Related papers: Data-Driven Reduced Modeling of Delayed Dynamical …
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
In this paper, we present an improved framework of the spectral-based Discrete Dislocation Dynamics (DDD) approach introduced in [1,2], that establishes a direct connection with the continuum Field Dislocation Mechanics (FDM) approach. To…
Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
We use video footage of a water tunnel experiment to construct a two-dimensional reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on an attracting spectral…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
Recent advances in learning dynamical systems from data have shown significant promise. However, many existing methods assume access to the full state of the system -- an assumption that is rarely satisfied in practice, where systems are…
Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…
This work introduces Physics-informed State-space neural network Models (PSMs), a novel solution to achieving real-time optimization, flexibility, and fault tolerance in autonomous systems, particularly in transport-dominated systems such…
Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…
We present a methodology for designing a dynamic controller with delayed output feedback for achieving non-collocated vibration suppression with a focus on the multi-frequency case. To synthesize the delay-based controller, we first remodel…
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying…
Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…
In this paper, we study delayed regulated state/output synchronization for discrete-time homogeneous and heterogeneous networks of multi-agent systems (MAS) subject to unknown, non-uniform and arbitrarily large communication delays. A delay…
In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
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…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…