Curve Fit Transient Functions using Optimization

I am trying to curve fit test data using optimization. I have 2 functions which characterize the data that are dependent on each other and their previous time steps, similar to what is shown below.

 ydata = csvread('testdata.csv')
 y1(t) = y1(t-1) + a^2 + b -( (c + y2(t-1) ) / d )
 y2(t) = (b*c/a) + ( y1(t-1) - y2(t-1) ) / d )
 err(t) = (y1(t) - ydata(t))^2
 total_err = sum(err)

I am trying to curve fit y1 to the data by minimizing the total_err term by adjusting a, b, c, and d. Would I use fmincon or lsqcurvefit for this? If so, I cannot figure out how to apply them to these equations. Any advice is appreciated.

Answer 1

[Alan Weiss]

Perhaps this example is relevant.

Alan Weiss

MATLAB mathematical toolbox documentation

[Alex R]

Thank you for the response. So I can plug in:

 x(1) = a
x(2) = b
x(3) = c
x(4) = d
y2 = @(x,xdata) (x(2)*x(3)/x(1)) + ( y1(xdata-1) - y2(xdata-1) ) / x(4) )
y1 = @(x,xdata) y1(xdata-1) + x(1)^2 + x(2) -( (x(3) + y2(xdata-1) ) / x(4) )
x0 = [1 1 1 0];
[x,resnorm,~,exitflag,output] = lsqcurvefit(y1,x0,t,y)

But the function still tries to reference itself evaluated at a previous time step. I know the initial value of the function at y1(0), so I calculate the rest by looping. However I am not sure how to capture that effect with an anonymous function.

[Alan Weiss]

You are free to write a full function, with as many conditions as you need to handle edge cases, something like

function z = myfun(x,xdata)
for I = 1:size(xdata,1)
    if I = 1
         % your code here
    else
         % more code here
    end
end

Alan Weiss

MATLAB mathematical toolbox documentation