A Novel Method to Solve a Class of Distributed Optimal Control Problems Using Bezier Curves

Darehmiraki, Majid; Farahi, Mohammad Hadi; Effati, Sohrab

doi:10.1115/1.4033755

Cited by 12 publications

(5 citation statements)

References 29 publications

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“…It is worth noticing that the use of Bezier curves to solve optimal control problems has already been proposed in [22][23][24][25][26] and several others. Here, however, Bezier curves are a natural result of the choice of Bernstein polynomials for the basis, which were chosen precisely because the resulting Bezier curves have the convex hull and variation diminishing property.…”

Section: Choice Of Basis Functionsmentioning

confidence: 99%

Multi-Objective Optimal Control of Re-entry and Abort Scenarios

Ricciardi

Maddock

Vasile

2018

2018 Space Flight Mechanics Meeting

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This version is available at https://strathprints.strath.ac.uk/63152/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Multi-Objective Optimal Control of Re-entry and Abort Scenarios

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Section: Choice Of Basis Functionsmentioning

confidence: 99%

Multi-Objective Optimal Control of Re-entry and Abort Scenarios

Ricciardi

Maddock

Vasile

2018

2018 Space Flight Mechanics Meeting

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“…A Legendre pseudo-spectral method is proposed to solve distributed optimal control of the viscous Burgers equations (Sabeh et al, 2016). Bezier curves are used to solve a class of D-O OCPs (Darehmiraki et al, 2016). Zaky proposed a Legendre collocation method to solve D-O FOCPs (Zaky, 2018).…”

Section: Introductionmentioning

confidence: 99%

Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method

Sabermahani

Ordokhani

2023

Journal of Vibration and Control

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A new approach to finding the approximate solution of distributed-order fractional optimal control problems (D-O FOCPs) is proposed. This method is based on Fibonacci wavelets (FWs). We present a new Riemann–Liouville operational matrix for FWs using the hypergeometric function. Using this, an operational matrix of the distributed-order fractional derivative is presented. Implementing the mentioned operational matrix with the help of the Gauss–Legendre numerical integration, the problem converts to a system of algebraic equations. Error analysis is proposed. Finally, the validation of the present technique is checked by solving some numerical examples.

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“…All the method mentioned so far, belong to discretize‐then‐optimize algorithms. On the other hand, for the optimize‐then‐discretize the constraints should be transformed to an algebraic system by using different methods such as FEM, finite difference method, or other existing method for discretization [6, 7, 21].…”

Section: Introductionmentioning

confidence: 99%

An interpolation method for the optimal control problem governed by the elliptic convection–diffusion equation

Darehmiraki

Rezazadeh

Ahmadian

et al. 2020

Numerical Methods Partial

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We know that due to the Weierstrass approximation theorem any continuous function over a closed interval can be approximated by a polynomial of sufficiently high degree. Therefore, they are frequently used to approximate functions. We proposed a Lagrange polynomial‐based approach for solving the optimal control problem governed by the elliptic convection–diffusion partial differential equation. This paper solves it by the barycentric interpolation method as a class of strong‐form numerical methods. Thanks to Lagrangian multipliers, optimality system is derived and then the barycentric collocation method is employed to discretize the state variable and adjoint variable. Barycentric interpolation method is a Lagrange polynomial interpolation that is fast and deserves to be known as a method of polynomial interpolation. The convergence of the proposed method is also proved. At the end, numerical experiments are employed to illustrate the theoretical findings.

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A Novel Method to Solve a Class of Distributed Optimal Control Problems Using Bezier Curves

Cited by 12 publications

References 29 publications

Multi-Objective Optimal Control of Re-entry and Abort Scenarios

Multi-Objective Optimal Control of Re-entry and Abort Scenarios

Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method

An interpolation method for the optimal control problem governed by the elliptic convection–diffusion equation

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