Nonlinear Observer Design for a Nonlinear Cable/String FEM Model using Contraction Theory

Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/ string FEM (Finite Element Method) model. The cable model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable configuration. It is shown that the estimated configuration converges exponentially to the actual configuration. Numerical results and simulations are shown to be in agreement with the theoretical results.