Related papers: Data-Driven Feedback Linearization using the Koopm…
We develop data-driven reinforcement learning (RL) control designs for input-affine nonlinear systems. We use Carleman linearization to express the state-space representation of the nonlinear dynamical model in the Carleman space, and…
Newton-Raphson controller is a powerful prediction-based variable gain integral controller. Basically, the classical model-based Newton-Raphson controller requires two elements: the prediction of the system output and the derivative of the…
Koopman operator theory is receiving increased attention due to its promise to linearize nonlinear dynamics. Neural networks that are developed to represent Koopman operators have shown great success thanks to their ability to approximate…
Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…
The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of…
This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental…
In this paper, we provide a tutorial overview and an extension of a recently developed framework for data-driven control of unknown nonlinear systems with rigorous closed-loop guarantees. The proposed approach relies on the Koopman operator…
This paper presents a novel parametrization approach for aeroelastic systems utilizing Koopman theory, specifically leveraging the Koopman Bilinear Form (KBF) model. To address the limitations of linear parametric dependence in the KBF…
In this paper we provide direct data-driven expressions for the Linear Quadratic Regulator (LQR), the Kalman filter, and the Linear Quadratic Gaussian (LQG) controller using a finite dataset of noisy input, state, and output trajectories.…
Effective and causal observable functions for low-order lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a…
This short note gives a new framework for dealing with nonlinear sampled-data systems. We introduce a new idea of lifting, which is well known for linear systems, but not successfully generalized to nonlinear systems. This paper introduces…
This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…
The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are…
Koopman Operator Theory has opened the doors to data-driven learning of globally linear representations of complex nonlinear systems. However, current methodologies for Koopman Operator discovery struggle with uncertainty quantification and…
We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources…
We consider the problem of steering, via output feedback, the state distribution of a discrete-time, linear stochastic system from an initial Gaussian distribution to a terminal Gaussian distribution with prescribed mean and maximum…
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,…
Linear dynamical systems are fully characterized by their eigenspectra, accessible directly from the generator of the dynamics. For nonlinear systems governed by partial differential equations, no equivalent theory exists. We introduce Lie…
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…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…