Algorithme de commande

Bonjour,
J'ai l'algorithme suivant que je vais écrire son programme,
Etape1: Choisir une matrices définie positive Q et une matrice D et fixer le paramétre tf=1.5s,
Etape2: Résoudre hors-ligne les équations de P, V et H (premier programme), fixer alpha et calculer la valeur de Sopt0. Si Sopt0=0 à t=0, alors t0=0 et passer à l'étape4. Sinon, passer à l'étape3.
Etape3: Appliquer la loi de commande v=-alpha*sign(D*Sopt0) jusqu'à l'instant t tel que Sopt0=0. Alors t0=t et passer à l'étpe4.
Etape4: pour t apprtenant à [t0, tf], appliquer la loi de commnde v=-alpha*sign(D*Sopt),
Etape5: pour t appartenant à [tf, infini[, appliquer la loi de commande v=-alpha*sign(D*Soptf).
Rq: Sopt=[Sopt1 Sopt2 Sopt3]' de meme por Sopt0 et Soptf.
Mon probléme je doit trouver x10 , x20 et x30 tendent vers zero mais avec mon programme je ne trouve pas ça, est ce que vous pouvez m'aider.
voici le premier programme à exécuter

Code:

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function y=exerart() P0=[0 0 0;0 0 0;0 0 0]; y1=0;y2=0;y3=0;y4=0;y5=0;y6=0;y7=0;y8=0;y9=0; V0=[1 0 0;0 1 0;0 0 1]; y10=1;y11=0;y12=0;y13=0;y14=1;y15=0;y16=0;y17=0;y18=1; H0=[0 0 0;0 0 0;0 0 0]; y19=0;y20=0;y21=0;y22=0;y23=0;y24=0;y25=0;y26=0;y27=0; I=[1 0 0;0 1 0;0 0 1]; h=0.001; for i=0:0.001:1.5; % Pour P k1=-P0*P0+I; k2=-(P0+(h/2)*k1)*(P0+(h/2)*k1)+I; k3=-(P0+(h/2)*k2)*(P0+(h/2)*k2)+I; k4=-(P0+h*k3)*(P0+h*k3)+I; P=P0+(h/6)*(k1+2*k2+2*k3+k4); % Pour V r1=-P0'*V0; r2=-P0'*(V0+(h/2)*r1); r3=-P0'*(V0+(h/2)*r2); r4=-P0'*(V0+h*r3); V=V0+(h/6)*(r1+2*r2+2*r3+r4); % Pour H l1=V0'*V0; % l1=l2=l3=l4 H=H0+(h/6)*(l1+2*l1+2*l1+l1); P0=P; V0=V; H0=H; % Pour P P1=P0(1); P2=P0(2); P3=P0(3); P4=P0(4); P5=P0(5); P6=P0(6); P7=P0(7); P8=P0(8); P9=P0(9); y1=[y1 P1]; y2=[y2 P2]; y3=[y3 P3]; y4=[y4 P4]; y5=[y5 P5]; y6=[y6 P6]; y7=[y7 P7]; y8=[y8 P8]; y9=[y9 P9]; %Pour V V1=V0(1); V2=V0(2); V3=V0(3); V4=V0(4); V5=V0(5); V6=V0(6); V7=V0(7); V8=V0(8); V9=V0(9); y10=[y10 V1]; y11=[y11 V2]; y12=[y12 V3]; y13=[y13 V4]; y14=[y14 V5]; y15=[y15 V6]; y16=[y16 V7]; y17=[y17 V8]; y18=[y18 V9]; % Pour H H1=H0(1); H2=H0(2); H3=H0(3); H4=H0(4); H5=H0(5); H6=H0(6); H7=H0(7); H8=H0(8); H9=H0(9); y19=[y19 H1]; y20=[y20 H2]; y21=[y21 H3]; y22=[y22 H4]; y23=[y23 H5]; y24=[y24 H6]; y25=[y25 H7]; y26=[y26 H8]; y27=[y27 H9]; save param4 y1 y2 y3 y4 y5 y6 y7 y8 y9 save param5 y10 y11 y12 y13 y14 y15 y16 y17 y18 save param6 y19 y20 y21 y22 y23 y24 y25 y26 y27 end plot(y1) grid

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Mon progrmme principle est

Code:

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load param4 load param5 load param6 h=0.001;alfa=2000; % X1=0;X2=0;X3=0; x10=0.2-1;x20=1.1-0.5;x30=-0.2;u0=[0 0 0]';Z10=[-0.8 0.6 -0.2]';Z20=[0 0 0]';u0=[0 0 0]'; D=[0.0005 0.0015 0.0015;0.0012 0.0005 0.002;0.002 0.0015 0.0005]; X1=0.2-1;X2=1.1-0.5;X3=-0.2;U1=0;U2=0;U3=0;I=1500;Z3=-0.8;Z4=0.6;Z5=-0.2; % Matrice P0 et Pf a1=y1(1500);b1=y1(1); a2=y2(1500);b2=y2(1); a3=y3(1500);b3=y3(1); a4=y4(1500);b4=y4(1); a5=y5(1500);b5=y5(1); a6=y6(1500);b6=y6(1); a7=y7(1500);b7=y7(1); a8=y8(1500);b8=y8(1); a9=y9(1500);b9=y9(1); % Matrice V0 et Vf a10=y10(1500);b10=y10(1); a11=y11(1500);b11=y11(1); a12=y12(1500);b12=y12(1); a13=y13(1500);b13=y13(1); a14=y14(1500);b14=y14(1); a15=y15(1500);b15=y15(1); a16=y16(1500);b16=y16(1); a17=y17(1500);b17=y17(1); a18=y18(1500);b18=y18(1); % Matrice H0 et Hf a19=y19(1500);b19=y19(1); a20=y20(1500);b20=y20(1); a21=y21(1500);b21=y21(1); a22=y22(1500);b22=y22(1); a23=y23(1500);b23=y23(1); a24=y24(1500);b24=y24(1); a25=y25(1500);b25=y25(1); a26=y26(1500);b26=y26(1); a27=y27(1500);b27=y27(1); P0=[a1 a4 a7;a2 a5 a8;a3 a6 a9]; V0=[a10 a13 a16;a11 a14 a17;a12 a15 a18]; H0=[a19 a22 a25;a20 a23 a26;a21 a24 a27]; a0=P0-V0*inv(H0)*V0'; Pf=[b1 b4 b7;b2 b5 b8;b3 b6 b9]; Vf=[b10 b13 b16;b11 b14 b17;b12 b15 b18]; Hf=[b19 b22 b25;b20 b23 b26;b21 b24 b27]; Soptf=Z20+(Pf-Vf*inv(Hf)*Vf')*Z10; af=Pf-Vf*inv(Hf)*Vf'; %for i=0:0.001:0.002; Sopt0=Z20+(P0-V0*inv(H0)*V0')*Z10; Sopt01=Z20(1)+a0(1)*Z10(1)+a0(4)*Z10(2)+a0(7)*Z10(3); Sopt02=Z20(2)+a0(2)*Z10(1)+a0(5)*Z10(2)+a0(8)*Z10(3); Sopt03=Z20(3)+a0(3)*Z10(1)+a0(6)*Z10(2)+a0(9)*Z10(3); if (Sopt01==0)&(Sopt02==0)&(Sopt03==0) j1=0; for s=j1:0.001:1.499; ct=floor(1500-(s/h)); % Matrice P z1=y1(ct); z2=y2(ct); z3=y3(ct); z4=y4(ct); z5=y5(ct); z6=y6(ct); z7=y7(ct); z8=y8(ct); z9=y9(ct); % Matrice V z11=y10(ct); z12=y11(ct); z13=y12(ct); z14=y13(ct); z15=y14(ct); z16=y15(ct); z17=y16(ct); z18=y17(ct); z19=y18(ct); % Matrice H z21=y19(ct); z22=y20(ct); z23=y21(ct); z24=y22(ct); z25=y23(ct); z26=y24(ct); z27=y25(ct); z28=y26(ct); z29=y27(ct); P=[z1 z4 z7;z2 z5 z8;z3 z6 z9]; V=[z11 z14 z17;z12 z15 z18;z13 z16 z19]; H=[z21 z24 z27;z22 z25 z28;z23 z26 z29]; deltaf1=cos(s)*(1+0.05*sin(4*s)+0.1*cos(s)); deltaf2=sin(s)*cos(s)*(1+0.05*sin(4*s)+0.1*cos(s)); deltaf3=(sin(s)^2)*(1+0.05*sin(4*s)+0.1*cos(s)); deltaf4=cos(s+h/2)*(1+0.05*sin(4*(s+h/2))+0.1*cos(s+h/2)); deltaf5=sin(s+h/2)*cos(s+h/2)*(1+0.05*sin(4*(s+h/2))+0.1*cos(s+h/2)); deltaf6=(sin(s+h/2)^2)*(1+0.05*sin(4*(s+h/2))+0.1*cos(s+h/2)); deltaf7=cos(s+h)*(1+0.05*sin(4*(s+h))+0.1*cos(s+h)); deltaf8=sin(s+h)*cos(s+h)*(1+0.05*sin(4*(s+h))+0.1*cos(s+h)); deltaf9=(sin(s+h)^2)*(1+0.05*sin(4*(s+h))+0.1*cos(s+h)); deltag1=0.01*sin(s+2.1)*(u0(1)-0.5*u0(3)); deltag2=0.01*cos(s)*(-0.2*u0(2)+0.8*u0(3)); deltag3=0.01*cos(s+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag4=0.01*sin(s+(h/2)+2.1)*(u0(1)-0.5*u0(3)); deltag5=0.01*cos(s+h/2)*(-0.2*u0(2)+0.8*u0(3)); deltag6=0.01*cos(s+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag7=0.01*sin(s+h+2.1)*(u0(1)-0.5*u0(3)); deltag8=0.01*cos(s+h)*(-0.2*u0(2)+0.8*u0(3)); deltag9=0.01*cos(s+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); % Methode de Runge Kutta d'ordre 4 l11=-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)); l12=x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)); l13=-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3)); l21=-(x20+(h/2)*l12)*(x30+(h/2)*l13)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l22=(x10+(h/2)*l11)*(x30+(h/2)*l13)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l23=-(1/3)*(x10+(h/2)*l11)*(x20+(h/2)*l12)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l31=-(x20+(h/2)*l22)*(x30+(h/2)*l23)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l32=(x10+(h/2)*l21)*(x30+(h/2)*l23)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l33=-(1/3)*(x10+(h/2)*l21)*(x20+(h/2)*l22)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l41=-(x20+h*l32)*(x30+h*l33)+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)); l42=(x10+h*l31)*(x30+h*l33)+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)); l43=-(1/3)*(x10+h*l31)*(x20+h*l32)+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3)); x1=x10+(h/6)*(l11+2*l21+2*l31+l41); x2=x20+(h/6)*(l12+2*l22+2*l32+l42); x3=x30+(h/6)*(l13+2*l23+2*l33+l43); q1=-(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; q2=-x20*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q3=-sin(s)*(1+0.05*sin(4*s)+0.1*cos(s))+cos(s)*(0.2*cos(4*s)-0.1*sin(s))+0.01*cos(s+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*s); fi1=q1+q2+q3; q4=(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; q5=x10*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q6=(cos(s)^2)*(1+0.05*sin(4*s)+0.1*cos(s))-(sin(s)^2)*(1+0.05*sin(4*s)+0.1*cos(s)); q7=sin(s)*cos(s)*(0.2*cos(4*s)-0.1*sin(s))-0.01*sin(s)*(-0.2*u0(2)+0.8*u0(3)); q8=(0.5^3)*cos(0.5*s)*cos(s)-(0.5^2)*sin(0.5*s)*sin(s)-(0.5^2)*sin(0.5*s)*sin(s)+0.5*cos(0.5*s)*cos(s); fi2=q4+q5+q6+q7+q8; q9=-(1/3)*x20*(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3))); q10=-(1/3)*x10*(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3))); q11=2*sin(s)*cos(s)*(1+0.05*sin(4*s)+0.1*cos(s))+(sin(s)^2)*(0.2*cos(4*s)-0.1*sin(s)); q12=-0.01*sin(s+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); q13=(0.5^3)*cos(0.5*s)*sin(s)+(0.5^2)*sin(0.5*s)*cos(s)+(0.5^2)*sin(0.5*s)*cos(s)+0.5*cos(0.5*s)*sin(s); fi3=q9+q10+q11+q12+q13; fi=[fi1 fi2 fi3]'; gama=[0.01*sin(s+2.1)+1 1.2 -0.005*sin(s+2.1)+1.5;1.5 -0.002*cos(s)+1 0.008*cos(s)+1.2;-0.002*cos(s+1.3)+1.2 -0.01*cos(s+1.3)+1.5 0.007*cos(s+1.3)+1]; qr1=-(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qr2=-(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qr3=-x20*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qr4=-x2*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qr5=-sin(s+(h/2))*(1+0.05*sin(4*(s+(h/2)))+0.1*cos(s+(h/2)))+cos(s+(h/2))*(0.2*cos(4*(s+(h/2)))-0.1*sin(s+(h/2)))+0.01*cos(s+(h/2)+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(s+(h/2))); qr6=-sin(s+h)*(1+0.05*sin(4*(s+h))+0.1*cos(s+h))+cos(s+h)*(0.2*cos(4*(s+h))-0.1*sin(s+h))+0.01*cos(s+h+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(s+h)); qr7=(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qr8=(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qr9=x10*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qr10=x10*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qr11=(cos(s+(h/2))^2)*(1+0.05*sin(4*(s+(h/2)))+0.1*cos(s+(h/2)))-(sin(s+(h/2))^2)*(1+0.05*sin(4*(s+(h/2)))+0.1*cos(s+(h/2))); qr12=(cos(s+h)^2)*(1+0.05*sin(4*(s+h))+0.1*cos(s+h))-(sin(s+h)^2)*(1+0.05*sin(4*(s+h))+0.1*cos(s+h)); qr13=sin(s+(h/2))*cos(s+(h/2))*(0.2*cos(4*(s+(h/2)))-0.1*sin(s+(h/2)))-0.01*sin(s+(h/2))*(-0.2*u0(2)+0.8*u0(3)); qr14=sin(s+h)*cos(s+h)*(0.2*cos(4*(s+h))-0.1*sin(s+h))-0.01*sin(s+h)*(-0.2*u0(2)+0.8*u0(3)); qr15=(0.5^3)*cos(0.5*(s+(h/2)))*cos(s+(h/2))-(0.5^2)*sin(0.5*(s+(h/2)))*sin(s+(h/2))-(0.5^2)*sin(0.5*(s+(h/2)))*sin(s+(h/2))+0.5*cos(0.5*(s+(h/2)))*cos(s+(h/2)); qr16=(0.5^3)*cos(0.5*(s+h))*cos(s+h)-(0.5^2)*sin(0.5*(s+h))*sin(s+h)-(0.5^2)*sin(0.5*(s+h))*sin(s+h)+0.5*cos(0.5*(s+h))*cos(s+h); qr17=-(1/3)*x20*(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3))); qr18=-(1/3)*x20*(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3))); qr19=-(1/3)*x10*(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3))); qr20=-(1/3)*x10*(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3))); qr21=2*sin(s+(h/2))*cos(s+(h/2))*(1+0.05*sin(4*(s+(h/2)))+0.1*cos(s+(h/2)))+(sin(s+(h/2))^2)*(0.2*cos(4*(s+(h/2)))-0.1*sin(s+(h/2))); qr22=2*sin(s+h)*cos(s+h)*(1+0.05*sin(4*(s+h))+0.1*cos(s+h))+(sin(s+h)^2)*(0.2*cos(4*(s+h))-0.1*sin(s+h)); qr23=-0.01*sin(s+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qr24=-0.01*sin(s+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qr25=(0.5^3)*cos(0.5*(s+(h/2)))*sin(s+(h/2))+(0.5^2)*sin(0.5*(s+(h/2)))*cos(s+(h/2))+(0.5^2)*sin(0.5*(s+(h/2)))*cos(s+(h/2))+0.5*cos(0.5*(s+(h/2)))*sin(s+(h/2)); qr26=(0.5^3)*cos(0.5*s+h)*sin(s+h)+(0.5^2)*sin(0.5*(s+h))*cos(s+h)+(0.5^2)*sin(0.5*(s+h))*cos(s+h)+0.5*cos(0.5*(s+h))*sin(s+h); fi11=qr1+qr3+qr5; fi12=qr2+qr4+qr6; fi21=qr7+qr9+qr11+qr13+qr15; fi22=qr8+qr10+qr12+qr14+qr16; fi31=qr17+qr19+qr21+qr23+qr25; fi32=qr18+qr20+qr22+qr24+qr26; gama1=[0.01*sin(s+(h/2)+2.1)+1 1.2 -0.005*sin(s+(h/2)+2.1)+1.5;1.5 -0.002*cos(s+(h/2))+1 0.008*cos(s+(h/2))+1.2;-0.002*cos(s+(h/2)+1.3)+1.2 -0.01*cos(s+(h/2)+1.3)+1.5 0.007*cos(s+(h/2)+1.3)+1]; gama2=[0.01*sin(s+h+2.1)+1 1.2 -0.005*sin(s+h+2.1)+1.5;1.5 -0.002*cos(s+h)+1 0.008*cos(s+h)+1.2;-0.002*cos(s+h+1.3)+1.2 -0.01*cos(s+h+1.3)+1.5 0.007*cos(s+h+1.3)+1]; fir1=[fi11 fi21 fi31]'; fir2=[fi12 fi22 fi32]'; Sopt=Z20+(P-V*inv(H)*V')*Z10; v=-alfa*sign(D*Sopt); % Methode de Runge Kutta d'ordre 4 k1=Z20; k2=Z20+(h/2)*k1; k3=Z20+(h/2)*k2; k4=Z20+h*k3; Z1=Z10+(h/6)*(k1+2*k2+2*k3+k4); r1=fi+gama*v; r2=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r1+(P-V*inv(H)*V')*(Z10+(h/2)*k1))); r3=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r2+(P-V*inv(H)*V')*(Z10+(h/2)*k2))); r4=fir2-alfa*gama2*sign(D*(Z20+h*r3+(P-V*inv(H)*V')*(Z10+h*k3))); Z2=Z20+(h/6)*(r1+2*r2+2*r3+r4); u=u0+h*v; u0=u; Z10=Z1; Z20=Z2; x10=x1; x20=x2; x30=x3; X1=[X1 x10]; end for i=1.499:0.001:2; Soptf=Z20+(Pf-Vf*inv(Hf)*Vf')*Z10; Soptf1=Z20(1)+af(1)*Z10(1)+af(4)*Z10(2)+af(7)*Z10(3); Soptf2=Z20(2)+af(2)*Z10(1)+af(5)*Z10(2)+af(8)*Z10(3); Soptf3=Z20(3)+af(3)*Z10(1)+af(6)*Z10(2)+af(9)*Z10(3); vf=-alfa*sign(D*Soptf); deltaf1=cos(i)*(1+0.05*sin(4*i)+0.1*cos(i)); deltaf2=sin(i)*cos(i)*(1+0.05*sin(4*i)+0.1*cos(i)); deltaf3=(sin(i)^2)*(1+0.05*sin(4*i)+0.1*cos(i)); deltaf4=cos(i+h/2)*(1+0.05*sin(4*(i+h/2))+0.1*cos(i+h/2)); deltaf5=sin(i+h/2)*cos(i+h/2)*(1+0.05*sin(4*(i+h/2))+0.1*cos(i+h/2)); deltaf6=(sin(i+h/2)^2)*(1+0.05*sin(4*(i+h/2))+0.1*cos(i+h/2)); deltaf7=cos(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); deltaf8=sin(i+h)*cos(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); deltaf9=(sin(i+h)^2)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); deltag1=0.01*sin(i+2.1)*(u0(1)-0.5*u0(3)); deltag2=0.01*cos(i)*(-0.2*u0(2)+0.8*u0(3)); deltag3=0.01*cos(i+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag4=0.01*sin(i+(h/2)+2.1)*(u0(1)-0.5*u0(3)); deltag5=0.01*cos(i+h/2)*(-0.2*u0(2)+0.8*u0(3)); deltag6=0.01*cos(i+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag7=0.01*sin(i+h+2.1)*(u0(1)-0.5*u0(3)); deltag8=0.01*cos(i+h)*(-0.2*u0(2)+0.8*u0(3)); deltag9=0.01*cos(i+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); % Methode de Runge Kutta d'ordre 4 l11=-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)); l12=x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)); l13=-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3)); l21=-(x20+(h/2)*l12)*(x30+(h/2)*l13)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l22=(x10+(h/2)*l11)*(x30+(h/2)*l13)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l23=-(1/3)*(x10+(h/2)*l11)*(x20+(h/2)*l12)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l31=-(x20+(h/2)*l22)*(x30+(h/2)*l23)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l32=(x10+(h/2)*l21)*(x30+(h/2)*l23)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l33=-(1/3)*(x10+(h/2)*l21)*(x20+(h/2)*l22)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l41=-(x20+h*l32)*(x30+h*l33)+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)); l42=(x10+h*l31)*(x30+h*l33)+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)); l43=-(1/3)*(x10+h*l31)*(x20+h*l32)+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3)); x1=x10+(h/6)*(l11+2*l21+2*l31+l41); x2=x20+(h/6)*(l12+2*l22+2*l32+l42); x3=x30+(h/6)*(l13+2*l23+2*l33+l43); q1=-(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; q2=-x20*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q3=-sin(i)*(1+0.05*sin(4*i)+0.1*cos(i))+cos(i)*(0.2*cos(4*i)-0.1*sin(i))+0.01*cos(i+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*i); fi1=q1+q2+q3; q4=(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; q5=x10*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q6=(cos(i)^2)*(1+0.05*sin(4*i)+0.1*cos(i))-(sin(i)^2)*(1+0.05*sin(4*i)+0.1*cos(i)); q7=sin(i)*cos(i)*(0.2*cos(4*i)-0.1*sin(i))-0.01*sin(i)*(-0.2*u0(2)+0.8*u0(3)); q8=(0.5^3)*cos(0.5*i)*cos(i)-(0.5^2)*sin(0.5*i)*sin(i)-(0.5^2)*sin(0.5*i)*sin(i)+0.5*cos(0.5*i)*cos(i); fi2=q4+q5+q6+q7+q8; q9=-(1/3)*x20*(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3))); q10=-(1/3)*x10*(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3))); q11=2*sin(i)*cos(i)*(1+0.05*sin(4*i)+0.1*cos(i))+(sin(i)^2)*(0.2*cos(4*i)-0.1*sin(i)); q12=-0.01*sin(i+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); q13=(0.5^3)*cos(0.5*i)*sin(i)+(0.5^2)*sin(0.5*i)*cos(i)+(0.5^2)*sin(0.5*i)*cos(i)+0.5*cos(0.5*i)*sin(i); fi3=q9+q10+q11+q12+q13; fi=[fi1 fi2 fi3]'; gama=[0.01*sin(i+2.1)+1 1.2 -0.005*sin(i+2.1)+1.5;1.5 -0.002*cos(i)+1 0.008*cos(i)+1.2;-0.002*cos(i+1.3)+1.2 -0.01*cos(i+1.3)+1.5 0.007*cos(i+1.3)+1]; qz1=-(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qz2=-(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qz3=-x20*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qz4=-x20*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qz5=-sin(i+(h/2))*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2)))+cos(i+(h/2))*(0.2*cos(4*(i+(h/2)))-0.1*sin(i+(h/2)))+0.01*cos(i+(h/2)+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(i+(h/2))); qz6=-sin(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h))+cos(i+h)*(0.2*cos(4*(i+h))-0.1*sin(i+h))+0.01*cos(i+h+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(i+h)); qz7=(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qz8=(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qz9=x10*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qz10=x10*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qz11=(cos(i+(h/2))^2)*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2)))-(sin(i+(h/2))^2)*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2))); qz12=(cos(i+h)^2)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h))-(sin(i+h)^2)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); qz13=sin(i+(h/2))*cos(i+(h/2))*(0.2*cos(4*(i+(h/2)))-0.1*sin(i+(h/2)))-0.01*sin(i+(h/2))*(-0.2*u0(2)+0.8*u0(3)); qz14=sin(i+h)*cos(i+h)*(0.2*cos(4*(i+h))-0.1*sin(i+h))-0.01*sin(i+h)*(-0.2*u0(2)+0.8*u0(3)); qz15=(0.5^3)*cos(0.5*(i+(h/2)))*cos(i+(h/2))-(0.5^2)*sin(0.5*(i+(h/2)))*sin(i+(h/2))-(0.5^2)*sin(0.5*(i+(h/2)))*sin(i+(h/2))+0.5*cos(0.5*(i+(h/2)))*cos(i+(h/2)); qz16=(0.5^3)*cos(0.5*(i+h))*cos(i+h)-(0.5^2)*sin(0.5*(i+h))*sin(i+h)-(0.5^2)*sin(0.5*(i+h))*sin(i+h)+0.5*cos(0.5*(i+h))*cos(i+h); qz17=-(1/3)*x20*(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3))); qz18=-(1/3)*x20*(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3))); qz19=-(1/3)*x10*(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3))); qz20=-(1/3)*x10*(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3))); qz21=2*sin(i+(h/2))*cos(i+(h/2))*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2)))+(sin(i+(h/2))^2)*(0.2*cos(4*(i+(h/2)))-0.1*sin(i+(h/2))); qz22=2*sin(i+h)*cos(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h))+(sin(i+h)^2)*(0.2*cos(4*(i+h))-0.1*sin(i+h)); qz23=-0.01*sin(i+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qz24=-0.01*sin(i+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qz25=(0.5^3)*cos(0.5*(i+(h/2)))*sin(i+(h/2))+(0.5^2)*sin(0.5*(i+(h/2)))*cos(i+(h/2))+(0.5^2)*sin(0.5*(i+(h/2)))*cos(i+(h/2))+0.5*cos(0.5*(i+(h/2)))*sin(i+(h/2)); qz26=(0.5^3)*cos(0.5*i+h)*sin(i+h)+(0.5^2)*sin(0.5*(i+h))*cos(i+h)+(0.5^2)*sin(0.5*(i+h))*cos(i+h)+0.5*cos(0.5*(i+h))*sin(i+h); fi11=qz1+qz3+qz5; fi12=qz2+qz4+qz6; fi21=qz7+qz9+qz11+qz13+qz15; fi22=qz8+qz10+qz12+qz14+qz16; fi31=qz17+qz19+qz21+qz23+qz25; fi32=qz18+qz20+qz22+qz24+qz26; gama1=[0.01*sin(i+(h/2)+2.1)+1 1.2 -0.005*sin(i+(h/2)+2.1)+1.5;1.5 -0.002*cos(i+(h/2))+1 0.008*cos(i+(h/2))+1.2;-0.002*cos(i+(h/2)+1.3)+1.2 -0.01*cos(i+(h/2)+1.3)+1.5 0.007*cos(i+(h/2)+1.3)+1]; gama2=[0.01*sin(i+h+2.1)+1 1.2 -0.005*sin(i+h+2.1)+1.5;1.5 -0.002*cos(i+h)+1 0.008*cos(i+h)+1.2;-0.002*cos(i+h+1.3)+1.2 -0.01*cos(i+h+1.3)+1.5 0.007*cos(i+h+1.3)+1]; fir1=[fi11 fi21 fi31]'; fir2=[fi12 fi22 fi32]'; % Methode de Runge Kutta d'ordre 4 k1=Z20; k2=Z20+(h/2)*k1; k3=Z20+(h/2)*k2; k4=Z20+h*k3; Z1=Z10+(h/6)*(k1+2*k2+2*k3+k4); r1=fi+gama*vf; r2=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r1+(Pf-Vf*inv(Hf)*Vf')*(Z10+(h/2)*k1))); r3=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r2+(Pf-Vf*inv(Hf)*Vf')*(Z10+(h/2)*k2))); r4=fir2-alfa*gama2*sign(D*(Z20+h*r3+(Pf-Vf*inv(Hf)*Vf')*(Z10+h*k3))); Z2=Z20+(h/6)*(r1+2*r2+2*r3+r4); u=u0+h*vf; u0=u; Z10=Z1; Z20=Z2; x10=x1; x20=x2; x30=x3; X1=[X1 x10]; end else j=0; J=0; while (abs(Sopt01)>0.01)|(abs(Sopt02)>0.01)|(abs(Sopt03)>0.01) deltaf1=cos(j)*(1+0.05*sin(4*j)+0.1*cos(j)); deltaf2=sin(j)*cos(j)*(1+0.05*sin(4*j)+0.1*cos(j)); deltaf3=(sin(j)^2)*(1+0.05*sin(4*j)+0.1*cos(j)); deltaf4=cos(j+h/2)*(1+0.05*sin(4*(j+h/2))+0.1*cos(j+h/2)); deltaf5=sin(j+h/2)*cos(j+h/2)*(1+0.05*sin(4*(j+h/2))+0.1*cos(j+h/2)); deltaf6=(sin(j+h/2)^2)*(1+0.05*sin(4*(j+h/2))+0.1*cos(j+h/2)); deltaf7=cos(j+h)*(1+0.05*sin(4*(j+h))+0.1*cos(j+h)); deltaf8=sin(j+h)*cos(j+h)*(1+0.05*sin(4*(j+h))+0.1*cos(j+h)); deltaf9=(sin(j+h)^2)*(1+0.05*sin(4*(j+h))+0.1*cos(j+h)); deltag1=0.01*sin(j+2.1)*(u0(1)-0.5*u0(3)); deltag2=0.01*cos(j)*(-0.2*u0(2)+0.8*u0(3)); deltag3=0.01*cos(j+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag4=0.01*sin(j+(h/2)+2.1)*(u0(1)-0.5*u0(3)); deltag5=0.01*cos(j+h/2)*(-0.2*u0(2)+0.8*u0(3)); deltag6=0.01*cos(j+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag7=0.01*sin(j+h+2.1)*(u0(1)-0.5*u0(3)); deltag8=0.01*cos(j+h)*(-0.2*u0(2)+0.8*u0(3)); deltag9=0.01*cos(j+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); % Methode de Runge Kutta d'ordre 4 l11=-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)); l12=x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)); l13=-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3)); l21=-(x20+(h/2)*l12)*(x30+(h/2)*l13)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l22=(x10+(h/2)*l11)*(x30+(h/2)*l13)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l23=-(1/3)*(x10+(h/2)*l11)*(x20+(h/2)*l12)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l31=-(x20+(h/2)*l22)*(x30+(h/2)*l23)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l32=(x10+(h/2)*l21)*(x30+(h/2)*l23)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l33=-(1/3)*(x10+(h/2)*l21)*(x20+(h/2)*l22)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l41=-(x20+h*l32)*(x30+h*l33)+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)); l42=(x10+h*l31)*(x30+h*l33)+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)); l43=-(1/3)*(x10+h*l31)*(x20+h*l32)+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3)); x1=x10+(h/6)*(l11+2*l21+2*l31+l41); x2=x20+(h/6)*(l12+2*l22+2*l32+l42); x3=x30+(h/6)*(l13+2*l23+2*l33+l43); q1=-(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; q2=-x20*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q3=-sin(j)*(1+0.05*sin(4*j)+0.1*cos(j))+cos(j)*(0.2*cos(4*j)-0.1*sin(j))+0.01*cos(j+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*j); fi1=q1+q2+q3; q4=(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; q5=x10*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q6=(cos(j)^2)*(1+0.05*sin(4*j)+0.1*cos(j))-(sin(j)^2)*(1+0.05*sin(4*j)+0.1*cos(j)); q7=sin(j)*cos(j)*(0.2*cos(4*j)-0.1*sin(j))-0.01*sin(j)*(-0.2*u0(2)+0.8*u0(3)); q8=(0.5^3)*cos(0.5*j)*cos(j)-(0.5^2)*sin(0.5*j)*sin(j)-(0.5^2)*sin(0.5*j)*sin(j)+0.5*cos(0.5*j)*cos(j); fi2=q4+q5+q6+q7+q8; q9=-(1/3)*x20*(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3))); q10=-(1/3)*x10*(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3))); q11=2*sin(j)*cos(j)*(1+0.05*sin(4*j)+0.1*cos(j))+(sin(j)^2)*(0.2*cos(4*j)-0.1*sin(j)); q12=-0.01*sin(j+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); q13=(0.5^3)*cos(0.5*j)*sin(j)+(0.5^2)*sin(0.5*j)*cos(j)+(0.5^2)*sin(0.5*j)*cos(j)+0.5*cos(0.5*j)*sin(j); fi3=q9+q10+q11+q12+q13; fi=[fi1 fi2 fi3]'; gama=[0.01*sin(j+2.1)+1 1.2 -0.005*sin(j+2.1)+1.5;1.5 -0.002*cos(j)+1 0.008*cos(j)+1.2;-0.002*cos(j+1.3)+1.2 -0.01*cos(j+1.3)+1.5 0.007*cos(j+1.3)+1]; qs1=-(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qs2=-(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qs3=-x20*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qs4=-x20*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qs5=-sin(j+(h/2))*(1+0.05*sin(4*(j+(h/2)))+0.1*cos(j+(h/2)))+cos(j+(h/2))*(0.2*cos(4*(j+(h/2)))-0.1*sin(j+(h/2)))+0.01*cos(j+(h/2)+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(j+(h/2))); qs6=-sin(j+h)*(1+0.05*sin(4*(j+h))+0.1*cos(j+h))+cos(j+h)*(0.2*cos(4*(j+h))-0.1*sin(j+h))+0.01*cos(j+h+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(j+h)); qs7=(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qs8=(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qs9=x10*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qs10=x10*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qs11=(cos(j+(h/2))^2)*(1+0.05*sin(4*(j+(h/2)))+0.1*cos(j+(h/2)))-(sin(j+(h/2))^2)*(1+0.05*sin(4*(j+(h/2)))+0.1*cos(j+(h/2))); qs12=(cos(j+h)^2)*(1+0.05*sin(4*(j+h))+0.1*cos(j+h))-(sin(j+h)^2)*(1+0.05*sin(4*(j+h))+0.1*cos(j+h)); qs13=sin(j+(h/2))*cos(j+(h/2))*(0.2*cos(4*(j+(h/2)))-0.1*sin(j+(h/2)))-0.01*sin(j+(h/2))*(-0.2*u0(2)+0.8*u0(3)); qs14=sin(j+h)*cos(j+h)*(0.2*cos(4*(j+h))-0.1*sin(j+h))-0.01*sin(j+h)*(-0.2*u0(2)+0.8*u0(3)); qs15=(0.5^3)*cos(0.5*(j+(h/2)))*cos(j+(h/2))-(0.5^2)*sin(0.5*(j+(h/2)))*sin(j+(h/2))-(0.5^2)*sin(0.5*(j+(h/2)))*sin(j+(h/2))+0.5*cos(0.5*(j+(h/2)))*cos(j+(h/2)); qs16=(0.5^3)*cos(0.5*(j+h))*cos(j+h)-(0.5^2)*sin(0.5*(j+h))*sin(j+h)-(0.5^2)*sin(0.5*(j+h))*sin(j+h)+0.5*cos(0.5*(j+h))*cos(j+h); qs17=-(1/3)*x20*(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3))); qs18=-(1/3)*x20*(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3))); qs19=-(1/3)*x10*(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3))); qs20=-(1/3)*x10*(x10*x3+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3))); qs21=2*sin(j+(h/2))*cos(j+(h/2))*(1+0.05*sin(4*(j+(h/2)))+0.1*cos(j+(h/2)))+(sin(j+(h/2))^2)*(0.2*cos(4*(j+(h/2)))-0.1*sin(j+(h/2))); qs22=2*sin(j+h)*cos(j+h)*(1+0.05*sin(4*(j+h))+0.1*cos(j+h))+(sin(j+h)^2)*(0.2*cos(4*(j+h))-0.1*sin(j+h)); qs23=-0.01*sin(j+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qs24=-0.01*sin(j+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qs25=(0.5^3)*cos(0.5*(j+(h/2)))*sin(j+(h/2))+(0.5^2)*sin(0.5*(j+(h/2)))*cos(j+(h/2))+(0.5^2)*sin(0.5*(j+(h/2)))*cos(j+(h/2))+0.5*cos(0.5*(j+(h/2)))*sin(j+(h/2)); qs26=(0.5^3)*cos(0.5*j+h)*sin(j+h)+(0.5^2)*sin(0.5*(j+h))*cos(j+h)+(0.5^2)*sin(0.5*(j+h))*cos(j+h)+0.5*cos(0.5*(j+h))*sin(j+h); fi11=qs1+qs3+qs5; fi12=qs2+qs4+qs6; fi21=qs7+qs9+qs11+qs13+qs15; fi22=qs8+qs10+qs12+qs14+qs16; fi31=qs17+qs19+qs21+qs23+qs25; fi32=qs18+qs20+qs22+qs24+qs26; gama1=[0.01*sin(j+(h/2)+2.1)+1 1.2 -0.005*sin(j+(h/2)+2.1)+1.5;1.5 -0.002*cos(j+(h/2))+1 0.008*cos(j+(h/2))+1.2;-0.002*cos(j+(h/2)+1.3)+1.2 -0.01*cos(j+(h/2)+1.3)+1.5 0.007*cos(j+(h/2)+1.3)+1]; gama2=[0.01*sin(j+h+2.1)+1 1.2 -0.005*sin(j+h+2.1)+1.5;1.5 -0.002*cos(j+h)+1 0.008*cos(j+h)+1.2;-0.002*cos(j+h+1.3)+1.2 -0.01*cos(j+h+1.3)+1.5 0.007*cos(j+h+1.3)+1]; fir1=[fi11 fi21 fi31]'; fir2=[fi12 fi22 fi32]'; Sopt0=Z20+(P0-V0*inv(H0)*V0')*Z10; v0=-alfa*sign(D*Sopt0); % Methode de Runge Kutta d'ordre 4 k1=Z20; k2=Z20+(h/2)*k1; k3=Z20+(h/2)*k2; k4=Z20+h*k3; Z1=Z10+(h/6)*(k1+2*k2+2*k3+k4); r1=fi+gama*v0; r2=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r1+(P0-V0*inv(H0)*V0')*(Z10+(h/2)*k1))); r3=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r2+(P0-V0*inv(H0)*V0')*(Z10+(h/2)*k2))); r4=fir2-alfa*gama2*sign(D*(Z20+h*r3+(P0-V0*inv(H0)*V0')*(Z10+h*k3))); Z2=Z20+(h/6)*(r1+2*r2+2*r3+r4); u=u0+h*v0; u0=u; Z10=Z1; Z20=Z2; x10=x1; x20=x2; x30=x3; Sopt01=Z20(1)+a0(1)*Z10(1)+a0(4)*Z10(2)+a0(7)*Z10(3); Sopt02=Z20(2)+a0(2)*Z10(1)+a0(5)*Z10(2)+a0(8)*Z10(3); Sopt03=Z20(3)+a0(3)*Z10(1)+a0(6)*Z10(2)+a0(9)*Z10(3); j=j+0.001; X1=[X1 x10]; J=[J j]; S1=[S1 Sopt01]; S2=[S2 Sopt02]; S3=[S3 Sopt03]; end K=j; for k=j:0.001:j+1.499; ct=floor(1500-((k-j)/h)); % Matrice P z1=y1(ct); z2=y2(ct); z3=y3(ct); z4=y4(ct); z5=y5(ct); z6=y6(ct); z7=y7(ct); z8=y8(ct); z9=y9(ct); % Matrice V z11=y10(ct); z12=y11(ct); z13=y12(ct); z14=y13(ct); z15=y14(ct); z16=y15(ct); z17=y16(ct); z18=y17(ct); z19=y18(ct); % Matrice H z21=y19(ct); z22=y20(ct); z23=y21(ct); z24=y22(ct); z25=y23(ct); z26=y24(ct); z27=y25(ct); z28=y26(ct); z29=y27(ct); P=[z1 z4 z7;z2 z5 z8;z3 z6 z9]; V=[z11 z14 z17;z12 z15 z18;z13 z16 z19]; H=[z21 z24 z27;z22 z25 z28;z23 z26 z29]; deltaf1=cos(k)*(1+0.05*sin(4*k)+0.1*cos(k)); deltaf2=sin(k)*cos(k)*(1+0.05*sin(4*k)+0.1*cos(k)); deltaf3=(sin(k)^2)*(1+0.05*sin(4*k)+0.1*cos(k)); deltaf4=cos(k+h/2)*(1+0.05*sin(4*(k+h/2))+0.1*cos(k+h/2)); deltaf5=sin(k+h/2)*cos(k+h/2)*(1+0.05*sin(4*(k+h/2))+0.1*cos(k+h/2)); deltaf6=(sin(k+h/2)^2)*(1+0.05*sin(4*(k+h/2))+0.1*cos(k+h/2)); deltaf7=cos(k+h)*(1+0.05*sin(4*(k+h))+0.1*cos(k+h)); deltaf8=sin(k+h)*cos(k+h)*(1+0.05*sin(4*(k+h))+0.1*cos(k+h)); deltaf9=(sin(k+h)^2)*(1+0.05*sin(4*(k+h))+0.1*cos(k+h)); deltag1=0.01*sin(k+2.1)*(u0(1)-0.5*u0(3)); deltag2=0.01*cos(k)*(-0.2*u0(2)+0.8*u0(3)); deltag3=0.01*cos(k+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag4=0.01*sin(k+(h/2)+2.1)*(u0(1)-0.5*u0(3)); deltag5=0.01*cos(k+h/2)*(-0.2*u0(2)+0.8*u0(3)); deltag6=0.01*cos(k+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag7=0.01*sin(k+h+2.1)*(u0(1)-0.5*u0(3)); deltag8=0.01*cos(k+h)*(-0.2*u0(2)+0.8*u0(3)); deltag9=0.01*cos(k+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); % Methode de Runge Kutta d'ordre 4 l11=-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)); l12=x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)); l13=-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3)); l21=-(x20+(h/2)*l12)*(x30+(h/2)*l13)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l22=(x10+(h/2)*l11)*(x30+(h/2)*l13)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l23=-(1/3)*(x10+(h/2)*l11)*(x20+(h/2)*l12)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l31=-(x20+(h/2)*l22)*(x30+(h/2)*l23)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l32=(x10+(h/2)*l21)*(x30+(h/2)*l23)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l33=-(1/3)*(x10+(h/2)*l21)*(x20+(h/2)*l22)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l41=-(x20+h*l32)*(x30+h*l33)+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)); l42=(x10+h*l31)*(x30+h*l33)+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)); l43=-(1/3)*(x10+h*l31)*(x20+h*l32)+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3)); x1=x10+(h/6)*(l11+2*l21+2*l31+l41); x2=x20+(h/6)*(l12+2*l22+2*l32+l42); x3=x30+(h/6)*(l13+2*l23+2*l33+l43); q1=-(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; q2=-x20*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q3=-sin(k)*(1+0.05*sin(4*k)+0.1*cos(k))+cos(k)*(0.2*cos(4*k)-0.1*sin(k))+0.01*cos(k+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*k); fi1=q1+q2+q3; q4=(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; q5=x10*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q6=(cos(k)^2)*(1+0.05*sin(4*k)+0.1*cos(k))-(sin(k)^2)*(1+0.05*sin(4*k)+0.1*cos(k)); q7=sin(k)*cos(k)*(0.2*cos(4*k)-0.1*sin(k))-0.01*sin(k)*(-0.2*u0(2)+0.8*u0(3)); q8=(0.5^3)*cos(0.5*k)*cos(k)-(0.5^2)*sin(0.5*k)*sin(k)-(0.5^2)*sin(0.5*k)*sin(k)+0.5*cos(0.5*k)*cos(k); fi2=q4+q5+q6+q7+q8; q9=-(1/3)*x20*(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3))); q10=-(1/3)*x10*(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3))); q11=2*sin(k)*cos(k)*(1+0.05*sin(4*k)+0.1*cos(k))+(sin(k)^2)*(0.2*cos(4*k)-0.1*sin(k)); q12=-0.01*sin(k+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); q13=(0.5^3)*cos(0.5*k)*sin(k)+(0.5^2)*sin(0.5*k)*cos(k)+(0.5^2)*sin(0.5*k)*cos(k)+0.5*cos(0.5*k)*sin(k); fi3=q9+q10+q11+q12+q13; fi=[fi1 fi2 fi3]'; gama=[0.01*sin(k+2.1)+1 1.2 -0.005*sin(k+2.1)+1.5;1.5 -0.002*cos(k)+1 0.008*cos(k)+1.2;-0.002*cos(k+1.3)+1.2 -0.01*cos(k+1.3)+1.5 0.007*cos(k+1.3)+1]; qb1=-(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qb2=-(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qb3=-x20*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qb4=-x20*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qb5=-sin(k+(h/2))*(1+0.05*sin(4*(k+(h/2)))+0.1*cos(k+(h/2)))+cos(k+(h/2))*(0.2*cos(4*(k+(h/2)))-0.1*sin(k+(h/2)))+0.01*cos(k+(h/2)+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(k+(h/2))); qb6=-sin(k+h)*(1+0.05*sin(4*(k+h))+0.1*cos(k+h))+cos(k+h)*(0.2*cos(4*(k+h))-0.1*sin(k+h))+0.01*cos(k+h+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(k+h)); qb7=(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qb8=(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qb9=x10*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qb10=x10*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qb11=(cos(k+(h/2))^2)*(1+0.05*sin(4*(k+(h/2)))+0.1*cos(k+(h/2)))-(sin(k+(h/2))^2)*(1+0.05*sin(4*(k+(h/2)))+0.1*cos(k+(h/2))); qb12=(cos(k+h)^2)*(1+0.05*sin(4*(k+h))+0.1*cos(k+h))-(sin(k+h)^2)*(1+0.05*sin(4*(k+h))+0.1*cos(k+h)); qb13=sin(k+(h/2))*cos(k+(h/2))*(0.2*cos(4*(k+(h/2)))-0.1*sin(k+(h/2)))-0.01*sin(k+(h/2))*(-0.2*u0(2)+0.8*u0(3)); qb14=sin(k+h)*cos(k+h)*(0.2*cos(4*(k+h))-0.1*sin(k+h))-0.01*sin(k+h)*(-0.2*u0(2)+0.8*u0(3)); qb15=(0.5^3)*cos(0.5*(k+(h/2)))*cos(k+(h/2))-(0.5^2)*sin(0.5*(k+(h/2)))*sin(k+(h/2))-(0.5^2)*sin(0.5*(k+(h/2)))*sin(k+(h/2))+0.5*cos(0.5*(k+(h/2)))*cos(k+(h/2)); qb16=(0.5^3)*cos(0.5*(k+h))*cos(k+h)-(0.5^2)*sin(0.5*(k+h))*sin(k+h)-(0.5^2)*sin(0.5*(k+h))*sin(k+h)+0.5*cos(0.5*(k+h))*cos(k+h); qb17=-(1/3)*x20*(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3))); qb18=-(1/3)*x20*(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3))); qb19=-(1/3)*x10*(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3))); qb20=-(1/3)*x10*(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3))); qb21=2*sin(k+(h/2))*cos(k+(h/2))*(1+0.05*sin(4*(k+(h/2)))+0.1*cos(k+(h/2)))+(sin(k+(h/2))^2)*(0.2*cos(4*(k+(h/2)))-0.1*sin(k+(h/2))); qb22=2*sin(k+h)*cos(k+h)*(1+0.05*sin(4*(k+h))+0.1*cos(k+h))+(sin(k+h)^2)*(0.2*cos(4*(k+h))-0.1*sin(k+h)); qb23=-0.01*sin(k+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qb24=-0.01*sin(k+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qb25=(0.5^3)*cos(0.5*(k+(h/2)))*sin(k+(h/2))+(0.5^2)*sin(0.5*(k+(h/2)))*cos(k+(h/2))+(0.5^2)*sin(0.5*(k+(h/2)))*cos(k+(h/2))+0.5*cos(0.5*(k+(h/2)))*sin(k+(h/2)); qb26=(0.5^3)*cos(0.5*k+h)*sin(k+h)+(0.5^2)*sin(0.5*(k+h))*cos(k+h)+(0.5^2)*sin(0.5*(k+h))*cos(k+h)+0.5*cos(0.5*(k+h))*sin(k+h); fi11=qb1+qb3+qb5; fi12=qb2+qb4+qb6; fi21=qb7+qb9+qb11+qb13+qb15; fi22=qb8+qb10+qb12+qb14+qb16; fi31=qb17+qb19+qb21+qb23+qb25; fi32=qb18+qb20+qb22+qb24+qb26; gama1=[0.01*sin(k+(h/2)+2.1)+1 1.2 -0.005*sin(k+(h/2)+2.1)+1.5;1.5 -0.002*cos(k+(h/2))+1 0.008*cos(k+(h/2))+1.2;-0.002*cos(k+(h/2)+1.3)+1.2 -0.01*cos(k+(h/2)+1.3)+1.5 0.007*cos(k+(h/2)+1.3)+1]; gama2=[0.01*sin(k+h+2.1)+1 1.2 -0.005*sin(k+h+2.1)+1.5;1.5 -0.002*cos(k+h)+1 0.008*cos(k+h)+1.2;-0.002*cos(k+h+1.3)+1.2 -0.01*cos(k+h+1.3)+1.5 0.007*cos(k+h+1.3)+1]; fir1=[fi11 fi21 fi31]'; fir2=[fi12 fi22 fi32]'; Sopt=Z20+(P-V*inv(H)*V')*Z10; v=-alfa*sign(D*Sopt); % Methode de Runge Kutta d'ordre 4 k1=Z20; k2=Z20+(h/2)*k1; k3=Z20+(h/2)*k2; k4=Z20+h*k3; Z1=Z10+(h/6)*(k1+2*k2+2*k3+k4); r1=fi+gama*v; r2=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r1+(P-V*inv(H)*V')*(Z10+(h/2)*k1))); r3=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r2+(P-V*inv(H)*V')*(Z10+(h/2)*k2))); r4=fir2-alfa*gama2*sign(D*(Z20+h*r3+(P-V*inv(H)*V')*(Z10+k*k3))); Z2=Z20+(h/6)*(r1+2*r2+2*r3+r4); u=u0+h*v; u0=u; Z10=Z1; Z20=Z2; x10=x1; x20=x2; x30=x3; X1=[X1 x10]; K=[K k]; end for i=(j+1.499):0.001:5; Soptf=Z20+(Pf-Vf*inv(Hf)*Vf')*Z10; Soptf1=Z20(1)+af(1)*Z10(1)+af(4)*Z10(2)+af(7)*Z10(3); Soptf2=Z20(2)+af(2)*Z10(1)+af(5)*Z10(2)+af(8)*Z10(3); Soptf3=Z20(3)+af(3)*Z10(1)+af(6)*Z10(2)+af(9)*Z10(3); vf=-alfa*sign(D*Soptf); deltaf1=cos(i)*(1+0.05*sin(4*i)+0.1*cos(i)); deltaf2=sin(i)*cos(i)*(1+0.05*sin(4*i)+0.1*cos(i)); deltaf3=(sin(i)^2)*(1+0.05*sin(4*i)+0.1*cos(i)); deltaf4=cos(i+h/2)*(1+0.05*sin(4*(i+h/2))+0.1*cos(i+h/2)); deltaf5=sin(i+h/2)*cos(i+h/2)*(1+0.05*sin(4*(i+h/2))+0.1*cos(i+h/2)); deltaf6=(sin(i+h/2)^2)*(1+0.05*sin(4*(i+h/2))+0.1*cos(i+h/2)); deltaf7=cos(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); deltaf8=sin(i+h)*cos(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); deltaf9=(sin(i+h)^2)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); deltag1=0.01*sin(i+2.1)*(u0(1)-0.5*u0(3)); deltag2=0.01*cos(i)*(-0.2*u0(2)+0.8*u0(3)); deltag3=0.01*cos(i+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag4=0.01*sin(i+(h/2)+2.1)*(u0(1)-0.5*u0(3)); deltag5=0.01*cos(i+h/2)*(-0.2*u0(2)+0.8*u0(3)); deltag6=0.01*cos(i+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); deltag7=0.01*sin(i+h+2.1)*(u0(1)-0.5*u0(3)); deltag8=0.01*cos(i+h)*(-0.2*u0(2)+0.8*u0(3)); deltag9=0.01*cos(i+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); % Methode de Runge Kutta d'ordre 4 l11=-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)); l12=x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)); l13=-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3)); l21=-(x20+(h/2)*l12)*(x30+(h/2)*l13)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l22=(x10+(h/2)*l11)*(x30+(h/2)*l13)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l23=-(1/3)*(x10+(h/2)*l11)*(x20+(h/2)*l12)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l31=-(x20+(h/2)*l22)*(x30+(h/2)*l23)+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)); l32=(x10+(h/2)*l21)*(x30+(h/2)*l23)+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)); l33=-(1/3)*(x10+(h/2)*l21)*(x20+(h/2)*l22)+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3)); l41=-(x20+h*l32)*(x30+h*l33)+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)); l42=(x10+h*l31)*(x30+h*l33)+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)); l43=-(1/3)*(x10+h*l31)*(x20+h*l32)+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3)); x1=x10+(h/6)*(l11+2*l21+2*l31+l41); x2=x20+(h/6)*(l12+2*l22+2*l32+l42); x3=x30+(h/6)*(l13+2*l23+2*l33+l43); q1=-(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; q2=-x20*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q3=-sin(i)*(1+0.05*sin(4*i)+0.1*cos(i))+cos(i)*(0.2*cos(4*i)-0.1*sin(i))+0.01*cos(i+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*i); fi1=q1+q2+q3; q4=(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; q5=x10*(-(1/3)*x10*x20+deltaf3+deltag3+(1.2*u0(1)+1.5*u0(2)+u0(3))); q6=(cos(i)^2)*(1+0.05*sin(4*i)+0.1*cos(i))-(sin(i)^2)*(1+0.05*sin(4*i)+0.1*cos(i)); q7=sin(i)*cos(i)*(0.2*cos(4*i)-0.1*sin(i))-0.01*sin(i)*(-0.2*u0(2)+0.8*u0(3)); q8=(0.5^3)*cos(0.5*i)*cos(i)-(0.5^2)*sin(0.5*i)*sin(i)-(0.5^2)*sin(0.5*i)*sin(i)+0.5*cos(0.5*i)*cos(i); fi2=q4+q5+q6+q7+q8; q9=-(1/3)*x20*(-x20*x30+deltaf1+deltag1+(u0(1)+1.2*u0(2)+1.5*u0(3))); q10=-(1/3)*x10*(x10*x30+deltaf2+deltag2+(1.5*u0(1)+u0(2)+1.2*u0(3))); q11=2*sin(i)*cos(i)*(1+0.05*sin(4*i)+0.1*cos(i))+(sin(i)^2)*(0.2*cos(4*i)-0.1*sin(i)); q12=-0.01*sin(i+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); q13=(0.5^3)*cos(0.5*i)*sin(i)+(0.5^2)*sin(0.5*i)*cos(i)+(0.5^2)*sin(0.5*i)*cos(i)+0.5*cos(0.5*i)*sin(i); fi3=q9+q10+q11+q12+q13; fi=[fi1 fi2 fi3]'; gama=[0.01*sin(i+2.1)+1 1.2 -0.005*sin(i+2.1)+1.5;1.5 -0.002*cos(i)+1 0.008*cos(i)+1.2;-0.002*cos(i+1.3)+1.2 -0.01*cos(i+1.3)+1.5 0.007*cos(i+1.3)+1]; qd1=-(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qd2=-(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3)))*x30; qd3=-x20*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qd4=-x20*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qd5=-sin(i+(h/2))*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2)))+cos(i+(h/2))*(0.2*cos(4*(i+(h/2)))-0.1*sin(i+(h/2)))+0.01*cos(i+(h/2)+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(i+(h/2))); qd6=-sin(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h))+cos(i+h)*(0.2*cos(4*(i+h))-0.1*sin(i+h))+0.01*cos(i+h+2.1)*(u0(1)-0.5*u0(3))-(0.5^2)*sin(0.5*(i+h)); qd7=(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qd8=(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3)))*x30; qd9=x10*(-(1/3)*x10*x20+deltaf6+deltag6+(1.2*u0(1)+1.5*u0(2)+u0(3))); qd10=x10*(-(1/3)*x10*x20+deltaf9+deltag9+(1.2*u0(1)+1.5*u0(2)+u0(3))); qd11=(cos(i+(h/2))^2)*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2)))-(sin(i+(h/2))^2)*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2))); qd12=(cos(i+h)^2)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h))-(sin(i+h)^2)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h)); qd13=sin(i+(h/2))*cos(i+(h/2))*(0.2*cos(4*(i+(h/2)))-0.1*sin(i+(h/2)))-0.01*sin(i+(h/2))*(-0.2*u0(2)+0.8*u0(3)); qd14=sin(i+h)*cos(i+h)*(0.2*cos(4*(i+h))-0.1*sin(i+h))-0.01*sin(i+h)*(-0.2*u0(2)+0.8*u0(3)); qd15=(0.5^3)*cos(0.5*(i+(h/2)))*cos(i+(h/2))-(0.5^2)*sin(0.5*(i+(h/2)))*sin(i+(h/2))-(0.5^2)*sin(0.5*(i+(h/2)))*sin(i+(h/2))+0.5*cos(0.5*(i+(h/2)))*cos(i+(h/2)); qd16=(0.5^3)*cos(0.5*(i+h))*cos(i+h)-(0.5^2)*sin(0.5*(i+h))*sin(i+h)-(0.5^2)*sin(0.5*(i+h))*sin(i+h)+0.5*cos(0.5*(i+h))*cos(i+h); qd17=-(1/3)*x20*(-x20*x30+deltaf4+deltag4+(u0(1)+1.2*u0(2)+1.5*u0(3))); qd18=-(1/3)*x20*(-x20*x30+deltaf7+deltag7+(u0(1)+1.2*u0(2)+1.5*u0(3))); qd19=-(1/3)*x10*(x10*x30+deltaf5+deltag5+(1.5*u0(1)+u0(2)+1.2*u0(3))); qd20=-(1/3)*x10*(x10*x30+deltaf8+deltag8+(1.5*u0(1)+u0(2)+1.2*u0(3))); qd21=2*sin(i+(h/2))*cos(i+(h/2))*(1+0.05*sin(4*(i+(h/2)))+0.1*cos(i+(h/2)))+(sin(i+(h/2))^2)*(0.2*cos(4*(i+(h/2)))-0.1*sin(i+(h/2))); qd22=2*sin(i+h)*cos(i+h)*(1+0.05*sin(4*(i+h))+0.1*cos(i+h))+(sin(i+h)^2)*(0.2*cos(4*(i+h))-0.1*sin(i+h)); qd23=-0.01*sin(i+(h/2)+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qd24=-0.01*sin(i+h+1.3)*(-0.2*u0(1)-u0(2)+0.7*u0(3)); qd25=(0.5^3)*cos(0.5*(i+(h/2)))*sin(i+(h/2))+(0.5^2)*sin(0.5*(i+(h/2)))*cos(i+(h/2))+(0.5^2)*sin(0.5*(i+(h/2)))*cos(i+(h/2))+0.5*cos(0.5*(i+(h/2)))*sin(i+(h/2)); qd26=(0.5^3)*cos(0.5*i+h)*sin(i+h)+(0.5^2)*sin(0.5*(i+h))*cos(i+h)+(0.5^2)*sin(0.5*(i+h))*cos(i+h)+0.5*cos(0.5*(i+h))*sin(i+h); fi11=qd1+qd2+qd5; fi12=qd2+qd4+qd6; fi21=qd7+qd9+qd11+qd13+qd15; fi22=qd8+qd10+qd12+qd14+qd16; fi31=qd17+qd19+qd21+qd23+qd25; fi32=qd18+qd20+qd22+qd24+qd26; gama1=[0.01*sin(i+(h/2)+2.1)+1 1.2 -0.005*sin(i+(h/2)+2.1)+1.5;1.5 -0.002*cos(i+(h/2))+1 0.008*cos(i+(h/2))+1.2;-0.002*cos(i+(h/2)+1.3)+1.2 -0.01*cos(i+(h/2)+1.3)+1.5 0.007*cos(i+(h/2)+1.3)+1]; gama2=[0.01*sin(i+h+2.1)+1 1.2 -0.005*sin(i+h+2.1)+1.5;1.5 -0.002*cos(i+h)+1 0.008*cos(i+h)+1.2;-0.002*cos(i+h+1.3)+1.2 -0.01*cos(i+h+1.3)+1.5 0.007*cos(i+h+1.3)+1]; fir1=[fi11 fi21 fi31]'; fir2=[fi12 fi22 fi32]'; % Methode de Runge Kutta d'ordre 4 k1=Z20; k2=Z20+(h/2)*k1; k3=Z20+(h/2)*k2; k4=Z20+h*k3; Z1=Z10+(h/6)*(k1+2*k2+2*k3+k4); r1=fi+gama*vf; r2=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r1+(Pf-Vf*inv(Hf)*Vf')*(Z10+(h/2)*k1))); r3=fir1-alfa*gama1*sign(D*(Z20+(h/2)*r2+(Pf-Vf*inv(Hf)*Vf')*(Z10+(h/2)*k2))); r4=fir2-alfa*gama2*sign(D*(Z20+h*r3+(Pf-Vf*inv(Hf)*Vf')*(Z10+h*k3))); Z2=Z20+(h/6)*(r1+2*r2+2*r3+r4); u=u0+h*vf; u0=u; Z10=Z1; Z20=Z2; x10=x1; x20=x2; x30=x3; X1=[X1 x10]; end end save paramx X1 J S1 S2 S3 K plot(X1)

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1 2	Mon probléme je doit trouver x10 , x20 et x30 tendent vers zero mais avec mon programme je ne trouve pas ça, est ce que vous pouvez m'aider.

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Où se situe ton problème exactement ?

Que veux tu dire par programme de commande ?

Donne un peu plus de détails.

Bonjour,


Je veut dire de programme de commande c'est un programme permettant d'appliquer une commande à un système pour le stabilizer à l'état d'équilibre zéro. Lorsque j'execute les deux progrmmes que j'ai envoyé je trouve que la sortie de mon système qui est un vecteur formé par x10, x20 est x30 diverge alors que je doit trouvé que x10, x20 et x30 tendent vers zéros. La commande que j'applique c'est u qui est l'intégrale de v.