Bézier control points method to solve constrained quadratic optimal control of time varying linear systems

Ghomanjani, Fateme; Farahi, Mohammad Hadi; Gachpazan, Mortaza

doi:10.1590/s1807-03022012000300001

Cited by 19 publications

(27 citation statements)

References 19 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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“…Ghomanjani et al [16] proved the convergence of this method where n→ ∞. Now, we define the residual function over the interval [t 0 , t f ] as follows:…”

Section: Problem Statementmentioning

confidence: 99%

“…Also the Bezier control points method is used for solving delay differential equation (see [15]). Some other applications of the Bezier functions and control points are found in (see [16]). In the present work, we suggest a technique similar to the one which was used in [16] for solving Riccati differential equations with delay.…”

Section: Introductionmentioning

confidence: 99%

Approximate solution for quadratic Riccati differential equation

Ghomanjani

Khorram

2017

Journal of Taibah University for Science

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The quadratic Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science. This paper introduces an efficient method for solving the quadratic Riccati differential equation and the Riccati differential-difference equation. In this technique, the Bezier curves method is considered as an algorithm to find the approximate solution of the nonlinear Riccati equation. Some examples in different cases are given to demonstrate simplicity and efficiency of the proposed method.

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“…the proposed algorithm is compared with some recently proposed algorithms. These methods consist of SUMT and SQP, proposed in [11], continuous genetic algorithm, CGA [1], (better than SUMT), IPSO-SQP [21], (more accurate than some heuristic algorithms such as GA [22], DE [8], and PSO [15]) and some numerical methods [12,14,29]. Because of the stochastic nature of the proposed algorithm, 10 different runs were made for each result.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

Ghanbari

Nezhadhosein

Heidari

2014

IJAMR

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Here, a two-phase algorithm based on integrating particle swarm optimization (PSO) with modified hybrid genetic algorithm (MHGA) is proposed for solving the associated nonlinear programming problem of a nonlinear optimal control problem. In the first phase, PSO starts with a completely random initial swarm of particles, where each of them contains two random matrices in time nodes. After phase 1, to achieve more accurate solutions, the number of time nodes is increased. The values of the associated new control inputs are estimated by linear or spline interpolations using the curves computed in the phase 1. In addition, to maintain the diversity in the population, some additional individuals are added randomly. Next, in the second phase, MHGA, starts by the new population constructed by the above procedure and tries to improve the obtained solutions at the end of phase 1. MHGA combines a GA with a successive quadratic programming, SQP, as a local search. Finally, we implement the proposed algorithm on some well-known nonlinear optimal control problems. The numerical results show that the proposed algorithm can find almost better solution than other proposed algorithms.

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Bézier control points method to solve constrained quadratic optimal control of time varying linear systems

Cited by 19 publications

References 19 publications

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

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

Approximate solution for quadratic Riccati differential equation

Integrating PSO with modified hybrid GA for solving nonlinear optimal control problems

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