کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599869 1336826 2013 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Decay rate estimations for linear quadratic optimal regulators
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Decay rate estimations for linear quadratic optimal regulators
چکیده انگلیسی

Let u(t)=−Fx(t)u(t)=−Fx(t) be the optimal control of the open-loop system x′(t)=Ax(t)+Bu(t)x′(t)=Ax(t)+Bu(t) in a linear quadratic optimization problem. By using different complex variable arguments, we give several lower and upper estimates of the exponential decay rate of the closed-loop system x′(t)=(A−BF)x(t)x′(t)=(A−BF)x(t). Main attention is given to the case of a skew-Hermitian matrix A. Given an operator A, for a class of cases, we find a matrix B that provides an almost optimal decay rate.We show how our results can be applied to the problem of optimizing the decay rate for a large finite collection of control systems (A,Bj)(A,Bj), j=1,…,Nj=1,…,N, and illustrate this on an example of a concrete mechanical system. At the end of the article, we pose several questions concerning the decay rates in the context of linear quadratic optimization and in a more general context of the pole placement problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 439, Issue 11, 1 December 2013, Pages 3332–3358
نویسندگان
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