Title :An intrinsic optimal control problem for Port Hamiltonian systems and its turnpike behavior.
Abstract: We suggest an intrinsic optimal control problem of (linear) port-Hamiltonian systems in which one aims to perform a state transition with minimal energy supply. We show that the set of reachable states is bounded with respect to a subspace obtained by decomposing the state space into dissipative and non-dissipative (or conservative) subspaces. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons , the optimal state trajectories evolve close to the conservative subspace most of the time. By analyzing the corresponding steady-state optimization problem, we show that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by some simple example and give some extensions to larger classes of systems.