Local Output Feedback Setpoint Control of an Input-Delayed Viscous Burgers' Equation
Résumé
This paper addresses the local output feedback setpoint control of viscous Burgers'-like equations in the presence of large input delays. We first study the case of a viscous Burgers' equation with delayed Neumann boundary control. The boundary measurement is selected as a Dirichlet trace. The control design consists of a predictor feedback that systematically achieves the local exponential stabilization of the plant around the equilibrium point of interest. In the second part of the paper, we extend this procedure to the case of the local stabilization of a viscous Burgers'-like equation defined on a ring (i.e., with periodic boundary conditions). Due to the possible occurrence of eigenvalues of geometric multiplicity two, the control design problem is addressed in the framework of a multi-input multi-output system. This is achieved by considering two delayed distributed inputs, possibly with distinct delays, and two pointwise Dirichlet measurements.
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