Related papers: Equation-Free Digital Twins for Nonlinear Structur…
This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…
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…
Digital twin (DT) technologies have emerged as a solution for real-time data-driven modeling of cyber physical systems (CPS) using the vast amount of data available by Internet of Things (IoT) networks. In this position paper, we elucidate…
A digital twin is a surrogate model that has the main feature to mirror the original process behavior. Associating the dynamical process with a digital twin model of reduced complexity has the significant advantage to map the dynamics with…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
Digital twins have attracted a great deal of recent attention from a wide range of fields. A basic requirement for digital twins of nonlinear dynamical systems is the ability to generate the system evolution and predict potentially…
This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
Axial piston pumps are crucial components in fluid power systems, where reliable fault diagnosis is essential for ensuring operational safety and efficiency. Traditional data-driven methods require extensive labeled fault data, which is…
Accurately capturing the nonlinear dynamic behavior of structures remains a significant challenge in mechanics and engineering. Traditional physics-based models and data-driven approaches often struggle to simultaneously ensure model…
We develop algorithms built around properties of the transfer operator and Koopman operator which 1) test for possible multiscale dynamics in a given dynamical system, 2) estimate the magnitude of the time-scale separation, and finally 3)…
Three-dimensional integrated circuit (3D IC) pack-aging and heterogeneous integration have emerged as central pillars of contemporary semiconductor scaling. Yet, the multi-physics coupling inherent to stacked architectures manifesting as…
Spatial temporal reconstruction of dynamical system is indeed a crucial problem with diverse applications ranging from climate modeling to numerous chaotic and physical processes. These reconstructions are based on the harmonious…
Elastically-supported section model tests are the most basic experimental technique in wind engineering, where helical springs are commonly employed to simulate the two-degree-of-freedom low-order modal motions of flexible structures.…
In this work, we develop a method to identify continuous-time nonlinear networked dynamics via the Koopman operator framework. The proposed technique consists of two steps: the first step identifies the neighbors of each node, and the…
We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference…
In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…
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…
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…
This paper presents a class of linear predictors for nonlinear controlled dynamical systems. The basic idea is to lift the nonlinear dynamics into a higher dimensional space where its evolution is approximately linear. In an uncontrolled…