Abstract
We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems. We study the reachability properties of the system and prove that optimal states exhibit a turnpike behavior with respect to the conservative subspace. Further, we derive a input-state turnpike towards a subspace for optimal control of port-Hamiltonian ordinary differential equations with a feed-through term and a turnpike property for the corresponding adjoint states towards zero. In an appendix we characterize the class of dissipative Hamiltonian matrices and pencils.
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