کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
756520 896188 2011 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Faà di Bruno Hopf algebra for a group of Fliess operators with applications to feedback
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
A Faà di Bruno Hopf algebra for a group of Fliess operators with applications to feedback
چکیده انگلیسی

A Faà di Bruno type Hopf algebra is developed for a group of integral operators known as Fliess operators, where operator composition is the group product. Such operators are normally written in terms of generating series over a noncommutative alphabet. Using a general series expansion for the antipode, an explicit formula for the generating series of the compositional inverse operator is derived. The result is applied to analytic nonlinear feedback systems to produce an explicit formula for the feedback product, that is, the generating series for the Fliess operator representation of the closed-loop system written in terms of the generating series of the Fliess operator component systems. This formula is employed to provide a proof that local convergence is preserved under feedback.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Systems & Control Letters - Volume 60, Issue 7, July 2011, Pages 441–449
نویسندگان
, ,