A combinatorial Hopf algebra for nonlinear output feedback control systems

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• 作者：Luis A. Duffaut Espinosa^a ; ^{lduffaut@gmu.edu" class="auth_mail" title="E-mail the corresponding author} ; Kurusch Ebrahimi-Fard^b ; ¹ ; ^{kurusch@icmat.es" class="auth_mail" title="E-mail the corresponding author} ; ^{kurusch.ebrahimi-fard@uha.fr" class="auth_mail" title="E-mail the corresponding author} ; ; W. Steven Gray^c ; ^{sgray@odu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Chen&ndash ; Fliess functional expansion ; Output feedback control system ; Faà ; di Bruno Hopf algebra ; Connected graded Hopf algebra ; Zimmermann's forest formula
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：453
• 期：Complete
• 页码：609-643
• 全文大小：623 K

文摘

In this work a combinatorial description is provided of a Faà di Bruno type Hopf algebra which naturally appears in the context of Fliess operators in nonlinear feedback control theory. It is a connected graded commutative and non-cocommutative Hopf algebra defined on rooted circle trees. A cancellation free forest formula for its antipode is given.