Controllability of higher order stochastic fractional control delay systems involving damping behavior

Arthi, G.; Suganya, K.

doi:10.1016/j.amc.2021.126439

Cited by 6 publications

(4 citation statements)

References 35 publications

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“…They provide a powerful framework for understanding and predicting the behavior of complex systems with memory, randomness, and time delays. See, for example, [1][2][3][4][5][6] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

Bai,

Bai

2024

Axioms

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In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo-type fractional stochastic delay differential systems(FSDDSs) with Poisson jumps by utilizing the delayed perturbation of the Mittag–Leffler function. Moreover, by using the Burkholder–Davis–Gundy inequality, Doob’s martingale inequality, and Hölder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

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Section: Introductionmentioning

confidence: 99%

The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

Bai,

Bai

2024

Axioms

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show abstract

“…They provide a powerful framework for understanding and predicting the behavior of complex systems with memory, randomness, and time delays. See for examples [1][2][3][4][5][6], and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

“…−2t sin(x 1 (t)) + 1 4 e −t sin3 t arctan(x 1 (t − 0.4)) + 1 7 1 3 e −2t cos(x 2 (t)) + 1 4 e −t cos 3 t arctan(x 2 (t − 0.4)) + 1 −t arctan(x 1 (t)) + 1 3 e −2t cos 2 t sin(x 1 (t − 0.4)) + 1 3 1 4 e −t sin(x 2 (t)) + 1 3 e −t sin 2 t arctan(x 2 (t − 0.4)) + 1 − y(t) + x(t − 0.4) − y(t − 0.4) ).f (t, x(t), x(t − 0.4)) − f (t, y(t), y(t − 0.4)) 3 ≤ 2 2 3 3 ( x(t) − y(t) 3 + x(t − 0.4) − y(t − 0.4) 3 ),…”

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The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

Bai,

Bai

2023

Preprint

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In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

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“…Saadatmand et al 36 have suggested a novel technique for LFO damping in the power system depending on optimum integration of generators compatible with the LPF and PSSs of the wide‐area measurement‐based fractional‐order proportional‐integral‐derivative (WMFOPID) controller. Arthi and Suganya 37 have introduced the issues of control of linear with nonlinear high‐order stochastic fractional control delay device with damping behavior that involved Caputo fractional derivative. The significant contributions were noted as follows: It was necessary to assume the fractional damped stochastic systems (FDSS) by high order.…”

Section: Introductionmentioning

confidence: 99%

Optimal design of proportional integral derivative acceleration controller for higher‐order nonlinear time delay system using m‐MBOA technique

Arulvadivu

Manoharan²,

Singh³

et al. 2022

Int J Numerical Modelling

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In general, the parameter adjustment is used to design the proportional‐integral‐derivative (PID) controllers. Despite that, to enhance the capacity of control performance by adjusting parameters is limited. Therefore, in this paper, an optimal design of proportional integral derivative acceleration (PIDA) controller is proposed for higher‐order nonlinear time delay system (TDS) using modified butterfly optimization algorithm (MBOA) with the aim of achieving optimal closed‐loop response, which is enhanced with mutualism system (m‐MBOA). In the proposed approach, the mutualism stage of symbiotic organisms search (SOS) and butterfly optimization algorithm (BOA) global exploration phase is considered. The major aim of the proposed approach is to “tune the gain of the PIDA controller to get the desired response.” It reduces the drawback of the PIDA controller in the higher‐order TDS using advanced control limits is the individuality of the proposed approach. Here, the proposed approach is employed to reduce the higher‐order delays together with reliability limits, like minor overshoots, time resolution, and fixed stage deficiency. To evaluate the proposed PIDA controller, the execution is done by the MATLAB/Simulink platform, also its efficiency is compared with existing approaches. Moreover, the proposed and existing approaches are analyzed with mean, median, and standard deviations. From the analysis, the proposed approach achieves the stability with minimal delay time and reduces the computational complexity. Finally, the simulation results demonstrate that the proposed approach can efficiently with accurately find the optimal global solutions.

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Controllability of higher order stochastic fractional control delay systems involving damping behavior

Cited by 6 publications

References 35 publications

The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps

Optimal design of proportional integral derivative acceleration controller for higher‐order nonlinear time delay system using m‐MBOA technique

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