Implicit Representation for Passivity-Based Boundary Controls

This paper derives a standard system representation for passivity-based boundary controls of Euler-Lagrange equations, called a distributed port-Lagrangian (DPL) system from implicit Lagrangian representations and the multi-symplectic instantaneous formalism. The DPL system is a local representation of implicit Lagrangian systems extended for field equations. First, we extend an induced Dirac structure to multi-symplectic instantaneous systems by defining a Stokes-Dirac differential and a field implicit Lagrangian system. Second, the DPL system is derived from the extended field implicit Lagrangian systems. Finally, we define passivity-based boundary controls based on a power balance equation of DPL systems.