320 research outputs found
Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results
In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.MSMT-7778/2014, FEDER, European Regional Development Fund; LO1303, FEDER, European Regional Development Fund; CZ.1.05/2.1.00/19.0376, FEDER, European Regional Development FundEuropean Regional Development Fund through the Project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; National Sustainability Program Project [LO1303 (MSMT-7778/2014)
Koopman Kernel Regression
Many machine learning approaches for decision making, such as reinforcement
learning, rely on simulators or predictive models to forecast the
time-evolution of quantities of interest, e.g., the state of an agent or the
reward of a policy. Forecasts of such complex phenomena are commonly described
by highly nonlinear dynamical systems, making their use in optimization-based
decision-making challenging. Koopman operator theory offers a beneficial
paradigm for addressing this problem by characterizing forecasts via linear
time-invariant (LTI) ODEs, turning multi-step forecasts into sparse matrix
multiplication. Though there exists a variety of learning approaches, they
usually lack crucial learning-theoretic guarantees, making the behavior of the
obtained models with increasing data and dimensionality unclear. We address the
aforementioned by deriving a universal Koopman-invariant reproducing kernel
Hilbert space (RKHS) that solely spans transformations into LTI dynamical
systems. The resulting Koopman Kernel Regression (KKR) framework enables the
use of statistical learning tools from function approximation for novel
convergence results and generalization error bounds under weaker assumptions
than existing work. Our experiments demonstrate superior forecasting
performance compared to Koopman operator and sequential data predictors in
RKHS.Comment: Accepted to the thirty-seventh Conference on Neural Information
Processing Systems (NeurIPS 2023
A Frequency-Domain Version of Willems' Fundamental Lemma
Willems' fundamental lemma has recently received an impressive amount of
attention in the (data-driven) control community. In this paper, we formulate a
frequency-domain equivalent of this lemma. In doing so, we bridge the gap
between recent developments in data-driven analysis and control and the
extensive knowledge on non-parametric frequency-domain identification that has
accumulated, particularly in industry, through decades of working with
classical (frequency-domain) control and identification techniques. Our
formulation also allows for the combination of multiple data sets in the sense
that, in the data, multiple input directions may be excited at the same
frequency. We also illustrate the usefulness of our results by demonstrating
how they can be applied to perform frequency-domain-data-driven simulation
A Compressed Sampling and Dictionary Learning Framework for WDM-Based Distributed Fiber Sensing
We propose a compressed sampling and dictionary learning framework for
fiber-optic sensing using wavelength-tunable lasers. A redundant dictionary is
generated from a model for the reflected sensor signal. Imperfect prior
knowledge is considered in terms of uncertain local and global parameters. To
estimate a sparse representation and the dictionary parameters, we present an
alternating minimization algorithm that is equipped with a pre-processing
routine to handle dictionary coherence. The support of the obtained sparse
signal indicates the reflection delays, which can be used to measure
impairments along the sensing fiber. The performance is evaluated by
simulations and experimental data for a fiber sensor system with common core
architecture.Comment: Accepted for publication in Journal of the Optical Society of America
A [ \copyright\ 2017 Optical Society of America.]. One print or electronic
copy may be made for personal use only. Systematic reproduction and
distribution, duplication of any material in this paper for a fee or for
commercial purposes, or modifications of the content of this paper are
prohibite
Stability and dynamics of a spectral graph model of brain oscillations
AbstractWe explore the stability and dynamic properties of a hierarchical, linearized, and analytic spectral graph model for neural oscillations that integrates the structural wiring of the brain. Previously, we have shown that this model can accurately capture the frequency spectra and the spatial patterns of the alpha and beta frequency bands obtained from magnetoencephalography recordings without regionally varying parameters. Here, we show that this macroscopic model based on long-range excitatory connections exhibits dynamic oscillations with a frequency in the alpha band even without any oscillations implemented at the mesoscopic level. We show that depending on the parameters, the model can exhibit combinations of damped oscillations, limit cycles, or unstable oscillations. We determined bounds on model parameters that ensure stability of the oscillations simulated by the model. Finally, we estimated time-varying model parameters to capture the temporal fluctuations in magnetoencephalography activity. We show that a dynamic spectral graph modeling framework with a parsimonious set of biophysically interpretable model parameters can thereby be employed to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases
Aircraft System Identification from Multisine Inputs and Frequency Responses
A frequency-domain approach is described for estimating parameters, such as stability and control derivatives, in aircraft flight dynamic models from measured input and output data. The approach uses orthogonal phase-optimized multisines for moving the aircraft control effectors, Fourier analysis for computing multiple-input multiple-output frequency responses, and a maximum likelihood estimator called frequency response error (FRE) for determining values and uncertainties for the model parameters. The approach is demonstrated using flight test data for two subscale airplanes: the T-2 generic transport model and the X-56A aeroelastic demonstrator. Results and comparisons with the output-error method indicated that the approach produced accurate estimates of stability and control derivatives and their uncertainties from flight test data
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