Output controllability in a long-time horizon

Abstract : In this article we consider a linear finite dimensional system. Our aim is to design a control such that the output of the system reach a given target at a final time T > 0. This notion is known as output controllability. We extend this notion to the one of long-time output controllability. More precisely, we consider the question: is it possible to steer the output of the system to some prescribed value in time T > 0 and then keep the output of the system at this prescribed value for all times t > T ? We provide a necessary and sufficient condition for this property to hold. Once the condition is satisfied, one can apply a feedback control that keeps the average fixed during a given time period. We also address the L2 -norm optimality of such controls. We apply our results to (long-time) averaged control problems.
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Submitted on : Wednesday, August 7, 2019 - 5:37:32 PM
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  • HAL Id : hal-01888043, version 2

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Martin Lazar, Jérôme Lohéac. Output controllability in a long-time horizon. 2019. ⟨hal-01888043v2⟩

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