How do I use the lsqcurvefit to find the best fit for my data?

Due to the fact that I am very new to MatLab, I am attempting to use the built in tools of MatLab, so please help me understand the problem.

So I am currently working on modelling a kinetic reaction, and I am using ODE23t to solve the differential equations, giving me an output I can plot against the data I have collected. How can I use lsqcurvefit to match the theoretical curve more closely with the experimental curve obtained?

Here is an idea of what I have used:

time=HaPer(:,1);
absorbance=HaPer(:,2);

tstart=time(1);
tend=time(end);
tinterval=(time(2)-time(1));
tspan=tstart:1:tend;

iconc=[0.00001,0.0001,0,0,0,0];

k1=50000;k2=100;k3=0.3;k4=0.1;

The k(n) variables above are estimates. Now I added a function m file in the equation

function [dCONCdt]=HaemPeroxide(I,D)

global k1 k2 k3 k4

A=D(1);
B=D(2);
C=D(3);
E=D(4);

dCONCdt=[-k1*A*B+k2*C;
    -k1*A*B+k2*C;
    k1*A*B-k2*C-k3*C;
    k3*C;
    k3*C;
    k4*E];

After which I use the ODE function to solve the differential equations

[T,CONCout]=ode23t('HaemPeroxide',tspan,iconc);

ext=[45635.167,0,0,0,0,0];

A=CONCout(:,1)*ext(1);

% Now I plot the two graphs against one another

hold off;
plot(time, absorbance)

hold on;
plot(time, A)

The corresponding graph shows that the two data sets does not match, and I want to try matching the theoretical data to the experimental data with lsqcurvefit by adapting the k(n) values. As I understand it, you need a function fun(x0, xdata) and your ydata. In my case, what would x0, xdata, and ydata represent? And can I use my function for 'fun', or is a different function setup required?

Answer 1

[Matt J]

 xdata=time;
 ydata=absorbance;
 x0 = k; %your initial estimate

For fun, you must write a function A=fun(k,time) that takes an arbitrary guess for the k vector as input and returns the corresponding A as output. It might also be a good idea to read this documentation which is specifically about using the Optimization Toolbox with ODEs.

Answer 2

[Star Strider]

If you want to fit your differential equation to your data, see Monod kinetics and curve fitting (link) for a relevant example.