Related papers: Kernel EDMD for data-driven nonlinear Koopman MPC …
Constraint handling during tracking operations is at the core of many real-world control implementations and is well understood when dynamic models of the underlying system exist, yet becomes more challenging when data-driven models are…
Empirical Dynamic Modeling (EDM) is a state-of-the-art non-linear time-series analysis framework. Despite its wide applicability, EDM was not scalable to large datasets due to its expensive computational cost. To overcome this obstacle,…
Online optimal control of quadrupedal robots would enable them to plan their movement in novel scenarios. Linear Model Predictive Control (LMPC) has emerged as a practical approach for real-time control. In LMPC, an optimization problem…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…
Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. However, Koopman operators can have continuous spectra and…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…
Data-enabled predictive control (DeePC) has emerged as a powerful technique to control complex systems without the need for extensive modeling efforts. However, relying solely on offline collected data trajectories to represent the system…
We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…
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…
This paper demonstrates how Extended Dynamic Mode Decomposition (EDMD), grounded in Koopman operator theory, can effectively identify the main contributor(s) to oscillations in power grids. We use PMU data recorded from a real 0.15 Hz…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
Koopman operator theory has been gaining momentum for model extraction, planning, and control of data-driven robotic systems. The Koopman operator's ability to extract dynamics from data depends heavily on the selection of an appropriate…
We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eigenfunctions of the Koopman semigroup when this semigroup is…
This paper presents a robust and kernelized data-enabled predictive control (RoKDeePC) algorithm to perform model-free optimal control for nonlinear systems using only input and output data. The algorithm combines robust predictive control…
Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
(Economic) nonlinear model predictive control ((e)NMPC) requires dynamic models that are sufficiently accurate and computationally tractable. Data-driven surrogate models for mechanistic models can reduce the computational burden of…
The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dynamics through spectral analysis. This review presents a…