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.

Keywords:

• dissipative PDE system
• inertial manifold
• state estimation
• observer design

AMS Subject Classifications:

• 35R10
• 35R20
• 93B07

Acknowledgements

This publication was made possible by NPRP grant number [4-451-2-168] from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors. This research was also supported in part by NSF 1021203 of United States.

Notes

This paper is dedicated to Professor Wei Lin on his 80th birthday.