Practical Tracking for Minimum-Phase 1-D Heat Equation With Arbitrary Uniformly Continuous Bounded Reference Signals
成果类型：
Article
署名作者：
Guo, Bao-Zhu; Wang, Ji-Xiao
署名单位：
Zhejiang University of Science & Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
刊物名称：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN/ISSBN：
0018-9286
DOI：
10.1109/TAC.2025.3601009
发表日期：
2026
关键词：
摘要：
In this research, we tackle the output tracking problem for a 1-D, minimum-phase heat equation, a longstanding and challenging issue in the field of partial differential equations. The control input is applied at the boundary, while the regulated output can be situated anywhere within the domain, leading to an inherently ill-posed scenario. First, we present an exponentially convergent tracking algorithm that utilizes tracking error feedback control for reference signals with sufficient smoothness. Subsequently, we propose a practical tracking method for uniformly continuous bounded reference signals, which entails approximating the reference signal with a smooth function. Our numerical simulations offer compelling empirical support for the theoretical findings.