Thread: Optimal Control question

Dear all,

I have more or less standard optimal control problem with one twist. There is an additional constraint that the control function q(x)=1 when x>=p where p is a parameter. Does anyone know how to write a Hamiltonian out of this or how to apply Pontryagin principle to this problem.

To be specific the problem is something like that

max_{b,q} int (b(x)q(x) dx)
s.t. V'(x)=q(x)f'(x-b(x))
V(x)>=0
V(x)=q(x)f(x-b(x))
q(x)=1 when x>=p.

As I understand without the last line the problem is pretty much standard: q and b are controls, V is state and f is given. But I have no idea how to write a Hamiltonian with the last line.

Thanks in advance!