An iterative approach for solving fractional optimal control problems

Alizadeh, Ali; Effati, Sohrab

doi:10.1177/1077546316633391

Cited by 45 publications

(33 citation statements)

References 49 publications

(42 reference statements)

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“…By replacing (17)- (22) in Equations (7)-(9) and discretizing the obtained equations at interpolating points {t k } N k=0 , we get…”

Section: Fractional Chebyshev Peudospectral Methodsmentioning

confidence: 99%

“…This problem has been considered by many researchers. Here, we compare our method with other works . The corresponding system can be written as

({, \begin{matrix} array_{0}^{C} D_{t}^{α} x (t) = - x (t) + u (t), & array 0 < t \leq 1, \\ array_{t} D_{1}^{α} λ (t) = x (t) - λ (t), & array 0 \leq t < 1, \\ array u (t) + λ (t) = 0, & array 0 \leq t \leq 1, \\ array x (0) = 1, λ (1) = 0 . \end{matrix})

…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Here, we compare our method with other works. 19,22,23,32,33 The corresponding system (7)-(9) can be written as…”

Section: Example 1 Consider the Following Focpmentioning

confidence: 99%

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Fractional Chebyshev pseudospectral method for fractional optimal control problems

Habibli

Skandari

2019

Optim Control Appl Methods

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Summary In this paper, we introduce and apply a fractional pseudospectral method for indirectly solving a generic form of fractional optimal control problems. By employing the fractional Lagrange interpolating functions and discretizing the necessary optimality conditions at Chebyshev‐Gauss‐Lobatto points, the problem is converted into an algebraic system. By solving this system, the optimal solution of the main fractional optimal control problem is approximated. Finally, in some numerical examples, we show the applicability, efficiency, and accuracy of the proposed method comparing with some other methods.

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“…By replacing (17)- (22) in Equations (7)-(9) and discretizing the obtained equations at interpolating points {t k } N k=0 , we get…”

Section: Fractional Chebyshev Peudospectral Methodsmentioning

confidence: 99%

“…This problem has been considered by many researchers. Here, we compare our method with other works . The corresponding system can be written as

({, \begin{matrix} array_{0}^{C} D_{t}^{α} x (t) = - x (t) + u (t), & array 0 < t \leq 1, \\ array_{t} D_{1}^{α} λ (t) = x (t) - λ (t), & array 0 \leq t < 1, \\ array u (t) + λ (t) = 0, & array 0 \leq t \leq 1, \\ array x (0) = 1, λ (1) = 0 . \end{matrix})

…”

Section: Numerical Examplesmentioning

confidence: 99%

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Fractional Chebyshev pseudospectral method for fractional optimal control problems

Habibli

Skandari

2019

Optim Control Appl Methods

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“…For today, one of the weak points in the field of optimum control is the lack of a theoretical base for the optimal control trajectory search method formalization [7][8][9].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Development of the method of quasi-optimal robust control for periodic operational processes

Lutsenko

Fomovskaya

Koval

et al. 2017

EEJET

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Пошук супремуму оптимальної траєк-торії управління практично недосяжний в реальних умовах. Це пов'язано з великою кількістю ступенів свободи керованої сис-теми, коливанням попиту, вхідних і вихід-них цін, істотною нелінійністю внутріш-ньосистемних процесів. Виходом в такій ситуації може бути розробка робастних методів квазіоптимального управління. Пропонований підхід заснований на встанов-ленні взаємозв'язку управління перетворю-вальної системи з поточним рівнем виробни-чих запасів Ключові слова: оптимізація пов'язаних систем, квазіоптимальний управління, ро-бастна оптимізація, квазіоптимальна трає-кторія управління Поиск супремума оптимальной траекто-рии управления практически недостижим в реальных условиях. Это связано с большим количеством степеней свободы управляе-мой системы, колебанием спроса, входных и выходных цен, существенной нелинейно-стью внутрисистемных процессов. Выходом в такой ситуации может быть разработ-ка робастных методов квазиоптимального управления. Предлагаемый подход основан на установлении взаимосвязи управления преобразовательной системы с текущим уровнем производственных запасов Ключевые слова: оптимизация связан-ных систем, квазиоптимальное управление, робастная оптимизация, квазиоптимальная траектория управления UDC 007.5

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“…Sufficient condition for controllability (controllability with memory) were derived. Some numerical methods for solving of FOCPs (including a combination of the perturbation homotopy and parameterization methods, variational iteration method, the Bezier curves method, a finite difference method) are proposed in [4,6,20,36]. In [11,38,39], the numerical method is based on the operational matrix of the Riemann-Liouville fractional integration with the help of the Legendre orthonormal polynomial basis.…”

Section: Introductionmentioning

confidence: 99%