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A common representation for the input-output map of a nonlinear control system is the Chen-Fliess functional series or Fliess operator. The objective of this paper is to further develop a generalization of this class of operators, so called fractional Fliess operators. These are functional series whose iterated integrals are defined in terms of fractional integrals and where the series coefficients...
A common way to represent a nonlinear input-output system in control theory is via a Chen-Fliess functional expansion or Fliess operator. The general goal of this paper is to describe how to approximate Fliess operators with iterated sums and to provide accurate error bounds for two different scenarios, one where the series coefficients are growing at a local convergence rate, and the other where...
A complete analysis is presented of the radius of convergence of the cascade connection of two analytic nonlinear input-output systems represented as Fliess operators. Such operators are described by convergent functional series, which are indexed by words over a noncommutative alphabet. Their generating series are therefore specified in terms of noncommutative formal power series. Given growth conditions...
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. 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...
The main objective of this paper is to describe a class of functional series expansions, known as Fliess operators, which admit inputs from a ball in an Lp space as well as Poisson random processes. It is shown that a continuous-time switched input-affine nonlinear system with a Poisson switching signal can be represented as a Fliess operator, and that the underlying combinatorics can be used to obtain,...
This paper describes the radius of convergence of a self-excited feedback interconnection of two locally convergent Fliess operators. A fundamental and achievable positive lower bound on the radius of convergence for the composite system is computed.
Fliess operators have been an object of study in connection with nonlinear systems acting on deterministic inputs since the early 1970's. They describe a broad class of nonlinear input-output maps using a type of functional series expansion. But in most applications, a system's inputs have noise components. It has been shown that the notion of a Fliess operator can be generalized to admit a class...
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