nonlinear H-infinity control

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jj kena 2014-11-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/162669-nonlinear-h-infinity-control

%the closed-loop system response W=[-0.0367; -0.0327; -0.0333; -0.0762; 0.0883; -0.0093; 503.0411; -9.4101; -45.3581; 0.0006];

x0=[-300 300 5000]'; X(:,1)=x0; h=x2^2/x3; T(1)=0; tf=1; delta_t=0.01; N_t=round(tf/delta_t)+1; r(1)=0; u(1)=0; sum_z=delta_t*((h'*h)+u(1)'*u(1)); w=[70*sin(0); 70*sin(pi/4); 70*cos(0)]; sum_w=delta_t*(w'*w); i=0; for i=2:N_t; x1=X(1,i-1);x2=X(2,i-1); x3=X(3,i-1); f=[x2^2/x3;-x1*x2/x3;x1]; g1=[0;1;0]; g2=[0;-1;0]; DBF= [ 2*x1 0 0 x2 x1 0 x3 0 x1 0 2*x2 0 0 x3 x2 0 0 2*x3 1/x3 0 -x1/x3^2 x2/x3 x1/x3 -x1*x2/x3^2 0 2*x2/x3 -x2^2/x3^2 0 4*x2^3/x3^2 -2*x2^4/x3^3]; uu=-0.5*g2'*DBF'*W; t=delta_t * (i-1); w=[70*sin(0.5*t); 70*sin(0.5*t+pi/4); 70*cos(0.5*t)];

       X(:,i)=X(:,i-1)+delta_t*(f+g2*uu+g1'*w);
       T(i)=t;
       u(i)=uu;
       sum_z=sum_z+delta_t*(h'*h+u(i)'*u(i));
       sum_w=sum_w+delta_t*(w'*w);
       r(i)=sum_z/sum_w;
end
% system states
figure(6)
plot(T,X(1,:),'-',T,X(2,:),'-.',T,X(3,:),'-*');
legend('x_1','x_2','x_3');
%control of the system
figure (7)
plot(T,u,'-');
legend('u');
% gamma with t
figure(8)
plot(T,r,'-');
legend('r_1');