{"title":"利用bsamizier控制点求解时变二次型最优控制问题","authors":"M. Gachpazan","doi":"10.1590/S1807-03022011000200007","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2011-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Solving of time varying quadratic optimal control problems by using Bézier control points\",\"authors\":\"M. Gachpazan\",\"doi\":\"10.1590/S1807-03022011000200007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":50649,\"journal\":{\"name\":\"Computational & Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2011-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational & Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1590/S1807-03022011000200007\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational & Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1590/S1807-03022011000200007","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.