Related papers: Data-Driven Bifurcation Analysis via Learning of H…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

This paper extends the Willems' Fundamental Lemma to nonlinear control-affine systems using the Koopman bilinear realization. This enables us to bypass the Extended Dynamic Mode Decomposition (EDMD)-based system identification step in…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control.…

Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…

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…

Linearising the dynamics of nonlinear mechanical systems is an important and open research area. A common approach is feedback linearisation, which is a nonlinear control method that transforms the input-output response of a nonlinear…

Several authors have reported that the echo state network reproduces bifurcation diagrams of some nonlinear differential equations using the data for a few control parameters. We demonstrate that a simpler feedforward neural network can…

We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…

This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to…

The increasing decentralization of power systems driven by a large number of renewable energy sources poses challenges in power flow optimization. Partially unknown power line properties can render model-based approaches unsuitable. With…

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…

Bifurcation phenomena are common in multi-dimensional multi-parameter dynamical systems. Normal form theory suggests that the bifurcations themselves are driven by relatively few parameters; however, these are often nonlinear combinations…

Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Pattern-forming systems can exhibit a diverse array of complex behaviors as external parameters are varied, enabling a variety of useful functions in biological and engineered systems. First-principles derivations of the underlying…

For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the…

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…