Brayton-Moser formulation of high-order distributed port-Hamiltonian systems with one-dimensional spatial domain

For a class of distributed port-Hamiltonian systems with dissipation characterised by high-order differential operators, one-dimensional domain, and boundary actuation and sensing, an equivalent Brayton-Moser formulation is obtained. The result is that the state evolution is described by a gradient equation with respect to a storage function, the "mixed-potential," that has the dimensions of power. This is the main difference with respect to the port-Hamiltonian form, where the dynamic depends on the derivatives up to a certain order and with respect to the spatial coordinate of the gradient of the Hamiltonian function, i.e. of the total energy. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.