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Full-Text Articles in Engineering
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray
Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
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 static output feedback is applied. The first step is to reconsider 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 Hopf algebra used to describe dynamic output …
Continuity Of Chen-Fliess Series For Applications In System Identification And Machine Learning, Rafael Dahmen, W. Steven Gray, Alexander Schmeding
Continuity Of Chen-Fliess Series For Applications In System Identification And Machine Learning, Rafael Dahmen, W. Steven Gray, Alexander Schmeding
Electrical & Computer Engineering Faculty Publications
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 …