Social spider optimisation based identification and optimal control of fractional order system

In this paper, we numerically investigate the chaotic behaviors of a fractional-order system. We find that chaotic behaviors exist in the fractional-order system with an order being less than 3. The lowest order we find to have chaos is 2.4 in such system. In addition, we numerically simulate the continuances of the chaotic behaviors in the fractional-order system with orders ranging from 2.7 to 3. Finally, a simple, but effective, linear state feedback controller is proposed for controlling the fractional-order chaotic system based on an inverse optimal control approach. Numerical simulations show the effectiveness and feasibility of the proposed controller.

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Optimal control problem for a linear stationary fractional order system in the form of a problem of moments: Problem setting and a study

Automation and Remote Control ◽

10.1134/s0005117914050014 ◽

2014 ◽

Vol 75 (5) ◽

pp. 805-817 ◽

Cited By ~ 11

Author(s):

V. A. Kubyshkin ◽

S. S. Postnov

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Fractional Order ◽

Fractional Order System ◽

Order System ◽

Problem Of Moments ◽

Moments Problem ◽

Problem Setting

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Online Parameter Estimation for Lithium-ion Battery by using Adaptive Observer for Fractional Order System

IEEJ Transactions on Electronics Information and Systems ◽

10.1541/ieejeiss.137.1015 ◽

2017 ◽

Vol 137 (8) ◽

pp. 1015-1023

Author(s):

Takahiro Takamatsu ◽

Hiromitsu Ohmori

Keyword(s):

Parameter Estimation ◽

Lithium Ion Battery ◽

Fractional Order ◽

Lithium Ion ◽

Fractional Order System ◽

Adaptive Observer ◽

Order System

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Simultaneous Identification of Fractional-order System Structure and Order and Parameters Based on Alternately Transforming Condensed Information Matrix

ACTA AUTOMATICA SINICA ◽

10.3724/sp.j.1004.2012.01280 ◽

2012 ◽

Vol 38 (8) ◽

pp. 1280 ◽

Cited By ~ 2

Author(s):

Cheng-Xiang ZHU ◽

Yun ZOU

Keyword(s):

Fractional Order ◽

Information Matrix ◽

Fractional Order System ◽

System Structure ◽

Order System ◽

Simultaneous Identification

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Fractional Order System Identification with Occupation Kernel Regression

IEEE Control Systems Letters ◽

10.1109/lcsys.2020.3046408 ◽

2020 ◽

pp. 1-1

Author(s):

Xiuying Li ◽

Joel A Rosenfeld

Keyword(s):

System Identification ◽

Fractional Order ◽

Kernel Regression ◽

Fractional Order System ◽

Order System

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Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.111018 ◽

2021 ◽

Vol 149 ◽

pp. 111018

Author(s):

Lingyun He ◽

Seddigheh Banihashemi ◽

Hossein Jafari ◽

Afshin Babaei

Keyword(s):

Differential Equations ◽

Fractional Order ◽

Delay Differential Equations ◽

Fractional Order System ◽

Computational Scheme ◽

Order System ◽

Numerical Treatment ◽

Stochastic Delay Differential Equations ◽

Stochastic Delay ◽

Delay Differential

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Adaptive Synchronization of a Stochastic Fractional-Order System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.733.939 ◽

2015 ◽

Vol 733 ◽

pp. 939-942

Author(s):

Xiao Jun Liu

Keyword(s):

Numerical Simulations ◽

Fractional Order ◽

Stochastic System ◽

Fractional Order System ◽

Adaptive Synchronization ◽

Order System ◽

Unknown Parameters ◽

Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

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