Fitting of the initialization function of fractional order systems

Zhao, Yong; Wei, Yiheng; Shuai, Jianmei; Wang, Yong

doi:10.1007/s11071-018-4278-y

Cited by 7 publications

(4 citation statements)

References 23 publications

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“…This issue is theoretically challenging, since ϕ is infinite dimensional, and the analytical relationship between ϕ and its response signal Ψ is relatively complex. In this regard, some discretization based data-driven strategies are notable [44][45][46], as it is difficult to apply the analytical methods. In addition, for more complex initialized fractional order systems, it may be difficult to calculate ϕ d and u d .…”

Section: Examplementioning

confidence: 99%

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Xu,

Lu,

Chen

2024

Fractal Fract

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Iterative learning control is widely applied to address the tracking problem of dynamic systems. Although this strategy can be applied to fractional order systems, most existing studies neglected the impact of the system initialization on operation repeatability, which is a critical issue since memory effect is inherent for fractional operators. In response to the above deficiencies, this paper derives robust convergence conditions for iterative learning control under non-repetitive initialization functions, where the bound of the final tracking error depends on the shift degree of the initialization function. Model nonlinearity, initial error, and channel noises are also discussed in the derivation. On this basis, a novel initialization learning strategy is proposed to obtain perfect tracking performance and desired initialization trajectory simultaneously, providing a new approach for fractional order system design. Finally, two numerical examples are presented to illustrate the theoretical results and their potential applications.

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Section: Examplementioning

confidence: 99%

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Xu,

Lu,

Chen

2024

Fractal Fract

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“…The initialization function is a time-varying function and can be viewed as a generalization of the constant of integration required for the order-one integral [31]. Zhao et al [26] also applied this procedure to the case of the internal force of an axially loaded viscoelastic bar and showed that the influence caused by the pre-initial process varies in time and reflects the memory of the whole pre-initial process, which explains the origin of the long memory property of fractional-order systems [26].…”

Section: The Decay Functionmentioning

confidence: 99%

“…To do this, we hypothesized that the initial voltage of a CPE with 0 < α < 1 may be written as v(0)g(t), where g(t) is a decay function between zero and one, with intermediate values and behavior between that of the resistor and that of the non-fractional capacitor. This decay function, closely related to the general initial function defined by other authors [17,18,26], is derived and analyzed for the CPE, ZARC (composed of the CPE in parallel with a resistor), and RC networks. In the paper, we also highlight the error tow which some definitions of the fractional derivative can lead.…”

Section: Introductionmentioning

confidence: 99%

Constant Phase Element in the Time Domain: The Problem of Initialization

López‐Villanueva

Rodríguez‐Bolívar

2022

Energies

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The constant phase element (CPE) is found in most battery and supercapacitor equivalent circuit models proposed to interpret data in the frequency domain. When these models are used in the time domain, the initial conditions in the fractional differential equations must be correctly imposed. The initial state problem remains controversial and has been analyzed by various authors in the last two decades. This article attempts to clarify this problem by proposing a procedure to prepare the initial state and defining a decay function that reveals the effect of the initial state in several illustrative examples. This decay function depends on the previous history, which is reflected in the time needed to prepare the initial state and on the current profile assumed for this purpose. This effect of the initial state is difficult to separate and can lead to the misinterpretation of the CPE parameter values.

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“…As a generalized form of integer order calculus, fractional calculus became an essential tool in modeling and control. Fractional calculus proved to be more effective in modeling dynamics with long memory and the hereditary properties [12]. Fractional order system modeling and control had superior performance [13].…”

Section: Introductionmentioning

confidence: 99%

A Fractional Order Generalized SEIR Model: The Role of “COVID-19 Symptom Data” in Receding Horizon Vaccine Policies

Zhao

Li-hong

Wang

et al. 2021

Preprint

Self Cite

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Novel Coronavirus (COVID-19) has spread worldwide, causing continued casualties and economic losses. To characterize the pandemic dynamics, we propose fractional order generalized SEIR epidemic models for COVID-19, considering real-world Facebook symptom data and state-level Google mobility. Fractional order models based on noninteger order calculus can better characterize inhomogeneity in human interactions and infection rates. Our models can describe psychological effect factors within the nonlinear incidence functions. Therefore, we can deliver better fitting and prediction performances. Comparative analysis of model predictions with different mitigation and intervention scenarios, which are affected by mobilities in California, are made. Now, vaccination is becoming a critical response so that the COVID-19 pandemic can become endemic in optimal possible ways.We propose the modified fractional order GSEIR model for near real-time COVID- 19 Receding Horizon vaccine policy study. The proposed Receding Horizon Control (RHC) optimal vaccine strategy can not only explicitly consider the constraints on vaccine availability, speed of replenishing, vaccine application rate, etc., but also can make the whole management in a closedloop manner with an optimization performance index. Additionally, our model can accommodate the age structure of the population, mobility level, community mitigation measures, the willingness to be vaccinated, etc. The closedloop vaccine system can achieve good tracking performance given a future desired and feasible trend. Specifically, our forecast trends of infections and death cases in different immunization scenarios can guide individual and policy decision-making processes in developing mitigation measures and monitoring community risk levels. Numerical simulations using Simulink Design Optimization (SLDO) are given to support our analysis.

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Fitting of the initialization function of fractional order systems

Cited by 7 publications

References 23 publications

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Convergence Analysis of Iterative Learning Control for Initialized Fractional Order Systems

Constant Phase Element in the Time Domain: The Problem of Initialization

A Fractional Order Generalized SEIR Model: The Role of “COVID-19 Symptom Data” in Receding Horizon Vaccine Policies

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