相关论文: Learning Stable Koopman Embeddings

We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear…

We study the metastability properties of a simple prototypical bistable system using the formalism of the Koopman operator. Instead of studying noise-induced transitions by following the trajectories of the system, we track them by studying…

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…

We propose a new non-parametric framework for learning incrementally stable dynamical systems x' = f(x) from a set of sampled trajectories. We construct a rich family of smooth vector fields induced by certain classes of matrix-valued…

In data-driven modelling of complex dynamic processes, it is often desirable to combine different classes of models to enhance performance. Examples include coupled models of different fidelities, or hybrid models based on physical…

Extracting predictive models from nonlinear systems is a central task in scientific machine learning. One key problem is the reconciliation between modern data-driven approaches and first principles. Despite rapid advances in machine…

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Representing and predicting high-dimensional and spatiotemporally chaotic dynamical systems remains a fundamental challenge in dynamical systems and machine learning. Although data-driven models can achieve accurate short-term forecasts,…

Learning-based control of linear systems received a lot of attentions recently. In popular settings, the true dynamical models are unknown to the decision-maker and need to be interactively learned by applying control inputs to the systems.…

We present a simple model-free control algorithm that is able to robustly learn and stabilize an unknown discrete-time linear system with full control and state feedback subject to arbitrary bounded disturbance and noise sequences. The…

The Koopman operator approach to the state estimation problem for nonlinear systems is a promising research area. The main goal of this paper is an attempt to provide a rigorous theoretical framework for this approach. In particular, the…

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…

This paper presents a novel framework for stabilizing nonlinear systems represented in state-dependent form. We first reformulate the nonlinear dynamics as a state-dependent parameter-varying model and synthesize a stabilizing controller…

We propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment the a priori known state-space model by reformulating parameters deemed uncertain…

In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…

We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian…

Sparked by the Willems' fundamental lemma, a class of data-driven control methods has been developed for LTI systems. At the same time, the Koopman operator theory attempts to cast a nonlinear control problem into a standard linear one…

We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…