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Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear…
The fundamental lemma from behavioral systems theory yields a data-driven non-parametric system representation that has shown great potential for the data-efficient control of unknown linear and weakly nonlinear systems, even in the…
We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long…
This paper proposes a Koopman-based linear model predictive control (LMPC) framework for safety-critical control of nonlinear discrete-time systems. Existing MPC formulations based on discrete-time control barrier functions (DCBFs) enforce…
Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable…
A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyse nonlinear dynamical systems brings new strategies for…
A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. In excavation, a bucket interacts with the surrounding soil in a highly nonlinear and complex…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
This paper contributes a theoretical framework for data-driven feedback linearization of nonlinear control-affine systems. We unify the traditional geometric perspective on feedback linearization with an operator-theoretic perspective…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
Data-driven model predictive control based on Willems' fundamental lemma has proven effective for linear systems, but extending stability guarantees to nonlinear systems remains an open challenge. In this paper, we establish conditions…
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…
We propose spectral methods for long-term forecasting of temporal signals stemming from linear and nonlinear quasi-periodic dynamical systems. For linear signals, we introduce an algorithm with similarities to the Fourier transform but…
Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in…
A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured…
We present a framework for model-free batch localization and SLAM. We use lifting functions to map a control-affine system into a high-dimensional space, where both the process model and the measurement model are rendered bilinear. During…
Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of…
In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…
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…