Continuity of Chen-Fliess series for applications in system identification and machine learning
Peer reviewed, Journal article
MetadataShow full item record
Original versionDahmen, R., Gray, W. S. & Schmeding, A. (2021). Continuity of Chen-Fliess series for applications in system identification and machine learning. IFAC-PapersOnLine, 54(9), 231-238. doi: 10.1016/j.ifacol.2021.06.080
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 Lp-space to a ball in an Lq-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.