Infinite-Dimensional Observers for High-Order Boundary-Controlled Port-Hamiltonian Systems

letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order N = 1. The convergence of the proposed observer depends on the number and location of available boundary measurements. Asymptotic convergence is assured for N = 1, and provided that enough boundary measurements are available, exponential convergence can be assured for the cases N = 1 and N = 2. Furthermore, in the case of partitioned BCPHS with N = 2, such as the Euler-Bernoulli beam, it is shown that exponential convergence can be assured considering less available measurements. The Euler-Bernoulli beam model is used to illustrate the design of the proposed observers and to perform numerical simulations.