Virtual Lagrangian construction method for infinite-dimensional systems with homotopy operators

This paper presents a general modeling method to construct a virtual Lagrangian for infinite-dimensional systems. If the system is self-adjoint in the sense of the Fretchet derivative, there exists some Lagrangian for a stationary condition of variational problems. A system having such a Lagrangian can be formulated as a field port-Lagrangian system by using a Stokes-Dirac structure on a variational complex. However, it is unknown whether any infinite-dimensional system can be expressed as an Euler-Lagrange equation. Then, we introduce a virtual Lagrangian with a homotopy operator. The virtual Lagrangian defines a self-adjoint subsystem, which is realized by a cancellation of non-self-adjoint error subsystems.