  We consider the singular optimal control problem of minimizing the energy
supply of linear dissipative port-Hamiltonian descriptor systems subject to
control and terminal state constraints. To this end, after reducing the problem
to an ODE with feed-through term, we derive an input-state turnpike towards a
subspace for optimal control of generalized port-Hamiltonian ordinary
differential equations. We study the reachability properties of the system and
prove that optimal states exhibit a turnpike behavior with respect to the
conservative subspace. By means of the port-Hamiltonian structure, we show
that, despite control constraints, this turnpike property is global in the
initial state. Further, we characterize the class of dissipative Hamiltonian
matrices and pencils.
