Control parametrization method for free planning time optimal control problems with time-delayed arguments

Wong, K. H.; Jennings, Leslie; Benyah, Francis

doi:10.1016/s0362-546x(01)00669-1

Cited by 9 publications

(3 citation statements)

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“…Control parameterization technique (CPT) belongs to the class of direct transcription methods (see [6,15]) for solving optimal control problems (OCPs) [10][11][12]. It relies on partitioning the time space, over which the OCP is to be solved using two types of partitions: first, the time space is partitioned by switching points representing the times at which the parameters of the control function (constant, linear, etc) switch their values; then in the second partition, each switching interval is partitioned by a number of quadrature points, at which the state variables are to be evaluated.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Optimal Regularization Parameters in Optimal Control Problems with time delay

Bashier

2016

JAM

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In this paper we use the L-curve method and the Morozov discrepancy principle for the estimation of the regularization parameter in the regularization of time-delayed optimal control computation. Zeroth order, first order and second order differential operators are considered. Two test examples show that the L-curve method and the two discrepancy principles give close estimations for the regularization parameters.

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Section: Introductionmentioning

confidence: 99%

Estimation of the Optimal Regularization Parameters in Optimal Control Problems with time delay

Bashier

2016

JAM

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“…This constrained optimal control problem is then solved by the well-known control parameterization method. (See [9], [11], [13], [14], [17], [21], and [22] for details.) Thus, based on the parameters given in [12], the optimal fishes' feeding rate and the optimal fishes' weight for harvest are obtained.…”

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confidence: 99%

Optimal control of fish-feeding in a three-dimensional calm freshwater pond considering environmental concern

Lee

Wong

Lee

2023

JIMO

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<p style='text-indent:20px;'>This paper describes the optimal fish-feeding in a three-dimensional calm freshwater pond based on the concentrations of seven water quality variables. A certain number of baby fishes are inserted into the pond simultaneously. They are then taken out of the pond simultaneously for harvest after having gone through a feeding program. This feeding program creates additional loads of water quality variables in the pond, which becomes pollutants. Thus, an optimal fish-feeding problem is formulated to maximize the final weight of the fishes, subject to the restrictions that the fishes are not under-fed and over-fed and the concentrations of the pollutants created by the fish-feeding program are not too large. A computational scheme using the finite element Galerkin scheme for the three-dimensional cubic domain and the control parameterization method is developed for solving the problem. Finally, a numerical example is solved.</p>

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“…in [18] and [19], Wong et.al. in [21] and [22]. More recently, based on the idea of Miser [23], Yu et.…”

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confidence: 99%

Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels

Wong

Lee

et al. 2018

Journal of Industrial &Amp; Management Optimization

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This paper considers an optimal production scheduling problem in a single-supplier-multi-manufacturer supply chain involving production and delivery time-delays, where the time-delays for the supplier and the manufacturers can have different values. The objective of both levels is to find an optimal production schedule so that their production rates and their inventory levels are close to the ideal values as much as possible in the whole planning horizon. Each manufacturer's problem, which involves one time-delayed argument, can be solved analytically by using the necessary condition of optimality. To tackle the supplier's problem involving n + 1 different time-delayed arguments (where n is the number of manufacturers) by the above approach, we need to introduce a model transformation technique which converts the original system of combined algebraic/differential equations with n + 1 time-delayed arguments into a sum of n subsystems , each of which consists of only two time-delayed arguments. Thus, the supplier's problem can also be solved analytically. Numerical examples consisting of a single supplier and four manufacturers are solved to provide insight of the optimal strategies of both levels.

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Control parametrization method for free planning time optimal control problems with time-delayed arguments

Cited by 9 publications

References 0 publications

Estimation of the Optimal Regularization Parameters in Optimal Control Problems with time delay

Estimation of the Optimal Regularization Parameters in Optimal Control Problems with time delay

Optimal control of fish-feeding in a three-dimensional calm freshwater pond considering environmental concern

Optimal production schedule in a single-supplier multi-manufacturer supply chain involving time delays in both levels

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