Control by interconnection beyond the dissipation obstacle of finite and infinite dimensional port-Hamiltonian systems

By exploiting the properties of the geometric structure of a port-Hamiltonian system, a general methodology for the definition of a new control port that allows to solve the so-called “dissipation obstacle” within the control by interconnection framework is discussed. This approach can be applied to a large class of port-Hamiltonian systems, both in the lumped, and in the distributed parameter cases. It is also shown how the limitations of the control by interconnection and energy-shaping via Casimir generation can be removed by interconnecting the controller to a different control port, i.e. how it is possible to compute a new passive output that is instrumental for removing the intrinsic constraints imposed by the dissipative structure of the system.