Kalantarov, Varga K.Özsarı, TürkerYılmaz, K. Cem2025-02-252025-02-252025-060018-9286https://hdl.handle.net/11693/116801We introduce a finite-dimensional version of backstepping controller design for stabilizing solutions of partial differential equations (PDEs) from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical backstepping controller which uses all (infinitely many) modes. We apply our method to the reaction-diffusion equation, which serves only as a canonical example but the method is applicable also to other PDEs whose solutions can be decomposed into a slow finite-dimensional part and a fast tail, where the former dominates the evolution in large time. One of the main goals is to estimate the sufficient number of modes needed to stabilize the plant at a prescribed rate. In addition, we find the minimal number of modes that guarantee the stabilization at a certain (unprescribed) decay rate. Theoretical findings are supported with numerical solutions.EnglishCC BY 4.0 DEED (Attribution 4.0 International)https://creativecommons.org/licenses/by/4.0/BacksteppingBoundary feedbackReaction-diffusion equationStabilizationArticle10.1109/TAC.2024.35218061558-2523