Output controllability in a long-time horizon. (March 2020)

• Record Type: Journal Article
• Authors: Lazar, Martin; Lohéac, Jérôme
• Is Part Of: Automatica. Volume 113(2020)
• Publication Date: 2020-03
• Subjects: Output controllability -- Controlled invariant subspace -- Linear optimal control -- Open-loop control systems -- Averaged control; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108762
• Languages: English
• ISSNs: 0005-1098

Abstract

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 L 2 -norm optimality of such controls. We apply our results to (long-time) averaged control problems .