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- W3161330240 abstract "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 <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$2 times 2$</tex-math></inline-formula> 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." @default.
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- W3161330240 date "2022-05-01" @default.
- W3161330240 modified "2023-10-07" @default.
- W3161330240 title "Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE" @default.
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- W3161330240 doi "https://doi.org/10.1109/tac.2021.3080503" @default.
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