Related papers: Beyond Carleman Linearization of Nonlinear Dynamic…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…
We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
This paper presents an averaging method for nonlinear systems defined on Riemannian manifolds. We extend closeness of solutions results for ordinary differential equations on $R^{n}$ to dynamical systems defined on Riemannian manifolds by…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
The paper deals with the observer design problem for a wide class of triangular nonlinear time-varying systems. The results of the present work generalize previous results in the literature dealing with the observer design problem for…
This paper presents a data-driven method to find a closed-loop optimal controller, which minimizes a specified infinite-horizon cost function for systems with unknown dynamics. Suppose the closed-loop optimal controller can be parameterized…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
Nonlinear Negative Imaginary (NI) systems arise in various engineering applications, such as controlling flexible structures and air vehicles. However, unlike linear NI systems, their theory is not well-developed. In this paper, we propose…
In this paper, we present an extensive study of linearly forced isotropic turbulence. By using an analytical method, we identified two parametric choices that are new to our knowledge. We proved that the underlying nonlinear dynamical…
A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\'e's geometric picture that focuses on "dynamics of states". While this picture has fueled our field for a century, it has shown…
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent structures that vary slowly over the large dimensions. Common…
Koopman operators, since introduced by the French-born American mathematician Bernard Koopman in 1931, have been employed as a powerful tool for research in various scientific domains, such as ergodic theory, probability theory, geometry,…
Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena…
This paper presents a study of the Koopman operator theory and its application to optimal control of a multi-robot system. The Koopman operator, while operating on a set of observation functions of the state vector of a nonlinear system,…
Integration of nonlinear dynamical systems is usually seen as associated to a symmetry reduction, e.g. via momentum map. In Lax integrable systems, as pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero system, one…
Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In…
In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear…