Exact Finite Dimensional Feedback Control via Inertial Manifold Theory with Application to the Chafee–Infante Equation |
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Authors: | Ricardo Rosa |
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Institution: | (1) Departamento de Matemática Aplicada, IM-UFRJ, Caixa Postal 68530, Rio de Janeiro, RJ, C.E.P, 21945-970, Brazil |
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Abstract: | A class of nonlinear parabolic partial differential equations is considered, and an exact finite dimensional feedback control law is designed in order to force the systems to behave in a prescribed way. The feedback law is obtained via inertial manifold theory by reducing the system to finite dimensions. The control achieved is exact, as opposed to approximate, as obtained in a previous work. The result is applied to the Chafee–Infante equation, a one-dimensional scalar reaction-diffusion equation, with distributed control. |
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Keywords: | feedback control inertial manifold |
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