کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9495926 1335200 2005 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Controllability cost of conservative systems: resolvent condition and transmutation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Controllability cost of conservative systems: resolvent condition and transmutation
چکیده انگلیسی
This article concerns the exact controllability of unitary groups on Hilbert spaces with unbounded control operator. It provides a necessary and sufficient condition not involving time which blends a resolvent estimate and an observability inequality. By the transmutation of controls in some time L for the corresponding second-order conservative system, it is proved that the cost of controls in time T for the unitary group grows at most like exp(αL2/T) as T tends to 0. In the application to the cost of fast controls for the Schrödinger equation, L is the length of the longest ray of geometric optics which does not intersect the control region. This article also provides observability resolvent estimates implying fast smoothing effect controllability at low cost, and underscores that the controllability cost of a system is not changed by taking its tensor product with a conservative system.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 218, Issue 2, 15 January 2005, Pages 425-444
نویسندگان
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