Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

Balasubramaniam, P.; Muthukumar, P.; Ratnavelu, Kuru

doi:10.1007/s11071-014-1865-4

Cited by 66 publications

(18 citation statements)

References 43 publications

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“…Dynamic-order fractional dynamic system. In recent years, the usage of fractional order dynamical systems play a vital role in real-world applications, including for examples, the affine cipher using date of birth fuzzy [77], fractional integral sliding mode control [10], fractional order modified Duffing systems [39], fractional order King Cobra chaotic system [75], digital cryptography [74], and authenticated encryption scheme [76]. Hence, we investigate the fractional order dynamical systems which have great application potentials in real-world engineering fields.…”

Section: Physical Discussion On Vo Fractional Integral and Derivativementioning

confidence: 99%

A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications

Sun

Chang

Zhang

et al. 2019

FCAA

282

138

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Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other variables dependent order have been successfully applied to investigate time and/or space dependent dynamics. This study aims to provide a survey of the recent relevant literature and findings in primary definitions, models, numerical methods and their applications. This review first offers an overview over the existing definitions proposed from different physical and application backgrounds, and then reviews several widely used numerical schemes in simulation. Moreover, as a powerful mathematical tool, the VO-FDE models have been remarkably acknowledged as an alternative and precise approach in effectively describing real-world phenomena. Hereby, we also make a brief summary on different physical models and typical applications. This review is expected to help the readers for the selection of appropriate definition, model and numerical method to solve specific physical and engineering problems.

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Section: Physical Discussion On Vo Fractional Integral and Derivativementioning

confidence: 99%

A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications

Sun

Chang

Zhang

et al. 2019

FCAA

282

138

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“…, and φ 4 (•) can have different dimensions, and it is easy to know that the uncertain terms considered in system (19) stand for a large range of system uncertainties. us, the economical model considered in some recent literature, for example, [10,16,18,[37][38][39], is a special case of our model (19). Our objective here is to design a proper controller u i (t) such that the state vector ζ(t) could track the desired signal…”

Section: Controller Design and Stability Analysismentioning

confidence: 99%

Robust Control of Disturbed Fractional‐Order Economical Chaotic Systems with Uncertain Parameters

Liu

et al. 2019

Complexity

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This paper focuses on the robust control of fractional-order economical chaotic system (FOECS) with parametric uncertainties and external disturbances. The dynamical behavior of FOECS is studied by numerical simulation, and circuit implementations of FOECS are also given. Based on fractional-order Lyapunov stability theorems, a robust adaptive controller, which can guarantee that all signals remain bounded and the tracking error tends to a small region, is designed. The proposed method can be used to control a large range of fractional-order systems with system uncertainties. Fractional-order adaptation laws are constructed to update the estimation of adaptive parameters. Finally, the robustness and effectiveness of our control method are indicated by simulation results.

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“…Therefore, such oscillations should be effectively suppressed. For this reason, various methods have been developed to stabilize non-linear chaotic systems, in which fractional order chaos control has also been focused, such as OGY type [25], feedback type [26][27][28], dynamic surface type [29], sliding mode type [30][31][32][33], backstepping type [34,35], etc.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Neural Network Control of Chaotic Fractional-Order Permanent Magnet Synchronous Motors Using Backstepping Technique

2020

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The backstepping technique is greatly effective for the integer-order triangular non-linear systems. Nevertheless, it is dramatically challenging to implement backstepping technique in the manipulation of fractional-order permanent magnet synchronous motors (FOPMSMs), since the fractional derivatives of the composite functions are deeply complex. In this paper, adaptive neural network (NN) backstepping-based control scheme for FOPMSMs on the basis of fractional Lyapunov stability criterion is established. First, we propose a novel adaptive synchronous controller for FOPMSMs by coupling with NNs and backstepping technique. Then, we present a detailed stability analysis in terms of FOPMSMs via the proposed controller. Finally, a simulation example is given to reveal that the proposed controller can effectively eliminate or restrain the chaos of FOPMSMs, and keep the tracking signals synchronous with the reference signals.

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Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

Cited by 66 publications

References 43 publications

A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications

A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications

Robust Control of Disturbed Fractional‐Order Economical Chaotic Systems with Uncertain Parameters

Adaptive Neural Network Control of Chaotic Fractional-Order Permanent Magnet Synchronous Motors Using Backstepping Technique

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