Related papers: Observability of Nonlinear Dynamical Systems over …
In this work, we develop a method to identify continuous-time nonlinear networked dynamics via the Koopman operator framework. The proposed technique consists of two steps: the first step identifies the neighbors of each node, and the…
In this paper we propose a new observer design technique for nonlinear systems. It combines the well-known Kazantzis-Kravaris-Luenberger observer and the recently introduced parameter estimation-based observer, which become special cases of…
The paper deals with the observer design problem for a wide class of triangular time-varying nonlinear systems, with unobservable linearization. Sufficient conditions are derived for the existence of a Luenberger-type observer, when it is a…
This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear…
Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…
The least squares linear filter, also called the Wiener filter, is a popular tool to predict the next element(s) of time series by linear combination of time-delayed observations. We consider observation sequences of deterministic dynamics,…
A discrete-time conditional Gaussian Koopman network (CGKN) is developed in this work to learn surrogate models that can perform efficient state forecast and data assimilation (DA) for high-dimensional complex dynamical systems, e.g.,…
Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…
Koopman operator theory and Willems' fundamental lemma both can provide (approximated) data-driven linear representation for nonlinear systems. However, choosing lifting functions for the Koopman operator is challenging, and the quality of…
In this paper, we consider a dynamic linear system in state-space form where the observation equation depends linearly on a set of parameters. We address the problem of how to dynamically calculate these parameters in order to minimize the…
We address the problem of retrieving the full state of a network of R\"ossler systems from the knowledge of the actual state of a limited set of nodes. The selection of the nodes where sensors are placed is carried out in a hierarchical way…
Koopman analysis can be used to understand the dynamics of a nonlinear dynamical system in terms a linear, but generally infinite dimensional operator. The isostable coordinate system focuses on the slowest decaying principal Koopman…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…
This paper presents a methodology to achieve lower-dimensional Koopman quasi-linear representations of nonlinear system dynamics using Koopman generalized eigenfunctions. The proposed approach considers the analytically derived Koopman…
In a recent article, we presented a framework to control nonlinear partial differential equations (PDEs) by means of Koopman operator based reduced models and concepts from switched systems. The main idea was to transform a control system…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…
The article is devoted to the problem of synthesis of observers of state variables for linear stationary objects operating under conditions of noise or disturbances in the measurement channel. The paper considers a fully observable linear…