Related papers: Episodic Koopman Learning of Nonlinear Robot Dynam…
This paper investigates Koopman operator-based approaches for multivariable control of a two-spool turbofan engine. A physics-based component-level model is developed to generate training data and validate the controllers. A meta-heuristic…
The challenge of finding exact and finite-dimensional Koopman embeddings of nonlinear systems has been largely circumvented by employing data-driven techniques to learn models of different complexities (e.g., linear, bilinear, input…
Accurate dynamics models are critical for the design of predictive controller for autonomous mobile robots. Physics-based models are often too simple to capture relevant real-world effects, while data-driven models are data-intensive and…
Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of…
This work presents a hybrid physics-informed and data-driven modeling framework for predictive control of autonomous off-road vehicles operating on deformable terrain. Traditional high-fidelity terramechanics models are often too…
A data-driven, model-free approach to modeling the temporal evolution of physical systems mitigates the need for explicit knowledge of the governing equations. Even when physical priors such as partial differential equations are available,…
This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system…
Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem for real-world and industrial applications. Koopman operator theory allows one to analyze nonlinear systems through the lens of…
This paper presents a generic motion model to capture mobile robots' dynamic behaviors (translation and rotation). The model is based on statistical models driven by white random processes and is formulated into a full state estimation…
Quadrotor systems are common and beneficial for many fields, but their intricate behavior often makes it challenging to design effective and optimal control strategies. Some traditional approaches to nonlinear control often rely on local…
Approximating nonlinear systems as linear ones is a common workaround to apply control tools tailored for linear systems. This motivates our present work where we developed a data-driven model predictive controller (MPC) based on the…
The Koopman operator framework can be used to identify a data-driven model of a nonlinear system. Unfortunately, when the data is corrupted by noise, the identified model can be biased. Additionally, depending on the choice of lifting…
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…
Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…
In recent years, the application of machine learning to physics has been actively explored. In this paper, we study a method for estimating the ground-state energy of quantum Hamiltonians by applying data-driven Koopman analysis within the…
We present the identification of the non-linear dynamics of a novel hovercraft design, employing end-to-end deep learning techniques. Our experimental setup consists of a hovercraft propelled by racing drone propellers mounted on a…
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…