Pyomo DAE optimal control problem with FREE end points

Question

I use pyomo.dae to solve differential equation optimization I defined a set

m.e = ContinuousSet(bounds=(e0, ef))

But I want ef to be free as variable. It's a flexible end points differential problem. How can I accomplish it?

Answer 1

You change your differential equation

y'(x) = f(x,y(x))

over a flexible interval [e0, ef] to a version over the standard interval [0,1] via

u'(s) = T*f(e0+T*s, u(s))

where now e0 and T=ef-e0 can be treated like any other parameter.