Adaptive, Fuzzy Boundary Observer for a Class of Euler-Bernoulli Beam Systems With Uncertainties

In this article, the problem of state estimation for a class of Euler-Bernoulli beam systems is considered, where the state over the length of the beam is estimated using only measurements at the boundary points of the Euler-Bernoulli beam system. In particular, we consider the presence of unknown parameters and unstructured uncertainties that may appear in-domain and at the boundary, which makes the accurate estimation of the system state difficult. The objective of this article is to simultaneously estimate the system state and uncertainties. For unknown parameters, we decouple the estimation of the parameters from the estimation of the system state by means of the appropriate finite-dimensional backstepping-like transformation. On the other hand, we introduce an interval type-2 fuzzy logic system to approximate the unstructured uncertainties that have entered the system domain. Based on the finite-dimensional backstepping-like transformation and an interval type-2 fuzzy logic system, an adaptive boundary observer is designed to simultaneously estimate the system state and the system uncertainties. The results are proved by the Lyapunov stability theory.