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Full-Text Articles in Engineering
Continuity Of Formal Power Series Products In Nonlinear Control Theory, W. Steven Gray, Mathias Palmstrøm, Alexander Schmeding
Continuity Of Formal Power Series Products In Nonlinear Control Theory, W. Steven Gray, Mathias Palmstrøm, Alexander Schmeding
Electrical & Computer Engineering Faculty Publications
Formal power series products appear in nonlinear control theory when systems modeled by Chen–Fliess series are interconnected to form new systems. In fields like adaptive control and learning systems, the coefficients of these formal power series are estimated sequentially with real-time data. The main goal is to prove the continuity and analyticity of such products with respect to several natural (locally convex) topologies on spaces of locally convergent formal power series in order to establish foundational properties behind these technologies. In addition, it is shown that a transformation group central to describing the output feedback connection is in fact an …
Entropy Of Generating Series For Nonlinear Input-Output Systems And Their Interconnections, W. Steven Gray
Entropy Of Generating Series For Nonlinear Input-Output Systems And Their Interconnections, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
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 interconnections can …
A Formal Power Series Approach To Multiplicative Dynamic And Static Output Feedback, Venkatesh Subbarao Guggilam
A Formal Power Series Approach To Multiplicative Dynamic And Static Output Feedback, Venkatesh Subbarao Guggilam
Electrical & Computer Engineering Faculty Publications
The goal of the paper is two-fold. The first of which is to derive an explicit formula to compute the generating series of a closed-loop system when a plant, given in a Chen-Fliess series description is in multiplicative output feedback connection with another system given in Chen-Fliess series description. In addition, the multiplicative dynamic output feedback connection has a natural interpretation as a transformation group acting on the plant. The second of the two-part goal of this paper is same as the first part albeit when the Chen-Fliess series in the feedback is replaced by a memoryless map, so called …
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 …
Siso Output Affine Feedback Transformation Group And Its Faá Di Bruno Hopf Algebra, W. Steven Gray, Kurusch Ebrahimi-Fard
Siso Output Affine Feedback Transformation Group And Its Faá Di Bruno Hopf Algebra, W. Steven Gray, Kurusch Ebrahimi-Fard
Electrical & Computer Engineering Faculty Publications
The general goal of this paper is to identify a transformation group that can be used to describe a class of feedback interconnections involving subsystems which are modeled solely in terms of Chen-Fliess functional expansions or Fliess operators and are independent of the existence of any state space models. This interconnection, called an output affine feedback connection, is distinguished from conventional output feedback by the presence of a multiplier in an outer loop. Once this transformation group is established, three basic questions are addressed. How can this transformation group be used to provide an explicit Fliess operator representation of …
On The Radius Of Convergence Of Interconnected Analytic Nonlinear Input-Output Systems, Makhin Thitsa, W. Steven Gray
On The Radius Of Convergence Of Interconnected Analytic Nonlinear Input-Output Systems, Makhin Thitsa, W. Steven Gray
Electrical & Computer Engineering Faculty Publications
A complete analysis is presented of the radii of convergence of the parallel, product, cascade and feedback interconnections of 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 for the coefficients of the generating series for the subsystems, the radius of convergence of each interconnected system is computed assuming the subsystems are either all locally convergent or all globally convergent. In the process of deriving the radius of …