Time-varying port-representation of dissipative structures with gauge transformations

A distributed-port-Hamiltonian system is a generalized model for passivity-based controls. The system representation has been extended to an infinite-dimensional conservative system derived from variational calculus, which is called a field-port-Lagrangian system. A lot of practical systems for control engineering include dissipative elements; however such a non-conservative structure usually cannot be defined by a variational problem. This paper shows that a system with the dissipative structure can be defined as a time-varying fieldport-Lagrangian system by a gauge transformation. First, we show that the gauge transformation generates a time-dependent Lagrangian density functional that introduces the time-varying port-representation. Next, we present that a class of dissipative systems can be identified with a conservative system possessing an internal irreversible energy flow. Finally, we illustrate an equation of elastic films with viscosity damping with the time-varying port-representation.