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Iterates of Fractional Order

Canadian Journal of Mathematics, 1950
The body of this paper is a complete answer to the following question:Let E be any space whatever. g(x) is a function mapping E into E. When does there exist a function f(x), of the same type, such that(1)
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Stabilization of fractional-order unstable delay systems by fractional-order controllers

Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2012
In the present paper stabilization of a class of fractional-order unstable delay systems by fractional-order controllers is investigated. To derive the sufficient conditions for stability, an analysis based on the Nyquist stability criterion has been adopted.
Iraj Kheirizad   +2 more
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Designing of Fractional Order PID Controller for Unstable Fractional Order System

2019 Joint International Conference on Digital Arts, Media and Technology with ECTI Northern Section Conference on Electrical, Electronics, Computer and Telecommunications Engineering (ECTI DAMT-NCON), 2019
This paper proposes the fractional-order proportional-integral-derivative (FOPID or $\mathbf { P } \mathbf { I } ^ { \lambda } \mathbf { D } ^ { \mu }$) controller design optimization for a stable fractional order (FO) system by using the flower pollination algorithm (FPA), one of the most efficient metaheuristic optimization search techniques.
Boonruk Chipipop, Deacha Puangdownreong
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Adaptive Backstepping Hybrid Fuzzy Sliding Mode Control for Uncertain Fractional-Order Nonlinear Systems Based on Finite-Time Scheme

IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2020
A fractional-order integral fuzzy sliding mode control scheme is proposed for a class of uncertain fractional-order nonlinear systems subject to uncertainties and external disturbances.
Shuai Song   +3 more
semanticscholar   +1 more source

Adaptive terminal sliding mode control scheme for synchronization of fractional-order uncertain chaotic systems.

ISA transactions, 2020
The main goal in this article is synchronization of fractional-order uncertain chaotic systems in the finite time. For this aim, a terminal sliding mode controller with fractional sliding surface is employed to synchronize the states of two different ...
A. Modiri, Saleh Mobayen
semanticscholar   +1 more source

Fractional‐order iterative learning control for fractional‐order linear systems

Asian Journal of Control, 2011
AbstractIn this paper, we discuss in time domain the convergence of the iterative process for fractional‐order systems. Fractional order iterative learning updating schemes are considered. For the linear time invariant (LTI) system case, the convergence conditions of the fractional‐order and integer‐order iterative learning schemes are proved to be ...
Li, Yan, Chen, YangQuan, Ahn, Hyo-Sung
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Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application

, 2020
The fractional-order chaotic systems have characteristics of the all chaotic systems, however, the improper fractional-order chaotic systems have more complexity random sequences, which more suitable for chaotic cryptosystems.
Feifei Yang   +3 more
semanticscholar   +1 more source

Fractional order PI observer for a class of fractional order systems

Memorias del Congreso Nacional de Control Automático, 2023
Currently the study of fractional order systems has become of great research interest, in particular the state estimation stands out within the lines of studies for this type of systems. Different methodologies have been proposed in order to solve this problem, however most of the techniques involve complete information of the system.
Rafael Martínez-Guerra   +1 more
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Fractional-order ADRC framework for fractional-order parallel systems

2020 39th Chinese Control Conference (CCC), 2020
This study discusses the control of parallel fractional order systems (FOSs) by the fractional-order active disturbance rejection control (FOADRC) technique. The FOADRC framework for linear FOSs and the necessary conditions for the existence of a stable controller of the system are given.
Zong-yang LI   +5 more
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The effect of the fractional-order controller's orders variation on the fractional-order control systems

Proceedings. International Conference on Machine Learning and Cybernetics, 2003
This paper concerns fractional-order controllers. The definitions and properties of fractional calculus are introduced. The mathematical descriptions of the fractional-order system and the fractional-order controller are outlined. The variation of the fractional-order controller's order and its effect on the fractional-order control systems are ...
null Qing-Shan Zeng   +2 more
openaire   +1 more source

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