Parameter estimation using shooting method

Hi All,

I want to do the following,

I have a set of 20 first order differential equations and I want to estimate some of the parameters . I've the following initial and boundary conditions.

The initial conditions of 20 variables (at t=0)

Boundary values of 20 variables (at time , t = 2000s)

Using shooting method , I want to estimate the values of 10 parameters using least square minimization ,using fmincon. The objective function will

minimize the difference between the target(Boundary values of 20 variables (at time , t = 2000s)) and the values obatined at the end of shoot using ode15s.

I'm not sure how to implement this. Could someone help?

I have a function which solves the 10 differential equation using ode15s, how do I proceed after this step?

[Deepa Maheshvare]

Hi All,

I'm going through the example given here,https://in.mathworks.com/help/matlab/math/solve-bvp-with-unknown-parameter.html

However, I'm not sure how the residual is calculated at the boundary (t=2000s)using the function 'mat4bc' given in the above link.

It is explained that ,

"To calculate the residual values, you need to put the boundary conditions into the form g(x,y)=0. "

Could someone explain how this has to be implemented in my example?

I'm trying the following,

The following function computes the residual,

function residual = LQminimization(initialConditions,tSpan,y_SS)
y0 = initialConditions;
[t,y] = ode15s(@myModel,tSpan,y0);
residual= (y[:,end] - y_SS).^2;

I have reached till this point.I'm not sure how to proceed with estimating parameters from here.

Any suggestions?