clear all; close all; clc;
a1=0.2;a2=0.3;
omega1=5;omega2=4;
G=1;C12=0.01;C21=0.02;
dt=0.01;
x1(1)=0.5;
y1(1)=0.5;
x2(1)=0.5;
y2(1)=0.5;
for i=2:1000
x1(i)=x1(i-1)+((a1-x1(i-1)^2-y1(i-1)^2)*x1(i-1)-omega1*y1(i-1)+G*C12*(x2(i-1)-x1(i-1)))*dt;
y1(i)=y1(i-1)+((a1-x1(i-1)^2-y1(i-1)^2)*y1(i-1)+omega1*x1(i-1)+G*C12*(y2(i-1)-y1(i-1)))*dt;
x2(i)=x2(i-1)+((a2-x2(i-1)^2-y2(i-1)^2)*x2(i-1)-omega2*y2(i-1)+G*C21*(x1(i-1)-x2(i-1)))*dt;
y2(i)=y2(i-1)+((a2-x2(i-1)^2-y2(i-1)^2)*y2(i-1)+omega2*x2(i-1)+G*C21*(y1(i-1)-y2(i-1)))*dt;
end
N_measurements=31;
N_basis=31;
index=randi([100,999],1,N_measurements);
Xdot1=zeros([1,N_measurements]);
Ydot1=zeros([1,N_measurements]);
Xdot2=zeros([1,N_measurements]);
Ydot2=zeros([1,N_measurements]);
for ni=1:N_measurements
Xdot1(ni)=(x1(index(ni)+1)-x1(index(ni)))/dt;
Ydot1(ni)=(y1(index(ni)+1)-y1(index(ni)))/dt;
Xdot2(ni)=(x2(index(ni)+1)-x2(index(ni)))/dt;
Ydot2(ni)=(y2(index(ni)+1)-y2(index(ni)))/dt;
end
M=zeros([N_measurements,N_basis]);
for i=1:N_measurements
for j=1:N_basis
if j==1
M(i,j)=1;
elseif j==2
M(i,j)=x1(index(i));
elseif j==3
M(i,j)=y1(index(i));
elseif j==4
M(i,j)=x2(index(i));
elseif j==5
M(i,j)=y2(index(i));
elseif j==6
M(i,j)=x1(index(i))^2;
elseif j==7
M(i,j)=x2(index(i))^2;
elseif j==8
M(i,j)=y1(index(i))^2;
elseif j==9
M(i,j)=y2(index(i))^2;
elseif j==10
M(i,j)=x1(index(i))*x2(index(i));
elseif j==11
M(i,j)=x1(index(i))*y1(index(i));
elseif j==12
M(i,j)=x1(index(i))*y2(index(i));
elseif j==13
M(i,j)=x2(index(i))*y1(index(i));
elseif j==14
M(i,j)=x2(index(i))*y2(index(i));
elseif j==15
M(i,j)=y1(index(i))*y2(index(i));
elseif j==16
M(i,j)=x1(index(i))^3;
elseif j==17
M(i,j)=y1(index(i))^3;
elseif j==18
M(i,j)=x2(index(i))^3;
elseif j==19
M(i,j)=y2(index(i))^3;
elseif j==20
M(i,j)=x1(index(i))^2*x2(index(i));
elseif j==21
M(i,j)=x1(index(i))^2*y1(index(i));
elseif j==22
M(i,j)=x1(index(i))^2*y2(index(i));
elseif j==23
M(i,j)=x2(index(i))^2*x1(index(i));
elseif j==24
M(i,j)=x2(index(i))^2*y1(index(i));
elseif j==25
M(i,j)=x2(index(i))^2*y2(index(i));
elseif j==26
M(i,j)=y1(index(i))^2*x1(index(i));
elseif j==27
M(i,j)=y1(index(i))^2*x2(index(i));
elseif j==28
M(i,j)=y1(index(i))^2*y2(index(i));
elseif j==29
M(i,j)=y2(index(i))^2*x1(index(i));
elseif j==30
M(i,j)=y2(index(i))^2*x2(index(i));
else
M(i,j)=y2(index(i))^2*y1(index(i));
end
end
end
Norms=zeros([1,N_basis]);
for j=1:N_basis
Norms(j)=norm(M(:,j));
end
for i=1:N_measurements
for j=1:N_basis
M(i,j)=M(i,j)/Norms(j);
end
end
lambda=0.001;
Xdot1=Xdot1';
cd 'E:\MATLAB\bin\cvx\cvx'
cvx_setup
cvx_begin
variable ksaix1(31);
minimize(norm(M*ksaix1-Xdot1)+ lambda*norm(ksaix1,1));
cvx_end
Ydot1=Ydot1';
cvx_setup
cvx_begin
variable ksaiy1(31);
minimize(norm(M*ksaiy1-Ydot1)+ lambda*norm(ksaiy1,1));
cvx_end
Xdot2=Xdot2';
cvx_setup
cvx_begin
variable ksaix2(31);
minimize(norm(M*ksaix2-Xdot2)+ lambda*norm(ksaix2,1));
cvx_end
Ydot2=Ydot2';
cvx_setup
cvx_begin
variable ksaiy2(31);
minimize(norm(M*ksaiy2-Ydot2)+ lambda*norm(ksaiy2,1));
cvx_end
for j=1:N_basis
ksaix1(j)=ksaix1(j)/Norms(j);
ksaiy1(j)=ksaiy1(j)/Norms(j);
ksaix2(j)=ksaix2(j)/Norms(j);
ksaiy2(j)=ksaiy2(j)/Norms(j);
end
ksaix1
ksaiy1
ksaix2
ksaiy2
figure
hold on
plot(x1,'r')
plot(x2,'g')
title('a1 = 0.2','Observation 1');
Error using title (line 21)
Incorrect number of input arguments
Error in Two_Coupled (line 165)
title('a1 = 0.2','Observation 1');
