On the use of structural invariants for the distributed control of infinite dimensional port-Hamitonian systems

In this paper the control by immersion and structural invariants is extended to the distributed control of infinite dimensional port-Hamiltonian systems defined on a 1D spatial domain. The main novelty lies in fact that the structural invariants are not used to shape the closed loop energy function but to modify the closed loop structure of the system by an appropriate choice of the controller structure. In particular it is shown that in the fully actuated case, this control strategy allows to transform an hyperbolic system composed of two conservation laws into a parabolic one. This work is illustrated on the example of the wave equation but can be easily generalised to a large class of systems encompassing vibrating strings and beam equations.