Related papers: Learning Noise-Robust Stable Koopman Operator for …
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
Learning-based dynamical models face a persistent tension between expressiveness and formal guarantees: richer model classes improve predictive accuracy, but their stability properties are typically verified only empirically, if at all.…
We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…
Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, behaviors with sudden accelerations that waste energy and lack…
Mobile robot navigation can be challenged by system uncertainty. For example, ground friction may vary abruptly causing slipping, and noisy sensor data can lead to inaccurate feedback control. Traditional model-based methods may be limited…
Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…
In this paper we prove new connections between two frameworks for analysis and control of nonlinear systems: the Koopman operator framework and contraction analysis. Each method, in different ways, provides exact and global analyses of…
Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in…
This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary…
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The…
Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine…
In this paper we consider the Koopman operator associated with the discrete and the continuous time random dynamical system (RDS). We provide results that characterize the spectrum and the eigenfunctions of the stochastic Koopman operator…
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…
This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error…
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 focuses on a key challenge in hybrid data-driven predictive control: the effect of measurement noise on Hankel matrices. While noise is handled in direct and indirect methods, hybrid approaches often overlook its impact during…
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…
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…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work,…