Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE

• 成果类型: Article
• 署名作者: Chen, Stephen; Vazquez, Rafael; Krstic, Miroslav
• 署名单位: University of California System; University of California San Diego; University of Sevilla
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3080503
• 发表日期: 2022
• 页码: 2389-2404
• 关键词: Backstepping; Distributed parameter systems; multiple input; partial differential equations (PDE)

摘要

We present a novel methodology for designing output-feedback backstepping bilateral boundary controllers for an unstable 1D diffusion-reaction partial differential equation (PDE) with spatially varying reaction. Using folding transforms the parabolic PDE into a 2 x 2 coupled PDE system with coupling through compatibility conditions. We apply a two-tiered backstepping approach, where the invertibility of the transformations guarantees the state-feedback controllers exponentially stabilize the trivial solution of the PDE system. A state observer is also designed for two collocated measurements at an arbitrary interior point, generating exponentially stable state estimates. The output feedback control law is formulated by composing the independently designed state-feedback controller with the observer, and the resulting dynamic feedback is shown to stabilize the trivial solution. Some numerical analysis on how the selection of these points affect the responses of the controller and observer are discussed, with simulations illustrating various choices of folding points and their effect on the stabilization in different performance indexes.