Chaos control in delayed phase space constructed by the Takens embedding theory

Hajiloo, Reza; Salarieh, Hassan; Alasty, Aria

doi:10.1016/j.cnsns.2017.05.022

Cited by 28 publications

(4 citation statements)

References 28 publications

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“…According to Takens theorems, a new phase state space could be reconstructed to stabilize time-series system through the measurable state [41], which could be presented as Equation (11), where x presents the previous phase state space, y presents the reconstructed phase state space, T is adopted to describe the delayed time, and m presents the number of the embedded dimensions [42]. The measurable state variables of LIBs in charge and discharge process also belong to nonlinear time-series system.…”

Section: Nonlinear State Space Reconstruction (Nssr)mentioning

confidence: 99%

Joint State of Charge (SOC) and State of Health (SOH) Estimation for Lithium-Ion Batteries Packs of Electric Vehicles Based on NSSR-LSTM Neural Network

Tang

et al. 2023

Energies

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Lithium-ion batteries (LIBs) are widely used in electrical vehicles (EVs), but safety issues with LIBs still occur frequently. State of charge (SOC) and state of health (SOH) are two crucial parameters for describing the state of LIBs. However, due to inconsistencies that may occur among hundreds to thousands of battery cells connected in series and parallel in the battery pack, these parameters can be difficult to estimate accurately. To address this problem, this paper proposes a joint SOC and SOH estimation method based on the nonlinear state space reconstruction (NSSR) and long short-term memory (LSTM) neural network. An experiment testbed was set up to measure the SOC and SOH of battery packs under different criteria and configurations, and thousands of charging/discharging cycles were recorded. The joint estimation algorithms were validated using testbed data, and the errors for SOC and SOH estimation were found to be within 2.5% and 1.3%, respectively, which is smaller than the errors obtained using traditional Ah-Integral and LSTM-only algorithms.

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Section: Nonlinear State Space Reconstruction (Nssr)mentioning

confidence: 99%

Joint State of Charge (SOC) and State of Health (SOH) Estimation for Lithium-Ion Batteries Packs of Electric Vehicles Based on NSSR-LSTM Neural Network

Tang

et al. 2023

Energies

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“…Sometimes chaotic behaviors appear to be irregular and random in time series but have a strong underlying order in phase space [65]. A phase space projection shows the dependency of each state to the next one; hence phase space is used to study chaotic dynamics [66] and topological characteristics of the system [67]. Numerical processes, like estimating the correlation dimension and the Lyapunov exponents or modeling and forecasting the time series, were done base on phase space [68].…”

Section: The Interacting Network Of Maternal and Fetal Heartmentioning

confidence: 99%

Separation of the fetal heart signal in a synchronous network consisting of maternal and fetal hearts

Zandi-Mehran

Golpayegani

2023

Scientia Iranica

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This paper studies the heart's oscillation model to separate fetal and maternal ECGs from abdominal recordings. To this aim, two phases are designed. A Modified version of the Duffing-Van der Pol oscillator is considered a computational heart model in the modeling phase. To evaluate the interaction effects of the maternal and fetal heart and the differences and features of the fetal heart structure, the fetal heart model is Modified based on the maternal heart model. A nonidentical network is employed as an interactive network of the mother and the fetus's heart. Then the degree of the network synchronization is measured with the help of a pattern synchronization index of the non-identical network. An attempt is made to separate the fetal signal from the mother's in abdominal signals in the separation phase. Two problem-solving approaches are explained; the step-by-step mode that calculates the signal at any given moment and the construction of general equations. These approaches end up calculating the variables, which stand for maternal and fetal signal. That makes it possible to achieve the separation of maternal and fetal ECGs.

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“…A particular application is to the control of chaos [42,22,51,55]. Generally, chaotic systems have unpredictable trajectories, and classical methods for chaos control include the determination of controls which result in chaotic synchronization [30,14] or which locally push trajectories toward unstable ones [22,51,27,52]. Since we seek to push trajectories globally over the given time period, our method can be construed as a global control framework, in which we simultaneously specify the required fate of all trajectories in our phase space.…”

mentioning

confidence: 99%

Controlling Trajectories Globally via Spatiotemporal Finite-Time Optimal Control

Zhang¹,

Balasuriya²

2020

SIAM J. Appl. Dyn. Syst.

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The problems of (i) maximizing or minimizing Lagrangian mixing in fluids via the introduction of a spatiotemporally varying control velocity and (ii) globally controlling the finite-time location of trajectories beginning at all initial conditions in a chaotic system are considered. A particular form of solution to these is designed which uses a new methodology for computing a spatiotemporally dependent optimal control. An L 2 -error norm for trajectory locations over a finite-time horizon is combined with a penalty energy norm for the control velocity in defining the global cost function. A computational algorithm for cost minimization is developed, and theoretical results on global error and cost presented. Numerical simulations (using velocities which are specified, and obtained as data from computational fluid dynamics simulations) are used to demonstrate the efficacy and validity of the approach in determining the required spatiotemporally defined control velocity.

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Chaos control in delayed phase space constructed by the Takens embedding theory

Cited by 28 publications

References 28 publications

Joint State of Charge (SOC) and State of Health (SOH) Estimation for Lithium-Ion Batteries Packs of Electric Vehicles Based on NSSR-LSTM Neural Network

Joint State of Charge (SOC) and State of Health (SOH) Estimation for Lithium-Ion Batteries Packs of Electric Vehicles Based on NSSR-LSTM Neural Network

Separation of the fetal heart signal in a synchronous network consisting of maternal and fetal hearts

Controlling Trajectories Globally via Spatiotemporal Finite-Time Optimal Control

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