110 citations · 337 across the 24 of their papers we have counts for
29 papers
Integral Formulation of QENDy for Robust Nonlinear System Identification
Nikhil Saran, Sushant Pokhriyal, Stefan Klus +2
This manuscript proposes an integral formulation of the newly defined quadratic embedding method for identifying nonlinear systems (QENDy). In the original algorithm, trajectory da…
A Dynamic Mode Decomposition Approach to Parameter Identification
Moad Abudia, Opeyemi Owolabi, Joel A. Rosenfeld +1
This paper develops a data-driven algorithm for simultaneous system and parameter identification in control-affine nonlinear systems. Parameter identification is achieved by traini…
Restricted Liouville Operator for the study of Non-Analytic Dynamics within the Disk
Sushant Pokhriyal, Joel A Rosenfeld
The study of Koopman and Liouville operators over reproducing kernel Hilbert spaces (RKHSs) has been gaining considerable interest over the past decade. In particular, these operat…
On Dynamic Mode Decomposition of Control-affine Systems
Moad Abudia, Joel A. Rosenfeld, Rushikesh Kamalapurkar
This paper builds on the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kern…
On Convergent Dynamic Mode Decomposition and its Equivalence with Occupation Kernel Regression
Moad Abudia, Joel A. Rosenfeld, Rushikesh Kamalapurkar
This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode d…
Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators
Zachary Morrison, Moad Abudia, Joel Rosenfeld +1
Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analys…
Carleman Lifting for Nonlinear System Identification with Guaranteed Error Bounds
Moad Abudia, Joel A. Rosenfeld, Rushikesh Kamalapurkar
This paper concerns identification of uncontrolled or closed loop nonlinear systems using a set of trajectories that are generated by the system in a domain of attraction. The obje…
Singular Dynamic Mode Decompositions
Joel A. Rosenfeld, Rushikesh Kamalapurkar
This manuscript is aimed at addressing several long standing limitations of dynamic mode decompositions in the application of Koopman analysis. Principle among these limitations ar…
An occupation kernel approach to optimal control
Rushikesh Kamalapurkar, Joel A. Rosenfeld
In this effort, a novel operator theoretic framework is developed for data-driven solution of optimal control problems. The developed methods focus on the use of trajectories (i.e.…
The kernel perspective on dynamic mode decomposition
Efrain Gonzalez, Moad Abudia, Michael Jury +2
This manuscript revisits theoretical assumptions concerning dynamic mode decomposition (DMD) of Koopman operators, including the existence of lattices of eigenfunctions, common eig…
Control Occupation Kernel Regression for Nonlinear Control-Affine Systems
Moad Abudia, Tejasvi Channagiri, Joel A. Rosenfeld +1
This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged…
Liouville Operators over the Hardy Space
Benjamin P. Russo, Joel A. Rosenfeld
The role of Liouville operators in the study of dynamical systems through the use of occupation measures have been an active area of research in control theory over the past decade…
Motion Tomography via Occupation Kernels
Benjamin P. Russo, Rushikesh Kamalapurkar, Dongsik Chang +1
The goal of motion tomography is to recover a description of a vector flow field using information on the trajectory of a sensing unit. In this paper, we develop a predictor correc…
Occupation Kernel Hilbert Spaces for Fractional Order Liouville Operators and Dynamic Mode Decomposition
Joel A. Rosenfeld, Benjamin Russo, Xiuying Li
This manuscript gives a theoretical framework for a new Hilbert space of functions, the so called occupation kernel Hilbert space (OKHS), that operate on collections of signals rat…
Theoretical Foundations for the Dynamic Mode Decomposition of High Order Dynamical Systems
Joel A. Rosenfeld, Benjamin P. Russo, Rushikesh Kamalapurkar
Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to for…
Dynamic Mode Decomposition with Control Liouville Operators
Joel A. Rosenfeld, Rushikesh Kamalapurkar
This paper builds the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel…
The Gradient descent method from the perspective of fractional calculus
Pham Viet Hai, Joel A. Rosenfeld
Motivated by gradient methods in optimization theory, we give methods based on -fractional derivatives of order in order to solve unconstrained optimization problems. The co…
Dynamic Mode Decomposition for Continuous Time Systems with the Liouville Operator
Joel A. Rosenfeld, Rushikesh Kamalapurkar, L. Forest Gruss +1
Dynamic Mode Decomposition (DMD) has become synonymous with the Koopman operator, where continuous time dynamics are examined through a discrete time proxy determined by a fixed ti…
The Occupation Kernel Method for Nonlinear System Identification
Joel A. Rosenfeld, Benjamin Russo, Rushikesh Kamalapurkar +1
This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integrati…
Verification for Machine Learning, Autonomy, and Neural Networks Survey
Weiming Xiang, Patrick Musau, Ayana A. Wild +5
This survey presents an overview of verification techniques for autonomous systems, with a focus on safety-critical autonomous cyber-physical systems (CPS) and subcomponents thereo…
Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers
Weiming Xiang, Hoang-Dung Tran, Joel A. Rosenfeld +1
In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neur…
Invariance-like results for Nonautonomous Switched Systems
Rushikesh Kamalapurkar, Joel A. Rosenfeld, Anup Parikh +2
This paper generalizes the Lasalle-Yoshizawa Theorem to switched nonsmooth systems. Filippov and Krasovskii regularizations of a switched system are shown to be contained within th…
Introducing the Polylogarithmic Hardy Space
Joel A. Rosenfeld
In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in…
State Following (StaF) Kernel Functions for Function Approximation
Joel A. Rosenfeld, Rushikesh Kamalapurkar, Warren E. Dixon
A function approximation method is developed that aims to approximate a function in a small neighborhood of a state that travels within a compact set. The development is based on t…