Boundary Stabilization and Observation of an Unstable Heat Equation in a General Multi-dimensional Domain

Autor:	Feng, Hongyinping, Lang, Pei-Hua, Liu, Jiankang
Rok vydání:	2021
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Analysis of PDEs 93C05 93B52 47A62
Druh dokumentu:	Working Paper
Popis:	In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed dynamics compensation approach. In contrast to the unstable one-dimensional partial differential equation (PDE), such as the transport equation, wave equation and the heat equation, that can be treated by the well-known PDE backstepping method, stabilization of unstable PDE in a general multi-dimensional domain is still a challenging problem. We treat the stabilization and observation problems separately. A dynamical state feedback law is proposed firstly to stabilize the unstable heat equation exponentially and then a state observer is designed via a boundary measurement. Both the stability of the closed-loop system and the well-posedness of the observer are proved. Some of the theoretical results are validated by the numerical simulations. Comment: 23 pages,8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.02492 Zobrazit plný text záznamu View this record from Arxiv