A new computational approach for optimal control problems with multiple time-delay

Wu, Di; Bai, Yanqin; Yu, Changjun

doi:10.1016/j.automatica.2018.12.036

Cited by 42 publications

(28 citation statements)

References 23 publications

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“…However, its calculation process is complicated and the efficiency is relatively low. DT transcribes the original DOP into a nonlinear programming (NLP) problem by an approximation scheme . To obtain the optimal performance index, the resulting NLP problem is solved on a sequence of refined meshes until a desired tolerance is reached .…”

Section: Introductionmentioning

confidence: 99%

“…DT transcribes the original DOP into a nonlinear programming (NLP) problem by an approximation scheme. [20,21] To obtain the optimal performance index, the resulting NLP problem is solved on a sequence of refined meshes until a desired tolerance is reached. [11] Particularly, DT has become popular in several areas due to the high accuracy in approximating non-analytic solutions with relatively few discretization points.…”

Section: Introductionmentioning

confidence: 99%

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A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

Xiao

Ma³

et al. 2019

Can J Chem Eng

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This paper presents an effective orthogonal collocation approach to approximate dynamic optimization problems into nonlinear programming problems, where the resulting problems can then be usually solved by first‐order sensitivity based algorithms. However, the results obtained fail to satisfy the timeliness and accuracy requirements of some dynamic optimization problems. A novel collocation approach with second‐order sensitivity information is therefore first proposed to improve the efficiency of the method. The resulting nonlinear programming problem is obtained through the orthogonal collocation on finite element combined with a single shooting approach. Three benchmark optimal control problems are considered to demonstrate the performance of the presented approach. Comparisons among the proposed approach, the BFGS method, and other literature solutions are also carried out in detail. Numerical results validate the effectiveness of the proposed method and the time saving benefit.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

Xiao

Ma³

et al. 2019

Can J Chem Eng

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show abstract

“…Ghanbari and Farahi [5] obtained optimal control pair for nonlinear delay HIV model with quadratic cost functional by using Fourier series approximation. Recent research work has been focused on optimal control problem of delayed HIV model (see for example [7,8,10,11] ). All these models considered the effect of control strategy on single pathogen virus.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Time Delayed HIV-1 Infection Model

Ali¹,

Chohan²,

Zaman³

2019

Eur. J. Pure Appl. Math.

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In this paper, an optimal control problem of HIV infection model of delay differential equations is taken into account. Then we set a control function which represents the efficiency of reverse transcriptase inhibitors. Objective functional is constructed to minimize the virus concentration as well as treatment costs.Adjoint system is derived using Pontryagins Maximum Principle. Optimality system is calculated and numerical simulation is carried out to illustrate the theoretical results. Finally, conclusion is drawn

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“…This method only maps the current state and control vectors into the new time scale, while the delayed state and control vectors remain in the original time scale. Recently, Wu et al [31] further improved this approach and presented a new computational method for solving TDOCP. Compared with the hybrid time-scaling transformation, the new approach provides an explicit closed-form expression for the delay time in the new time horizon.…”

mentioning

confidence: 99%

“…In [31] and [34], control parametrization approach was used to discretize the control function, control switching times were optimized via time-scaling transformation technique, and the gradient formulae are obtained by variational method. To further improve the computational efficiency, in this paper, we derive the co-state system and the gradient formulae for TDOCP.…”

mentioning

confidence: 99%

A new gradient computational formula for optimal control problems with time-delay

Yu¹,

Yuan²,

Su³

2022

JIMO

Self Cite

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In this paper, we consider a class of time-delay optimal control problem (TDOCP) with canonical equality and inequality constraints. By applying control parameterization method together with time-scaling transformation, a TDOCP can be readily solved by gradient-based optimization methods. The partial derivative of the cost as well as the constraint functions with respect to the decision variables are obtained by variational approach, which is inefficient when the discretization for the control function is relatively dense. For general optimal control problem without time-delay, co-state approach is an effective way to compute the gradients, however, when time-delay is involved in the dynamic system, the co-state system is not known. In this paper, we derive the co-state system for TDOCP to compute the gradients of the cost and constraints. Numerical results show that the computational efficiency is much higher when compared with the traditional variational approach.

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A new computational approach for optimal control problems with multiple time-delay

Cited by 42 publications

References 23 publications

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems

Optimal Control of a Time Delayed HIV-1 Infection Model

A new gradient computational formula for optimal control problems with time-delay

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