Control of port-Hamiltonian systems with minimal energy supply

We investigate optimal control of linear port-Hamiltonian systems with constraints, in which one aims to perform a state transition minimal energy supply. Decomposing the space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that set reachable states is bounded w.r.t. subspace. prove problem exhibits turnpike property respect subspace, i.e., for varying initial conditions time horizons trajectories evolve close conservative subspace most time. analyze corresponding steady-state optimization all steady lie conclude this paper by illustrating these results numerical example from mechanics.