This manuscript presents a novel approach to nonlinear system identification leveraging
densely defined Liouville operators and a new “kernel” function that represents an …

Koopman and Perron–Frobenius operators for dynamical systems are becoming popular in
a number of fields in science recently. Properties of the Koopman operator essentially …

This manuscript presents a novel approach to nonlinear system identification leveraging
densely defined Liouville operators and a new" kernel" function that represents an …

In this paper, we give an in-depth error analysis for surrogate models generated by a variant
of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an …

In this paper, we provide a novel solution to an open problem on the global uniform stability
of switched nonlinear systems. Our results are based on the Koopman operator approach …

One of the central challenge for extracting governing principles of dynamical system via
Dynamic Mode Decomposition (DMD) is about the limit data availability or formally called as …

Modern data science problems revolves around the Koopman operator C φ (or Composition
operator) approach, which provides the best-fit linear approximator to the dynamical system …

The progress towards intelligent systems and digitalization relies heavily on the use of
automation technology. However, the growing diversity of control objects presents significant …

In this thesis, we describe and analyze an interplay between dynamical systems, sparse
structures, convex analysis, and functional analysis. We approach global attractors through …