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We consider the singular optimal control problem of minimizing the energysupply of linear dissipative port-Hamiltonian descriptor systems subject tocontrol and terminal state constraints. To this end, after reducing the problemto an ODE with feed-through term, we derive an input-state turnpike towards asubspace for optimal control of generalized port-Hamiltonian ordinarydifferential equations. We study the reachability properties of the system andprove that optimal states exhibit a turnpike behavior with respect to theconservative subspace. By means of the port-Hamiltonian structure, we showthat, despite control constraints, this turnpike property is global in theinitial state. Further, we characterize the class of dissipative Hamiltonianmatrices and pencils.

Optimal control of port-Hamiltonian descriptor systems with minimal energy supply