Boundary Stabilization and Observation of an Unstable Heat Equation in a General Multi-dimensional Domain
Autor: | Feng, Hongyinping, Lang, Pei-Hua, Liu, Jiankang |
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Rok vydání: | 2021 |
Předmět: | |
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 |
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