MATLAB: Linear ODE as a constraint within an milp problem

Question

Good Morning,

I have a syntax question regarding a milp problem that I would like to solve with intlinprog function:

My objective function that I would like to minimize is f = 2 x1 + 3 x2 where x1 and x2 are binary variables.

Furthermore,

y01 = 5 x1 & y02 = 5 x2

where y01 and y02 are the initial conditions used to solve following first order linear ODE system:

dy1/dl = -a0 & dy2/dl = b0

y1 and y2 over whole interval L are calculated by iterational solving of the ODE system using ODE45 (since the parameters a0 and b0 are different on each small interval)

Now I have a constraint which is C sum(y1) + D sum(y2) < 100.

Following documentation it is easy to define the objective function and the binary variables:

f=[2;3];
intcon=1:2

However now I have no idea how to integrate the solving of the ODE routine into the constraint expression.

Can you give some hint?

Thanks!!

Answer 1

Well, I take it that a0, b0, C and D are known constants, so the ODEs have trivial analytical solutions

y1=5*x1-a0*l
y2=5*x2-b0*l

and so the constraint reduces to a simple linear inequality

C*(5*N*x1-a0*sum(l)) + D*(5*N*x2+b0*sum(l))<=100