Document Type

Article

Publication Date

2017

DOI

10.1137/140997348

Publication Title

SIAM Journal on Control & Optimization

Volume

55

Issue

2

Pages

885-912

Abstract

The general goal of this paper is to identify a transformation group that can be used to describe a class of feedback interconnections involving subsystems which are modeled solely in terms of Chen-Fliess functional expansions or Fliess operators and are independent of the existence of any state space models. This interconnection, called an output affine feedback connection, is distinguished from conventional output feedback by the presence of a multiplier in an outer loop. Once this transformation group is established, three basic questions are addressed. How can this transformation group be used to provide an explicit Fliess operator representation of such a closed-loop system? Is it possible to use this feedback scheme to do system inversion purely in an input-output setting? In particular, can feedback input-output linearization be posed and solved entirely in this framework, i.e., without the need for any state space realization? Last, what can be said about feedback invariants under this transformation group? A final objective of the paper is to describe the Lie algebra of infinitesimal characters associated with the group in terms of a pre-Lie product.

Comments

©2017 Society for Industrial and Applied Mathematics:

"The Author may post the final published version of the Work on the Author's personal web site and on the web server of the Author's institution, provided that proper notice of the Publisher's copyright is included, and that no separate or additional fees are collected for access to or distribution of the work."

Original Publication Citation

Gray, W. S., & Ebrahimi-Fard, K. (2017). SISO output affine feedback transformation group and its Faà di Bruno Hopf algebra. SIAM Journal on Control & Optimization, 55(2), 885-912. doi:10.1137/140997348

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