2012
DOI: 10.1590/s1807-03022012000300001
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Abstract: A computational method based on Bézier control points is presented to solve optimal control problems governed by time varying linear dynamical systems subject to terminal state equality constraints and state inequality constraints. The method approximates each of the system state variables and each of the control variables by a Bézier curve of unknown control points.The new approximated problems converted to a quadratic programming problem which can be solved more easily than the original problem. Some example… Show more

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Cited by 20 publications
(25 citation statements)
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References 19 publications
(25 reference statements)
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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%
“…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%
“…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%
“…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%