Cheap controls for disturbances compensation in hyperbolic delayed systems

摘要

This work applies to the remediability problem for a class of hyperbolic perturbed systems with constant or time-varying delays. With a convenient choice of input operator (control) and through the observation (output), we show how to remedy the effect of any disturbance f on the considered system. We give the main properties and characterisations of the concept according to the delay. Then, under the appropriate hypothesis, we prove how to find the optimal control ensures the compensation of a disturbance using the corresponding observation only. The usual case of actuators and sensors is examined. An application and numerical results for a one-dimensional wave equation with delay are also presented.