利用bsamizier控制点求解时变二次型最优控制问题

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2011-07-18 DOI:10.1590/S1807-03022011000200007

M. Gachpazan

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引用次数: 20

摘要

本文采用基于Bezier控制点的最小二乘法求解线性二次型光控制问题。我们将包含t的区间分成k个子区间，用Bezier曲线近似轨迹和控制函数。我们选择Bezier曲线作为三次的逐次多项式，并通过四个控制点确定任意子区间上的Bezier曲线。利用最小二乘法引入一个优化问题，并通过求解该优化问题计算控制点。数值实验说明了所提出的方法。

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Solving of time varying quadratic optimal control problems by using Bézier control points

In this paper, linear quadratic optial control probles are solved by applying least square method based on Bezier control points. We divide the interval which includes t, into k subintervals and approximate the trajectory and control functions by Bezier curves. We have chosen the Bezier curves as piacewise polynomials of degree three, and determined Bezier curves on any subinterval by four control points. By using least square ethod, e introduce an optimization problem and compute the control points by solving this optimization problem. Numerical experiments are presented to illustrate the proposed method.

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来源期刊

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.