Boundary control of a cascade of two parabolic PDEs with different diffusion coefficients

説明

In this paper, a state feedback control law is proposed for boundary coupled two different one-dimensional parabolic partial differential equations (PDEs). The control input is assumed to act only at a boundary of one side. The feedback law is designed based on the backstepping method. As a novelty of this paper, a state transformation involving a `discontinuous' integral kernel is introduced in order to handle the difference of diffusion coefficients. This enables us to develop a well-posed backstepping framework for cascades of parabolic PDEs and an exponentially stabilizing controller is derived. The performance of the proposed controller is also validated by numerical simulation.

収録刊行物

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