Related papers: Tensor-based computation of the Koopman generator …
This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…
Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers…
The Koopman Operator (KO) is a mathematical construct that maps nonlinear (state space) dynamics to corresponding linear dynamics in an infinite-dimensional functional space. For practical applications, finite-dimensional approximations can…
The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…
While Koopman operator lifts a nonlinear system into an infinite-dimensional function space and represents it as a linear dynamics, its definition is restricted to autonomous systems, i.e., does not incorporate inputs or disturbances. To…
Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…
We propose a multilevel tensor-train (TT) framework for solving nonlinear partial differential equations (PDEs) in a global space-time formulation. While space-time TT solvers have demonstrated significant potential for compressed…
Tensor train (TT) decomposition represents an $N$-order tensor using $O(N)$ matrices (i.e., factors) of small dimensions, achieved through products among these factors. Due to its compact representation, TT decomposition has found wide…
Controlling nonlinear dynamical systems remains a central challenge in a wide range of applications, particularly when accurate first-principle models are unavailable. Data-driven approaches offer a promising alternative by designing…
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…
Networked nonlinear dynamics underpin the complex functionality of many engineering, social, biological, and ecological systems. Monitoring the networked dynamics via the minimum subset of nodes is essential for a variety of scientific and…
Certified model reduction for high-dimensional nonlinear control systems remains challenging: unlike balanced truncation for LTI systems, most nonlinear reduction methods either lack computable worst-case error bounds or rely on intractable…
The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting. Koopman eigenfunctions represent the…
We report a new approach to estimating power system inertia directly from time-series data on power system dynamics. The approach is based on the so-called Koopman Mode Decomposition (KMD) of such dynamic data, which is a nonlinear…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system.…
For every non-autonomous system, there is the related family of Koopman operators $\mathcal{K}^{(t,t_0)}$, parameterized by the time pair $(t,t_0)$. In this paper we are investigating the time dependency of the spectral properties of the…
This paper presents a data-learned linear Koopman embedding of nonlinear networked dynamics and uses it to enable real-time model predictive emergency voltage control in a power network. The approach involves a novel data-driven…
Online optimal control of quadruped robots would enable them to adapt to varying inputs and changing conditions in real time. A common way of achieving this is linear model predictive control (LMPC), where a quadratic programming (QP)…
Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…