New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems

Kahouli, Omar; Jmal, Assaad; Naifar, Omar; Nagy, A. M.; Makhlouf, Abdellatif Ben

doi:10.3390/math10111814

Cited by 8 publications

(3 citation statements)

References 33 publications

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“…To see some of these applications, the feedback control into the logistic model 1 , nonanalytic dynamic systems 2 , application to identification problems 3 , economic growth model and so on 4, -7 . Fractional optimal control problems (FOCPs) are the generalization of the OCPs with fractional dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

Holel

Hasan²

2023

Baghdad Sci.J

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The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

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Section: Introductionmentioning

confidence: 99%

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

Holel

Hasan²

2023

Baghdad Sci.J

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“…Compared with the other methods, the model of the CPG-based method owns fewer control parameters. Meanwhile, the CPG-based method can control various forms of locomotion, perform smooth transition, and easily integrate abundant sensing signals [17,18]. Fractional calculus and the investigation of fractional-order systems have been extensively studied in the last decades [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A Novel Double-Layered Central Pattern Generator-Based Motion Controller for the Hexapod Robot

et al. 2023

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To implement the various movement control of the hexapod robot, a motion controller based on the double-layered central pattern generator (CPG) is proposed in this paper. The novel CPG network is composed of a rhythm layer and a pattern layer. The CPG neurons are constructed based on Kuramoto nonlinear oscillator. The parameters including the frequency, coupling strength, and phase difference matrix of the CPG network for four typical gaits are planned. The mapping relationship between the signals of the CPG network and the joint trajectories of the hexapod robot is designed. The co-simulations and experiments have been conducted to verify the feasibility of the proposed CPG-based controller. The actual average velocities of the wave gait, the tetrapod gait, the tripod gait, and the self-turning gait are 10.8 mm/s, 25.5 mm/s, 37.8 mm/s and 26°/s, respectively. The results verify that the hexapod robot with the proposed double-layered CPG-based controller can perform stable and various movements.

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“…Fractional calculus has captured the attention of many scientists and engineers working in a variety of fields in recent years [3][4][5][6][7]. This is mostly owing to its ability to more accurately model specific physical systems than the traditional integer-order option, such as manipulator systems, multi-area power systems, multisource renewable energy systems, and electrical vehicles [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Multivariable Adaptive Control Based on a Nonlinear Scalar Update Law

2022

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This paper proposes a new fractional-order model reference adaptive control (FOMRAC) framework for a fractional-order multivariable system with parameter uncertainty. The designed FOMRAC scheme depends on a fractional-order nonlinear scalar update law. Specifically, the scalar update law does not change as the input–output dimension changes. The main advantage of the proposed adaptive controller is that only one parameter online update is needed such that the computational burden in the existing FOMRAC can be relieved. Furthermore, we show that all signals in this adaptive scheme are bounded and the mean value of the squared norm of the error converges to zero. Two illustrative numerical examples are presented to demonstrate the efficiency of the proposed control scheme.

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New Result for the Analysis of Katugampola Fractional-Order Systems—Application to Identification Problems

Cited by 8 publications

References 33 publications

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

A Novel Double-Layered Central Pattern Generator-Based Motion Controller for the Hexapod Robot

Fractional-Order Multivariable Adaptive Control Based on a Nonlinear Scalar Update Law

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