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

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 toward 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 toward zero. In an appendix we characterize the class of dissipative Hamiltonian matrices and pencils.

Subjects

differential algebraic equations

dissipativity

port-Hamitonian systems

turnpike properties

DDC Class

530: Physics

Options

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