 Ranze and Jhanssn, -AC Jhanssn, Spnge-Velag, [ ( ] [ δ ] ( M ( δ ( ε ( m ε δ M ma (, m mn ( χ ε : χ (MLD -: : Med Lgal Dynamal Sysem A B B δ B z( ( δ {,} z R l Bempad and Ma, Amaa 999 y C D D δ D z( ( E ( E δ Ez( E E Heemels, She, and Bempad, Amaa MLD LC Med Lgal Dynamal(MLD Peewse Ane( Lnea Cmplemenay(LC Eended Lnea Cmplemenay(ELC Ma-Mn-Pls-Salng(MMPS ELC MMPS 6 HYSDEL MLD hyspwa EH(Zh an e( an e UP Adapve Cse Cnl 7 8 8
9 ( A B y C D ( Q R P J, J LQR P( K K R B P( B B P( ( A 9 ( A B y C D mn { } mn ma mn ma ( Q R P, (Epl K h X A. Bempad, M. Ma, V. Da, and E. Pspls (Amaa, [.] y.8. mn. {, } K K h X Regn Regn,, Regn,7,8 Regn 6 Regn 9. [ ]. [ ].6 [ ].6 [ ] Ml-Paame lb Ml-Paame lb (MP ve.. IA URL hp://nl.ee.ehz.h/~mp/ (Lnea Pgammng (Qada Pgammng (Med Inege Pgammng (Ml-Paame Pgammng 9
10 MLD Dynamal : X : X : X / / ( X X X O mn J (, : { Q { } sbje Q Q ( ( δ δ e Q( z ze ( Q ( y y } e e A B B Bz y C D Dδ D z Eδ Ez E E E mn ma mn ma δ e e MLD (Med Inege Pgammng } { 6 sbje ( A B y ( C D g X X mn { } ( R Q Q se L I L (, [ ] X ( F G X 7 MLD (Med Inege Pgammng n-lne( mn -lne p (mp-lp { p p } G p G p S Fξ ( d d d d 8 s sn.8 α α snα( sα( π / [ ] α( π / [ ] < [,] [,] [,] R mn { } ( R Q Q Q I Q 9 HYSDEL MLD Ml-Paame lb hyspwa Ml-Paame lb * K h, X 6
11 Epl 6 X X. : ( (... : [,] [,] [,] R Q I mn ( R Q Q { } Q X X O 6 Epl (mp-lp mn p { p p } G p G p S Fξ ( d -lne d d d mnmm-me nlle ne-sep nlle 6 6 O X I Q PF P X A BF P( A BF P Q F RF I D ( F( F( l( P. Gede, M.Kavana, M.Ba, M.Ma(Amaa, 6 X X P X A BF P( A BF P Q F RF I D ( mnγ BMI(blnea ma neqaly : sbje Y, Z,γ Y Z Z F Z Z P >, Z γ.. Z ( A ( ( Z BY Q Z R Y ( A Z BY Z. ( Q Z I I γ. ( R Y γi LMI(lnea ma neqaly : P. Gede, M.Kavana, M.Ba, M.Ma(Amaa, 66
12 mnγ sbje Y, Z,γ Y Z Z F Z Z P >, Z γ.. Z ( A ( ( Z BY Q Z R Y ( A Z BY Z. ( Q Z γi. ( R Y γi Q PF ( A B F O I Q O P. Gede, M.Kavana, M.Ba, M.Ma(Amaa, 67 ( A B * J ( ( mn mnγ sbje { } Y, Z,γ Z >, Z Z Z ( A Z BY ( A Z BY Z. ( Q Z. ( R Y ( R Q Q P. Gede, M.Kavana, M.Ba, M.Ma(Amaa, 68 Y F Z ( Q Z. ( R Y. γi γi I ( A O Z P γ P ( B F lw mpley mnmm-me nlle O X X : O O Ml-Paame X O O X X X P. Gede, M.Kavana, M.Ba, M.Ma(Amaa, 69 lw mpley ne-sep nlle X X Ml-Paame O X P. Gede, M.Kavana, M.Ba, M.Ma(Amaa, 7 s sn.8 α α snα( sα( π / [ ] α( π / [ ] < [,] [,], mn { } [ ] ( R Q Q R Q I Q 7 Epl
13 mnmm-me nlle ne-sep nlle Lyapnv Lyapnv Cmmn qada Lyapnv nn Cmmn sm--sqaes Lyapnv nn Peewse ane Lyapnv nn Peewse qada Lyapnv nn EH(Zh Elen hle Sma Dampng Maeals Fg.. Peewse qada Lyapnv nn Fg.. Peewse ane Lyapnv nn P. Bswas, P.Gede, J.Lbeg, M.Ma(IFAC, 7 76 Vehle Fman ewed Cnl Fg..6 hp:// 77 Dsbed Reedng Hzn Cnl Dsbed Reedng Hzn( (Cenalzed Reedng Hzn Mase Dsbed Reedng Hzn ewed Cnl Sysem Dsbed ewed 78
14 Dsbed Reedng Hzn Cnl Wllam B. Dnba and Rhad M. May, Dsbed Reedng Hzn Cnl wh Applan Ml-Vehle Fman Sablzan, Aeped Amaa, Jne,. Revsn sbmed May,.. Kevzy, F. Bell and G. J. Balas A Sdy n Deenalzed Reedng Hzn Cnl Depled Sysems ehnal Rep, Unvesy Mnnesa, Mnneapls. Mah. ewed Cnl Sysem 79 Dsbed Reedng Hzn Cnl * J ( mn ( j L( ( s, s s ds γ Sbje & ( ( τ :, ( τ : L(,, : & ( ( τ :, ( τ : : : X : : : P : γ : ( Ω ( ε : Wllam B. Dnba and Rhad M. May, (Amaa, 8 P Dsbed Reedng Hzn Cnl * ~ j j j j J (, mn l (,,,,,,, l (,,, U Sbje, (,,,, X, j j j j j j j j, (,,, j, X,, j j j g (,,,,,,, j j j, X, X j j,,. Kevzy, F. Bell and G. J. Balas (ehnal Rep, Unvesy Mnnesa, (nnlnea mdel pedve nl (bs mdel pedve nl (as sysems (hybd sysems 8 HYSEL Ml-Paame l b Hybd Sysem Despn Langage (HYSDEL ve... (Hybd Dsee Aman I-hen-else HYSDEL hp://nl.ee.ehz.h/~hybd/hysdel/ Med Lgal Dynamal (MLD ( A B Bδ Bz( y C D D δ D z( ( δ Ez( E E E E 8 8
15 SYSEM a{ IERFACE{ SAE{ } IPU{ } OUPU{ } PARAMEER{ } } IMPLEMEAIO{ COIUOUS{ } OUPU{ } MUS{ } AUX{ } AD{ } DA{ IF HE } LOGIC{ } } } HYSDEL ADe.g. δ DA e.g. IF δ HE 8 y } Inse ehnlgy HYSDEL SYSEM a{ IERFACE{ SAE{ REAL psn [-, ]; Zh,. REAL speed [-*/6, */6]; } IPU{ REAL qe [-,]; REAL F_bae [,9]; REAL slpe [, ]; BOOL gea, gea, gea, gea, gea, gear; } p OUPU{ REAL psn_y, speed_y, w_y; } PARAMEER{ REAL mass ; REAL s.; REAL g 9.8; REAL bea_n ; REAL Rgea.77; REAL Rgea.8; } ( ( p( v( v ( s F.D. s and A. Bempad, HYSDEL A l Geneang Cmpanal Hybd Mdels Analyss and Synhess Pblems, ehnal Rep: AU -, EH, 86 HYSDEL ( IMPLEMEAIO{ AUX{ REAL Fe, Fe, Fe, Fe, Fe, FeR, w, w, w, w, w, BOOL dpwl, dpwl, dpwl, dpwl; } AD{ dpwl wpwl - (w w w w w wr < ; } DA{ Fe {IF gea HE qe / speed_a * Rgea}; w {IF gea HE speed / speed_a * Rgea}; DCe {IF dpwl HE (apwl - apwl (bpwl -bpwl * (w w w w wr}; } COIUOUS{ psn psn s * speed; speed speed s / mass * (Fe Fe Fe Fe Fe FeR - F_bae - bea_n * speed -g *slpe; } OUPU{ psn_y psn; speed_y speed; w_y w w w w w wr; } MUS{ -w < -wemn; w < wema; -w < -wemn; w < wema; -qe - ( apwl bpwl * (w w w w w wr < ;} } } 87 HYSDEL SYSEM a{ IMPLEMEAIO{ AUX{ REAL Fe, IERFACE{ Fe, Fe, Fe, Fe, FeR, BOOL dpwl, dpwl, SAE{ dpwl, dpwl; } AD{ REAL psn [-, ]; dpwl wpwl - (w REAL w speed w [-*/6, w w */6]; } DA{ IPU{ Fe {IF gea HE REAL qe qe / speed_a [-,]; * Rgea}; w {IF gea HE speed REAL / F_bae speed_a [,9]; * Rgea}; DCe {IF dpwl HE REAL (apwl slpe [, - apwl ]; ( COIUOUS{ BOOL gea, gea, gea, gea, gea, gear; } psn psn s * speed; OUPU{ speed speed s / mass * (Fe Fe Fe Fe REAL psn_y, speed_y, w_y; } OUPU{ PARAMEER{ psn_y psn; speed_y speed; REAL mass ; w_y w w w REAL w w s wr;.; } MUS{ REAL g 9.8; -w < -wemn; w < REAL wema; bea_n -w < - ; ; -qe - ( apwl bpwl REAL * Rgea (w w.77; } REAL Rgea.8; } } } Med Lgal Dynamal (MLD 88 HYSDEL Peewse Ane ( Plgn: hyspwa.. Med Lgal Dynamal ( A B Bδ Bz( y C D D δ D z( ( δ Ez( E E E E hyspwa hp://nl.ee.ehz.h/~hybd/hysdel/hysdel.msql Peewse Ane ( A B D I, ( Ml-Paame lb (MP ve.. IA URL hp://nl.ee.ehz.h/~mp/ MALAB LP slve SeDM Ml-Paame lb Lnpg (MALAB CDD (Fee CPLEX (Cmmeal AC slve (Cmmeal 89 9
16 ( A B y C D J ( mn * Q l R l {, } {, K, } X, K, U, X se Q l Q Q {, } A B,, K, Q Q Q ma Q {, } l, J ( mn * Q l R l Q {, } {, K, } X, K, U, X se A B,, K, J ( ( Y mn * GU W E [ ] U, K, U l {, } { U H U ( F U } 9 9 * J ( ( Y mn * GU W E [ ] U, K, U ( F G U (Epl { U H U ( F U }, A. Bempad, M. Ma, V. Da and E.. Pspls (Amaa, F. Bell (Cnsaned Opmal Cnl Lnea and Hybd Sysems, P. n { R H K } 9 Eample y mn Sbje 9 y syss Eample syss.a[ ; ]; syss.b[;]; syss.c[ ; ]; syss.d[;]; syss.mn-; syss.ma; syss.ymn[- -]'; syss.yma[ ]'; mn pbs Eample pbs.nm; pbs.qeye(; pbs.r; pbs.; pbs.obnds; pbs.sbp_lev; pbs.p_; pbs.nsan;
17 syss pbs [ls]mp_cnl(syss,pbs; ls { } * n P R H K U ( F G Eample ls mp_plpan(ls Eample - Cnlle pan wh egns Eample Eample pbs.sbp_lev; - Cnlle pan wh egns [X,U,Y,D,s,ajey,easble] mp_mpeajey(ls,[8;-], me me Eample GUI [X,U,s,ajey]mp_plajey(lS GUI MALABmmand wndw mp_sd Clsed-Lp ajey nal sae [7.96,-.68]
V 0 = + r pv (H) + qv (T ) = + r ps (H) + qs (T ) = S 0 X n+ (T ) = n S n+ (T ) + ( + r)(x n n S n ) = ( + r)x n + n (d r)s n = ( + r)v n + V n+(h) V
I (..2) (0 < d < + r < u) X 0, X X = 0 S + ( + r)(x 0 0 S 0 ) () X 0 = 0, P (X 0) =, P (X > 0) > 0 0 H, T () X 0 = 0, X (H) = 0 us 0 ( + r) 0 S 0 = 0 S 0 (u r) X (T ) = 0 ds 0 ( + r) 0 S 0 = 0 S 0 (d r)
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24 I 1.1.. ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x 1 (t), x 2 (t),, x n (t)) ( ) ( ), γ : (i) x 1 (t),
More informationX G P G (X) G BG [X, BG] S 2 2 2 S 2 2 S 2 = { (x 1, x 2, x 3 ) R 3 x 2 1 + x 2 2 + x 2 3 = 1 } R 3 S 2 S 2 v x S 2 x x v(x) T x S 2 T x S 2 S 2 x T x S 2 = { ξ R 3 x ξ } R 3 T x S 2 S 2 x x T x S 2
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数論 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/008142 このサンプルページの内容は, 第 2 版 1 刷発行当時のものです. Daniel DUVERNEY: THÉORIE DES NOMBRES c Dunod, Paris, 1998, This book is published
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127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
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