Variational and Dirac structures for interconnected distributed-discrete systems

We present how the interconnection of distributed and discrete systems can be realized within the setting of variational principles and Dirac structures on the Lagrangian side. For the distributed system we focus on the case when the configuration space is an infinite-dimensional vector space and the system is subject to boundary energy flow. A key property of our approach is that it systematically extends the canonical variational and symplectic structures of finite and infinite-dimensional Lagrangian and Hamiltonian mechanics.