How do I optimize my code with respect to 4 variables (x_1 x_3 k1 k2 k3)?

%%Parameters
format short
% Constants
rho=1.225;
U=170;
s=1;
c=0.5;
c_2=1;
b=0.5*c;
m=5;
I_CG=0.05;
m_p=0.5;
% x_p=(0:0.01:c);
zero=[0 0; 0 0];
% Variables
x_g=0.5*c;
x_ac=0.25*c;
x_1=0.1*c;
x_3=0.7*c;
q=0.5*rho*u^2;
c_2=1;
%x_1 x_3 k1 k2 k3 have to changed in order to result in the highest u;
%k1+ k2+ k3 <30000

for u = [0:1:75]
M=[ m   -m*(x_ac - x_g);  -m*(x_ac - x_g)       I_CG + m*(x_ac - x_g)^2  ];
E=[k1 + k2 + k3     k1*(x_1 - x_ac) + k3*(x_3 - x_ac); k1*(x_1 - x_ac) + k3*(x_3 - x_ac)  k1*(x_1 - x_ac)^2 + k3*(x_3 - x_ac)^2];
B=[1+c_2/(pi*s*c*rho) c/2; 0 c^2/16];
Bbar=pi*s*c*rho*[B];
K=[0 1; 0 0];
Kbar=pi*s*c*rho*[K];
A=[[M] u*[Bbar];[zero] [M]];
C=[[zero] [E]+u^2*[Kbar] ; -[M] [zero] ];
c_2;
u;
lambda=eig(C,-A);
   if any(lambda>0) 
   break 
   end 
u

[Walter Roberson]

I do not understand?

You define a variable U, but you do not use it.

On the line

q=0.5*rho*u^2;

you use u before having defined it.

Your comment says,

%x_1 x_3 k1 k2 k3 have to changed in order to result in the highest u;

but you do

for u = [0:1:75]

which changes u instead of calculating u from those 5 parameters ??

[Alex M]

It is an iterative process, a random velocity is being inputed into the system where my code checks its stability eigenvalues eig(C,-A), if any of the eigenvalues in the 4by1 matrix are positive then flutter speed has occurred and the loop terminated giving me the highest value before such flutter speed occurs. What i want is to be able to run as many iteration as possible before the loop breaks.

[Alex M]

u velocities are being tested, and the best combination of the x_1 x_3 k1 k2 k3 will give me the greatest u velocity before the code reads a positive value in the eigenvector.

[Walter Roberson]

Okay.

I do not observe anything that indicates how those five variables are to be changed as you go?