A Hidden-Memory Variable-Order Time-Fractional Optimal Control Model: Analysis and Approximation

Zheng, Xiangcheng; Hong, Wei

doi:10.1137/20m1344962

Cited by 44 publications

(9 citation statements)

References 45 publications

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“…Therefore, CFPSO is more suitable for helping physicians quickly determine whether a patient has heart disease through the learned model. In future work, variable-order fractional operators (VOFO) can be involved in this topic for coping with complicated real-world issues because VOFO can provide the robustness and flexibility characteristics more in control theory [34][35][36][37][38].…”

Section: Discussionmentioning

confidence: 99%

Controllability of Fractional-Order Particle Swarm Optimizer and Its Application in the Classification of Heart Disease

et al. 2021

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This study proposes a method to improve fractional-order particle swarm optimizer to overcome the shortcomings of traditional swarm algorithms, such as low search accuracy in a high-dimensional space, falling into local minimums, and nonrobust results. In natural phenomena, our controllable fractional-order particle swarm optimizer can explore search spaces in detail to obtain high resolutions. Moreover, the proposed algorithm is memorable, i.e., position updates focus on the particle position of previous and last generations, rendering it conservative when updating the position, and obtained results are robust. For verifying the algorithm’s effectiveness, 11 test functions compare the average value, overall best value, and standard deviation of the controllable fractional-order particle swarm optimizer and controllable particle swarm optimizer; experimental results show that the stability of the former is better than the latter. Furthermore, the solution position found by the controllable fractional-order particle swarm optimizer is more reliable. Therefore, the improved method proposed herein is effective. Moreover, this research describes how a heart disease prediction application uses the optimizer we proposed to optimize XGBoost hyperparameters with custom target values. The final verification of the obtained prediction model is effective and reliable, which shows the controllability of our proposed fractional-order particle swarm optimizer.

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Section: Discussionmentioning

confidence: 99%

Controllability of Fractional-Order Particle Swarm Optimizer and Its Application in the Classification of Heart Disease

et al. 2021

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“…6. Based on literatures, [52][53][54][55][56] variable-order fractional neural networks should be researched.…”

Section: The Highly Accurate Schemes Of Mittag-lefflermentioning

confidence: 99%

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Luo

Zhang

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In recent years, exponential Euler difference methods for first-order semi-linear differential equations have been developed rapidly, and various exponential Euler difference methods have become a very important research topic. For fractional-order shunting inhibitory cellular neural networks with time lags, this article first establishes a new difference method named Mittag-Leffler Euler difference, which includes exponential Euler difference. Second, the existence of unique global bounded solution and equilibrium point, exponential stability and synchronization of the derived difference model are investigated. Compared with the classical fractional-order Euler difference method, the Mittag-Leffler discrete shunting inhibitory cellular neural networks can better describe and maintain the dynamic properties of the corresponding continuous-time models. More importantly, it opens up a new way to study discrete-time fractional-order systems and establishes a set of theory and methods to study Mittag-Leffler discrete neural networks.

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“…In recent decades, fractional calculus (FC) has played a significant role in science and engineering, and therefore, the scientists focused on its applications to model the real phenomena [2,23,24,29]. The fractional derivative and integrals were recognized to be an efficient tool to describe the properties of complex dynamical processes more accurately than the standard integer derivative and integral [14,17,21,27,38]. Fractional partial differential equations (FPDEs) are a fascinating subject, because they are frequently used to explain a variety of phenomena in real-world situations, including signal processing control theory, fluid flow, potential theory, information theory, finance, and entropy [7,9,25,32].…”

Section: Introductionmentioning

confidence: 99%

Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices

2023

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This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As a matter of fact, the variable-order fractional derivative (VFD) that has been used is in the Caputo sense. The first step of this technique is constructive on the construction of the solution using the shifted Legendre–Laguerre polynomials with unknown coefficients. The second step involves using a combination of the collocation method and the operational matrices (OMs) of the shifted Legendre–Laguerre polynomials, as well as the Newton–Cotes nodal points, to find the unknown coefficients. The final step focuses on solving the resulting algebraic equations by employing Newton’s iterative method. To illustrate and demonstrate the technique’s efficacy and applicability, two examples have been provided.

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A Hidden-Memory Variable-Order Time-Fractional Optimal Control Model: Analysis and Approximation

Cited by 44 publications

References 45 publications

Controllability of Fractional-Order Particle Swarm Optimizer and Its Application in the Classification of Heart Disease

Controllability of Fractional-Order Particle Swarm Optimizer and Its Application in the Classification of Heart Disease

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Solving fractional time-delay diffusion equation with variable-order derivative based on shifted Legendre–Laguerre operational matrices

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