Observer Design for a Class of Semilinear Hyperbolic PDEs With Distributed Sensing and Parametric Uncertainties

• 成果类型: Article
• 署名作者: Holta, Haavard; Aamo, Ole Morten
• 署名单位: Norwegian University of Science & Technology (NTNU)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3050730
• 发表日期: 2022
• 页码: 134-145
• 关键词: Observers; uncertainty; Transmission line measurements; oils; Integrated circuits; Eigenvalues and eigenfunctions; Production; Distributed parameter systems; Adaptive systems; state estimation-observers

摘要

We study a class of heterodirectional semilinear hyperbolic partial differential equations, where the distributed state vector is partially measured. An observer estimating the unmeasured part of the state vector is designed. The design is, for instance, applicable to multiphase 1-D fluid models, where the pressure is measured, but the distributed flow and phase concentrations are not. Furthermore, the observer is extended to systems with parametric uncertainties appearing in the dynamics of the unmeasured part of the state. While required to be linear in the uncertain parameter, the uncertain term may be nonlinear in the state, even in the unmeasured part of the state. Terms of this type appear often in applications and cover, for instance, viscous drag in fluid flow systems. A noteworthy property of the design is that convergence of the state estimate is achieved without requiring persistent excitation. Two example applications are presented, and the design is illustrated in a simulation.