Boundary stabilization and observation of a multi-dimensional unstable heat equation
Abstract
In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is hard to apply to the considered problems. The unstable dynamics of the heat equation are treated by combining the finite-dimensional spectral truncation method and the dynamics compensation method. By introducing additional finite-dimensional actuator/sensor dynamics, the unbounded stabilization/observation turns to be a bounded one. As a result, the controller/observer design becomes more easier. Both the full state feedback stabilizer and the state observer are designed. The exponential stability of the closed-loop and the wellposedness of the observer are obtained.
Keywords
Cite
@article{arxiv.2203.12847,
title = {Boundary stabilization and observation of a multi-dimensional unstable heat equation},
author = {Yusen Meng and Hongyinping Feng},
journal= {arXiv preprint arXiv:2203.12847},
year = {2022}
}
Comments
16 pages