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arXiv · 2309.02196

Finite dimensional backstepping controller design

Varga Kalantarov·Türker Özsarı·Kemal Cem Yılmaz
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Abstract

We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of 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.

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Varga Kalantarov, Türker Özsarı, Kemal Cem Yılmaz. 2023-09-05. Finite dimensional backstepping controller design. https://arxiv.org/abs/2309.02196

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