A combinatorial Hopf algebra for nonlinear output feedback control systems

作者：Espinosa Luis A Duffaut; Ebrahimi Fard Kurusch^*; Gray W Steven

来源：Journal of Algebra, 2016, 453: 609-643.

DOI：10.1016/j.jalgebra.2016.01.004

• Chen-Fliess functional expansion
• Output feedback control system
• Faa di Bruno Hopf algebra
• Connected graded Hopf algebra
• Zimmermann's forest formula

In this work a combinatorial description is provided of a Faa 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.

• 出版日期2016-5-1