Nonlinear boundary control with gain scheduled control for the porous elastic system

Abstract

In this paper, nonlinear boundary controls associated with two control gain for a one-dimensional continuous porous elastic system are designed, with the primary goal of uniformly stabilizing the model. The nonlinear boundary controllers were designed based on the spillover effect generated by high-frequency problems that generate so-called spurious oscillations. The existence and uniqueness of the solutions are proven using the Galerkin approximation method with a special basis constructed using the Gram-Schmidt process. Uniform stabilization is achieved using the method introduced by Lasiecka-Tataru.

Keywords

Galerkin method / porous elastic materials / uniform decay rates

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