Inertial manifold and state estimation of dissipative nonlinear PDE systems

Abstract

In this paper, we study the state estimation problem of dissipative PDE systems that possess inertial manifolds. We show that if a sufficient large number of finite modes are observable, then an observer can be constructed to estimate the state of the PDE system. The convergence of the corresponding error dynamics is exponential and global, and the convergent rate is identified. A numerical example is provided to illustrate the theoretical result of the proposed approach.