engleski

Output controllability in a long time horizon

In this article we consider a linear nite dimensional system. Our aim is to design a control such that the output of the system reach a given target at a nal 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 sucient condition for this property to hold. Once the condition is satis ed, one can apply a feedback control that keeps the average xed 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.

output controllability ; controlled invariant subspace ; linear optimal control ; open-loop control systems ; averaged control.

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