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This paper presents a robust moving horizon estimation (MHE) approach with provable estimation error bounds for solving the simultaneous localization and mapping (SLAM) problem. We derive sufficient conditions to guarantee robust stability…
This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis…
We present a novel data-driven approach for learning linear representations of a class of stable nonlinear systems using Koopman eigenfunctions. By learning the conjugacy map between a nonlinear system and its Jacobian linearization through…
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…
Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…
The development of advanced closed-loop irrigation systems requires accurate soil moisture information. In this work, we address the problem of soil moisture estimation for the agro-hydrological systems in a robust and reliable manner. A…
We illustrate a novel version of Willems' lemma for data-based representation of continuous-time systems. The main novelties compared to previous works are two. First, the proposed framework relies only on measured input-output trajectories…
Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
We investigate the Continuous-Time Koopman Autoencoder (CT-KAE) as a lightweight surrogate model for long-horizon ocean state forecasting in a two-layer quasi-geostrophic (QG) system. By projecting nonlinear dynamics into a latent space…
We introduce two novel generalizations of the Koopman operator method of nonlinear dynamic modeling. Each of these generalizations leads to greatly improved predictive performance without sacrificing a unique trait of Koopman methods: the…
The Koopman framework proposes a linear representation of finite-dimensional nonlinear systems through a generally infinite-dimensional globally linear embedding. Originally, the Koopman formalism has been derived for autonomous systems. In…
This paper introduces a data-dependent approximation of the forward kinematics map for certain types of animal motion models. It is assumed that motions are supported on a low-dimensional, unknown configuration manifold $Q$ that is…
A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…
This study investigates the use of machine learning based mesh adaptivity, specifically mesh movement methods (UM2N), with depth integrated non-hydrostatic shallow water models. Motivation for this comes from the need for models which…
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is…
Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer from shortcomings in…
This paper introduces an input-output bilinear Koopman realization with an optimization algorithm of lifting functions. For nonlinear systems with inputs, Koopman-based modeling is effective because the Koopman operator enables a…
Distribution System State Estimation (DSSE) plays an increasingly-important role in modern power grids due to the integration of distributed energy resources (DERs). The inherent characteristics of distribution systems make classical…
We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data…