arXiv subjects

Joel Rosenfeld

Publications and source records attributed to Joel Rosenfeld.

3 recordsLinked to original sources

arXiv2024

Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators

Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature.

math.OC↗

arXiv2018

Verification for Machine Learning, Autonomy, and Neural Networks Survey

This survey presents an overview of verification techniques for autonomous systems, with a focus on safety-critical autonomous cyber-physical systems (CPS) and subcomponents thereof. Autonomy in CPS is enabling by recent advances in artificial intelligence (AI) and machine learning (ML) through approaches such as deep neural networks (DNNs), embedded in so-called learning enabled components (LECs) that accomplish tasks from classification to control. Recently, the formal methods and formal verification community has developed methods to characterize behaviors in these LECs with eventual goals of formally verifying specifications for LECs, and this article presents a survey of many of these recent approaches.

cs.AI↗

arXiv2014

The Sarason Sub-Symbol and the Recovery of the Symbol of Densely Defined Toeplitz Operators over the Hardy Space

While the symbol map for the collection of bounded Toeplitz operators is well studied, there has been little work on a symbol map for densely defined Toeplitz operators. In this work a family of candidate symbols, the Sarason Sub-Symbols, is introduced as a means of reproducing the symbol of a densely defined Toeplitz operator. This leads to a partial answer to a question posed by Donald Sarason in 2008. In the bounded case the Toeplitzness of an operator can be classified in terms of its Sarason Sub-Symbols. This justifies the investigation into the application of the Sarason Sub-Symbols on densely defined operators. It is shown that analytic closed densely defined Toeplitz operators are completely determined by their Sarason Sub-Symbols, and it is shown for a broader class of operators that they extend closed densely defined Toeplitz operators (of multiplication type).

math.FA↗