# Parameter estimation using shooting method

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 got 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 the shooting method, I want to estimate the values of 10 parameters using least squares 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 obtained 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?

Edit: I have a defined afunction that 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?