Feedback control of unknown chaotic dynamical systems based on time-series data

1999 ◽  
Vol 46 (5) ◽  
pp. 640-644 ◽  
Author(s):  
Gang Chen ◽  
Guanrong Chen ◽  
R.J.P. de Figueiredo
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Time Series Data ◽  
Series Data ◽  
Chaotic Dynamical Systems

scholarly journals Extracting Nonlinear Dynamics from Psychological and Behavioral Time Series Through HAVOK Analysis

2020 ◽  
Author(s):  
Robert Glenn Moulder ◽  
Elena Martynova ◽  
Steven M. Boker
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Nonlinear Dynamical Systems ◽  
Series Data ◽  
Alternative View ◽  
Unified Framework ◽  
Nonlinear Dynamical ◽  
Depth Analysis ◽  
Analysis Of Time Series

Analytical methods derived from nonlinear dynamical systems, complexity, and chaos theories offer researchers a framework for in-depth analysis of time series data. However, relatively few studies involving time series data obtained from psychological and behavioral research employ such methods. This paucity of application is due to a lack of general analysis frameworks for modeling time series data with strong nonlinear components. In this article, we describe the potential of Hankel alternative view of Koopman (HAVOK) analysis for solving this issue. HAVOK analysis is a unified framework for nonlinear dynamical systems analysis of time series data. By utilizing HAVOK analysis, researchers may model nonlinear time series data in a linear framework while simultaneously reconstructing attractor manifolds and obtaining a secondary time series representing the amount of nonlinear forcing occurring in a system at any given time. We begin by showing the mathematical underpinnings of HAVOK analysis and then show example applications of HAVOK analysis for modeling time series data derived from real psychological and behavioral studies.

scholarly journals Observation error covariance specification in dynamical systems for data assimilation using recurrent neural networks

2021 ◽  
Author(s):  
Sibo Cheng ◽  
Mingming Qiu
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Recurrent Neural Networks ◽  
Time Series Data ◽  
Series Data ◽  
Observation Data ◽  
Observation Error ◽  
Error Covariance

AbstractData assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modeling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive, especially for systems of large dimensions. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) to improve both the accuracy and the efficiency of observation covariance specification in data assimilation for dynamical systems. Learning the covariance matrix from observed/simulated time-series data, the proposed approach does not require any knowledge or assumption about prior error distribution, unlike classical posterior tuning methods. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water twin experiments framework with different covariance parameterization using ensemble assimilation. This novel method shows significant advantages in observation covariance specification, assimilation accuracy, and computational efficiency.

A Modified 0-1 Test for Chaos Detection in Oversampled Time Series Observations

2014 ◽  
Vol 24 (05) ◽  
pp. 1450063 ◽  
Author(s):  
J. S. Armand Eyebe Fouda ◽  
Bertrand Bodo ◽  
Samrat L. Sabat ◽  
J. Yves Effa
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Continuous Time ◽  
Time Series Data ◽  
Series Data ◽  
Local Maxima ◽  
Chaos Detection ◽  
Simulation Results ◽  
Discrete Map

The use of binary 0-1 test for chaos detection is limited to detect chaos in oversampled time series observations. In this paper we propose a modified 0-1 test in which, binary 0-1 test is applied to the discrete map of local maxima and minima of the original observable in contrast to the direct observable. The proposed approach successfully detects chaos in oversampled time series data. This is verified by simulating different numerical simulations of Lorenz and Duffing systems. The simulation results show the efficiency and computational gain of the proposed test for chaos detection in the continuous time dynamical systems.

scholarly journals Analysis of EEG Data Using Complex Geometric Structurization

2021 ◽  
pp. 1-28
Author(s):  
E. A. Kwessi ◽  
L. J. Edwards
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Data ◽  
Health Condition ◽  
Series Data ◽  
Complex Structures ◽  
Embedding Theory ◽  
Novel Approach ◽  
Eeg Data ◽  
Electroencephalogram Eeg

Abstract Electroencephalogram (EEG) is a common tool used to understand brain activities. The data are typically obtained by placing electrodes at the surface of the scalp and recording the oscillations of currents passing through the electrodes. These oscillations can sometimes lead to various interpretations, depending on, for example, the subject's health condition, the experiment carried out, the sensitivity of the tools used, or human manipulations. The data obtained over time can be considered a time series. There is evidence in the literature that epilepsy EEG data may be chaotic. Either way, the Embedding Theory in dynamical systems suggests that time series from a complex system could be used to reconstruct its phase space under proper conditions. In this letter, we propose an analysis of epilepsy EEG time series data based on a novel approach dubbed complex geometric structurization. Complex geometric structurization stems from the construction of strange attractors using Embedding Theory from dynamical systems. The complex geometric structures are themselves obtained using a geometry tool, the α-shapes from shape analysis. Initial analyses show a proof of concept in that these complex structures capture the expected changes brain in lobes under consideration. Further, a deeper analysis suggests that these complex structures can be used as biomarkers for seizure changes.

Online Discovery and Classification of Operational Regimes From an Ensemble of Time Series Data

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Chandrachur Bhattacharya ◽  
Asok Ray
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Analysis ◽  
Time Series Data ◽  
Real Life ◽  
Series Data ◽  
Markov Modeling ◽  
Stable Regime ◽  
Series Analysis ◽  
Symbolic Time Series Analysis

Abstract One of the pertinent problems in decision and control of dynamical systems is to identify the current operational regime of the physical process under consideration. To this end, there has been an upsurge in (data-driven) machine learning methods, such as symbolic time series analysis, hidden Markov modeling, and artificial neural networks, which often rely on some form of supervised learning based on preclassified data to construct the classifier. However, this approach may not be adequate for dynamical systems with a variety of operational regimes and possible anomalous/failure conditions. To address this issue, the technical brief proposes a methodology, built upon the concept of symbolic time series analysis, wherein the classifier learns to discover the patterns so that the algorithms can train themselves online while simultaneously functioning as a classifier. The efficacy of the methodology is demonstrated on time series of: (i) synthetic data from an unforced Van der Pol equation and (ii) pressure oscillation data from an experimental Rijke tube apparatus that emulates the thermoacoustics in real-life combustors where the process dynamics undergoes changes from the stable regime to an unstable regime and vice versa via transition to transient regimes. The underlying algorithms are capable of accurately learning and capturing the various regimes online in a (primarily) unsupervised manner.

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