Generating Series for Networks of Chen-Fliess Series

Combining Learning and Model Based Control via Discrete-Time Chen-Fliess Series

A learning control system is presented suitable for control affine nonlinear plants based on discrete-time Chen-Fliess series and capable of incorporating knowledge of a given physical model. The underlying noncommutative algebraic and combinatorial structures needed to realize the multivariable case are also described. The method is demonstrated using a two-input, two-output Lotka-Volterra system.

Additive Networks of Chen-Fliess Series: Local Convergence and Relative Degree

Given an additive network of input-output systems where each node of the network is modeled by a locally convergent Chen-Fliess series, two basic properties of the network are established. First, it is shown that every input-output map between a given pair of nodes has a locally convergent Chen-Fliess series representation. Second, sufficient conditions are given under which the input-output map between a pair of nodes has a well defined relative degree as defined by its generating series. This analysis leads to the conclusion that this relative degree property is generic in a certain sense.

参数依赖的 Chen--Fliess 级数及其非递归互连

Parameter Dependent Chen--Fliess Series and Their Nonrecursive Interconnections

引入系数取自非交换环的参数依赖 Chen--Fliess 级数，证明其可表示偏微分方程 Cauchy 初值问题的形式解以刻画分布控制系统输入-输出映射，并验证其在非递归互连下的封闭性。

基于Chen-Fliess级数的神经ODE的Rademacher复杂度

Rademacher Complexity of Neural ODEs via Chen-Fliess Series

本研究利用Chen–Fliess级数将连续深度神经ODE构建为单层无限宽网络，推导了这类ODE模型的Rademacher复杂度简洁表达式，给出特定系统的界实例并展望后续工作。

Formal Power Series Approach to Nonlinear Systems with Additive Static Feedback

The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and an additive static output feedback is applied. The first step is to consider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback …

Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections

This paper has two main objectives. The first is to introduce a notion of entropy that is well suited for the analysis of nonlinear input-output systems that have a Chen-Fliess series representation. The latter is defined in terms of its generating series over a noncommutative alphabet. The idea is to assign an entropy to a generating series as an element of a graded vector space. The second objective is to describe the entropy of generating series originating from interconnected systems of Chen-Fliess series that arise in the context of control theory. It is shown that one set of interconnect…