Boundary Output Feedback Stabilization of Nonlinear Diffusion Equations
Résumé
This paper studies the problem of output feedback stabilization of a nonlinear diffusion equation, generally referred to as the generalized porous media equation. This equation occurs in a number of physical phenomena involving fluid flow, heat transfer or nonlinear diffusion. The generalized porous media equation differs from classical reaction-diffusion equations due to the presence of a nonlinear version of the Laplacian operator. This nonlinearity induces numerous challenges in terms of stability assessment and control design. In this context, the present paper reports one of the very first contributions regarding the output feedback control of the porous media equation. The reported approach takes advantage of the monotonicity property of the nonlinearity and adopts a perturbation-based approach by leveraging spectral reduction methods.
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