论文标题
用于系统识别和机器学习应用程序的陈 - 流利系列的连续性
Continuity of Chen-Fliess Series for Applications in System Identification and Machine Learning
论文作者
论文摘要
模型连续性在系统识别，自适应控制和机器学习等应用中起重要作用。本文提供了足够的条件，在这些条件下，以本地收敛的陈出陈列式系列表示的输入输出系统相对于其生成系列是共同连续的，并且作为操作员以$ L_P $ -SPACE将球映射到$ L_Q $ -SPACE的球，其中$ P $和$ p $和$ Q $是$ Q $是偶发的指示。起点是引入一类称为SILVA空间的拓扑矢量空间，以解决问题，然后采用直接极限的概念来描述收敛。主要连续性结果的证明结合了文献中出现其他形式的连续性的证明要素，以产生预期的结论。
Model continuity plays an important role in applications like system identification, adaptive control, and machine learning. This paper provides sufficient conditions under which input-output systems represented by locally convergent Chen-Fliess series are jointly continuous with respect to their generating series and as operators mapping a ball in an $L_p$-space to a ball in an $L_q$-space, where $p$ and $q$ are conjugate exponents. The starting point is to introduce a class of topological vector spaces known as Silva spaces to frame the problem and then to employ the concept of a direct limit to describe convergence. The proof of the main continuity result combines elements of proofs for other forms of continuity appearing in the literature to produce the desired conclusion.
