Optimising parameters in ODE with fminsearch or fmincon and ode15s

I am trying to optimise two parameters, a0 and a1 to minimise Cb at z=2 for the following function:

function dCbdz = myModel(z,Cb,a0,a1)

T=a0+a1.*z;

R= 8.3145;

Ca0 = 0.7;

k1 = 1.37.*10^10.*exp(-75000./(R.*a));

k2 = 1.19.*10^17.*exp(-125000./(R.*a));

dCbdz = 1./(4.*1.37.*10^10.*exp(-75000./(R.*a)).*Ca0.*exp(-4.*.*z)-4.*k2.*Cb)

I've then put my objective function into a separate script:

function obj = myObj(a0,a1)

n = 10;

length = linspace(0,2,n);

Cb0 = 0;

[z,Cb]= ode45(@(z,Cb) myModel(z,Cb,a0,a1),length,Cb0);

Finally, I call the minimisation function

a = fminsearch('myObj',[300 0]);

I get an error of not enough input arguments

Error using myObj (line 6)

Not enough input arguments.

Any help please?

Answer 1

[Stephan]

I had to make some guesses, check how to adapt the code:

a = fminsearch(@myObj,[300 0]);

function obj = myObj(a)  % only one input as vector
a0 = a(1);  % unpack vector a
a1 = a(2);  % unpack vector a
n = 10;
length = [0 n];
Cb0 = 0;
[~,Cb]= ode45(@(z,Cb)myModel(z,Cb,a0,a1),length,Cb0);
obj = sum(Cb);  % you did not make a scalar return to minimze, what should be minimized?
end


function dCbdz = myModel(z,Cb,a0,a1)
T=a0+a1.*z;  % T is unsued
R= 8.3145;
Ca0 = 0.7;
k1 = 1.37.*10^10.*exp(-75000./(R.*a0));  % replaced a with a0 --> correct?
k2 = 1.19.*10^17.*exp(-125000./(R.*a1)); % replaced a with a1 --> correct?
 
dCbdz = 1./(4.*1.37.*10^10.*exp(-75000./(R.*a0)).*Ca0.*exp(-4.*k1.*z)-4.*k2.*Cb);
%                                            ^                 ^  
%                                            |                 |
%                                   replaced a with a0         |
%                                                      your code: exp(-4.*.*z)
end