The solutions of time-delayed optimal control problems by the use of modified line-up competition algorithm

Sun, Daim-Yuang; Huang, Tzu-Chen

doi:10.1016/j.jtice.2009.04.013

Cited by 21 publications

(12 citation statements)

References 31 publications

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“…For the time step size h = 0.4,0.04,0.004, Figs and show the simulation curves of x ( t ) and u ( t ) for the OCP ()‐() with constant time‐delay τ ( t ) = 1 and time‐varying delay

τ (t) = 1 + \frac{1}{2} \frac{t^{2}}{1 + t}

, respectively. These figures indicate that the numerical solution of the new approximation scheme is in good agreement with the available litreture .…”

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 71%

“…From Table it is observed that for the time step size h = 0.004 and constant time‐delay τ ( t ) = 1, a minimum value of the cost functional is obtained as J = 4.796786. As it is shown in Table , this value of J computed by the proposed scheme is compared very well with those achieved by the single‐term Walsh series , iterative dynamic programming , Legendre multi‐wavelets , modified line‐up competition algorithm and recursive shooting method . Comparison results reveal the validity of the proposed FD method for solving the TDOCP ()–().…”

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 59%

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An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

Jajarmi

Hajipour

2016

Asian Journal of Control

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In this paper, an efficient finite difference method is presented for the solution of time‐delay optimal control problems with time‐varying delay in the state. By using the Pontryagin's maximum principle, the original time‐delay optimal control problem is first transformed into a system of coupled two‐point boundary value problems involving both delay and advance terms. Then the derived system is converted into a system of linear algebraic equations by using a second‐order finite difference formula and a Hermite interpolation polynomial for the first‐order derivatives and delay terms, respectively. The convergence analysis of the proposed approach is provided. The new scheme is also successful for the optimal control of time‐delay systems affected by external persistent disturbances. Numerical examples are included to demonstrate the validity and applicability of the new technique. Some comparative results are included to illustrate the effectiveness of the proposed method.

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“…For the time step size h = 0.4,0.04,0.004, Figs and show the simulation curves of x ( t ) and u ( t ) for the OCP ()‐() with constant time‐delay τ ( t ) = 1 and time‐varying delay

τ (t) = 1 + \frac{1}{2} \frac{t^{2}}{1 + t}

, respectively. These figures indicate that the numerical solution of the new approximation scheme is in good agreement with the available litreture .…”

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 71%

Section: The Second‐order Two‐step Fd Methodssupporting

confidence: 59%

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

Jajarmi

Hajipour

2016

Asian Journal of Control

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“…Table shows the numerical results obtained with Legendre multiwavelets by using eight basis functions, hybrid Bernoulli polynomials with k =2, M =2, hybrid function and Páde approximation with N =2, M =2, modified line‐up competition algorithm with eight time divisions and 200 trial members in one generation using line‐up competition algorithm.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Example 6. Consider the following example: Numerical methods J Hybrid Bernoulli polynomials 24 3.21663 Semigroup approximation 50 3.2587 Hybrid function and Páde approximation 53 3.3208 Modified line-up competition algorithm 54 3.4004 Legendre multiwavelets 27 3.43254 Hybrid Legendre polynomials 55 3 subject to the time-delay system…”

Section: Examplementioning

confidence: 99%

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

Sabermahani

Ordokhani

Yousefi

2019

Optim Control Appl Methods

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Summary In this paper, a numerical method for solving time‐varying delay equations and optimal control problems with time‐varying delay systems is discussed. This method is based upon Fibonacci wavelets and Petrov‐Galerkin method. To solve these problems, first, the Fibonacci wavelets are presented. With the aid of operational matrices of integration and delay for Fibonacci wavelets and using Petrov‐Galerkin method and Newton's iterative method, we solve two classes of time‐varying delay problems, numerically. The approximate solutions achieved by this method satisfy all the initial conditions. In addition, an estimation of the error is given. Numerical results are included to demonstrate the accuracy and applicability of the present technique.

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“…The Line-up algorithm has been successfully applied to various fields such as mathematical function optimization [19], [20]; separation process optimization [21]; optimal control problems [22], [23], among other applications.…”

Section: Line-up Algorithmmentioning

confidence: 99%

Multi-Objective Optimization Line-Up Algorithm Applied to the Design of a Nonlinear Vibration Absorber

Borges¹,

Lobato²,

Steffen³

2014

Proceedings of 10th World Congress on Computational Mechanics

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The solutions of time-delayed optimal control problems by the use of modified line-up competition algorithm

Cited by 21 publications

References 31 publications

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

Fibonacci wavelets and their applications for solving two classes of time‐varying delay problems

Multi-Objective Optimization Line-Up Algorithm Applied to the Design of a Nonlinear Vibration Absorber

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