A modified teaching–learning-based optimization for optimal control of Volterra integral systems

Khanduzi, Raheleh; Ebrahimzadeh, Asyieh; Peyghami, M. Reza

doi:10.1007/s00500-017-2933-8

Cited by 9 publications

(8 citation statements)

References 14 publications

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“…Table 5 presents the RMSE of the approximate solutions for ν = 1. The comparison of the obtained optimal values J with those reported in Khanduzi et al (2018), Maleknejad and Ebrahimzadeh (2014) is shown in Table 6. From these Tables, we can conclude that the SHP is an effective tool for solving this OCP and that the RMSE of the approximate solutions significantly decreases as the number of basis functions increases.…”

Section: Example 2 Let Us Consider Minimization Of the Following Performance Indexmentioning

confidence: 75%

“…The optimal control problems (OCP) involve the minimization of a cost function (performance index) subject to dynamic constraints on the states and controls. The OCP occur in many applications of distinct areas such as economics, engineering, geometry, and mathematics (Banks and Burns, 1978;Heydari and Avazzadeh, 2018;Khanduzi et al, 2018;Mohammadi et al, 2018;Moradi et al, 2019;Palanisamy and Ganti Prasada, 1983;Wang, 2007). Most of the OCP do not have exact analytic solutions (Bhrawy et al, 2017;Heydari and Avazzadeh, 2018;Moradi et al, 2019) and the development of numerical methods became an important topic.…”

Section: Introductionmentioning

confidence: 99%

“…Because of the relevance of such applications, various numerical methods were proposed to approximate the solution of such OCP. We can mention the Legendre wavelets (Maleknejad and Ebrahimzadeh, 2014), Legendre polynomials (Tohidi and Samadi, 2013), discrete approximation (Belbas, 2007), variational equations (Belbas, 1999), hybrid functions (Mashayekhi et al, 2013), shifted Chebyshev series (Chou and Horng, 1987), and teaching-learning-based optimization methods (Khanduzi et al, 2018). In this study, a direct numerical approach based on the shifted Hahn polynomials (SHP) is developed for the solution of the OCP governed by fractional Volterra integro-differential equations (FVIDEs).…”

Section: Introductionmentioning

confidence: 99%

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A discrete polynomials approach for optimal control of fractional Volterra integro-differential equations

Mohammadi

Moradi

Machado

2020

Journal of Vibration and Control

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This study develops an efficient numerical method for optimal control problems governed by fractional Volterra integro-differential equations. A new type of polynomials orthogonal with respect to a discrete norm, namely discrete Hahn polynomials, is introduced and its properties investigated. Fractional operational matrices for the orthogonal polynomials are also derived. A direct numerical algorithm supported by the discrete Hahn polynomials and operational matrices is used to approximate solution of optimal control problems governed by fractional Volterra integro-differential equations. Several examples are analyzed and the results compared with those of other methods. The required CPU time assesses the computational cost and complexity of the proposed method.

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Section: Example 2 Let Us Consider Minimization Of the Following Performance Indexmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A discrete polynomials approach for optimal control of fractional Volterra integro-differential equations

Mohammadi

Moradi

Machado

2020

Journal of Vibration and Control

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“…Example 4. Consider the following optimal control problem subject to fractional Volterra integro-differential Equation (42) (Khanduzi et al, 2018):…”

Section: Illustrative Test Problemsmentioning

confidence: 99%

Numerical solution for a class of fractional optimal control problems using the fractional-order Bernoulli functions

Valian

Ordokhani

Vali

2021

Transactions of the Institute of Measurement and Control

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The main purpose of this paper is to provide an efficient method for solving some types of fractional optimal control problems governed by integro-differential and differential equations, and because finding the analytical solutions to these problems is usually difficult, a numerical method is proposed. In this study, the fractional-order Bernoulli functions (F-BFs) are applied as basis functions and a new operational matrix of fractional integration is constructed for these functions. In the first step, the problem is transformed into an equivalent variational problem. Then the F-BFs, the constructed operational matrix, the Gauss quadrature formula, and necessary conditions for optimization are used to convert the problem into a system of algebraic equations. Finally, with the aid of Newton’s iterative method, the system of algebraic equations is solved and the approximate solution of the problem is obtained. Several numerical examples have been analysed for illustrating the efficiency and accuracy of the proposed method, and the results have been compared with the exact solutions and the results of other methods. The results show that the method provides accurate solutions.

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“…Teaching-learning-based optimization algorithm has been presented by Rao et al [65] for optimization in the design problems of mechanical systems. Due to its simplicity and effectiveness, TLBO was studied in several other engineering problems [66][67][68][69][70][71][72][73]. Regarding structural damage detection, Pholdee and Bureerat [74] combined TLBO with Broyden-Fletcher-Goldfarb-Shanno algorithm (BFGS) to detect damage in complex truss structures using natural frequencies.…”

Section: Literature Reviewmentioning

confidence: 99%

Teaching–learning-based optimization algorithm for solving structural damage detection problem in frames via changes in vibration responses

Kundu

Mishra

Maity

2021

Archit. Struct. Constr.

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Optimization algorithms are primarily responsible for efficiency in vibration-based damage detection particularly when utilizing the inverse approach. A complex problem of damage detection tends to converge into local minima, generated by a false damaged state which produces a response that is almost similar to the actual damaged state. Hence, there is a need for an efficient and accurate soft computing technique that can find the global minima or the actual damaged state. Recently, the teaching-learning based optimization (TLBO) algorithm has become quite popular due to its superior performance especially when compared to other metaheuristic algorithms. In this paper, damage estimation capability of the TLBO for frame structures and a benchmark problem of cantilever beam is studied and comparisons are made with some established soft computing techniques. TLBO is observed to produce better results relative to the other artificial intelligence-based techniques used for structural health monitoring.

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A modified teaching–learning-based optimization for optimal control of Volterra integral systems

Cited by 9 publications

References 14 publications

A discrete polynomials approach for optimal control of fractional Volterra integro-differential equations

A discrete polynomials approach for optimal control of fractional Volterra integro-differential equations

Numerical solution for a class of fractional optimal control problems using the fractional-order Bernoulli functions

Teaching–learning-based optimization algorithm for solving structural damage detection problem in frames via changes in vibration responses

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