Parameter estimation with fminsearch and ODE23s

Hi all,

I am trying to write a code to estimate two parameters in a small system of ODEs. The ODEs are

and the output function is , with a and b the parameters to be estimated. The code I have so far is

x0=[0.0510e-9;0.1190e-9];

t1=linspace(0,50,21);
data=1e-9*[0.2376,0.2345,0.2316,0.2238,0.2141,0.2110,0.2140,0.2054,0.2003,0.2006,0.1881...
    0.1917,0.1833,0.1814,0.1768,0.1664,0.1725,0.1623,0.1545,0.1513,0.1581];

p0=[1e3;1e-6];
opts = optimset('TolX',1e-15,'MaxFunEvals',5000,'TolFun',1e-15);
[B,l] = fminsearch(@(p) fit_data_diss(p,t1,x0,data), p0, opts)
B(1)
B(2)

p=[B(1),B(2)];
[t2,y2]= ode23s(@(t,y)dissociation(t,y,p),t1,x0);
Approx=-2*y2(:,1)-y2(:,2)+2*p(2);

figure
hold on
plot(t1,data,'*')
plot(t2,Approx)

function err = fit_data_diss(p,t,x0,dat)                      
[t,ys]=ode23s(@(t,y)dissociation(t,y,p),t,x0);
yr = -2*ys(:,1)-ys(:,2)+2*p(2);
err = norm(dat-yr);
end

function dydt = dissociation(t,y,p)
dydt = zeros(2,1);
dydt(1)=p(1)*y(2);
dydt(2)=p(1)*(p(2)-y(1)-2*y(2));
end

However, when I use the estimated parameters to plot the function it is nowhere near to the data. I have tried reducing the stopping tolerances but that makes no difference. Can anyone please point out what I am doing wrong? Thanks, Carla.

Answer 1

[Matt J]

See here for general guidelines,

https://www.mathworks.com/help/optim/ug/optimizing-a-simulation-or-ordinary-differential-equation.html