Problem in inputting constrains for fmincon with ODE45

I have the following problem:

I am trying to regress a set of parameters of a set of reactions. My reaction rate expressions are formulated as shown below:

R1 = beta(1)*k1*y(1);

R2 = beta(2)*k2*y(2);

R3 = beta(3)*k3*k4*y(1)*y(2);

k1, k2, k3, k4 are all constants fed to the code.

The rate of change of specie y(1) and y(2) are formulated using ode functions

dydz(1) = -R1+R2;

dydz(2) = R3;

these ODEs are implemented in matlab's ode45 solver.

in order to regress the fitting parameters (beta), I am using fmincon to determine the values of these fitting parameters.

Now, my question is:

I have some linear and non-linear constraints on the values of y(1), y(2) that I want to put in the optimisation. but I don't know how to do that. This is because matlab deals with the constraints as function of the optimisation variables (beta(1), beta(2), beta(3)).

Do you have any idea on how to solve this problem??

Thanks

[Torsten]

Since y(1), y(2) are functions of z, you will have to tell us the z-value(s) at which you want to constrain y(1) and y(2).

Best wishes

Torsten.

[Mohamed Al Jamri]

I am solving the problem in the range of zspan = [0:0.01:1]; and I want to constrain y(1) and y(2) at z = 1;

Answer 1

[Torsten]

If you want to set the constraint y1(z=1) <= 3, e.g, you can just set

c(1)=y(end,1)-3.0

in fmincon's "nonlcon" function.

Best wishes

Torsten.

[Mohamed Al Jamri]

I did the following:

function [c,ceq] = nonlcon(y)

ceq = y(end,1)-0.158;

c = [];

end

and in the solve statement i did

@nonlcon

however, I am getting the following error

''index y out of bounds''

any suggestion?

[Torsten]

You get the actual parameters "params" to be fitted handed to nonlcon:

function [c,ceq] = nonlcon(params)

Now with these parameters, solve your differential equations

[T,Y]=ode45(...)

and return

ceq(1) = Y(end,1)-0.158;
c=[];

Best wishes

Torsten.