Initial values for Riccati ODEs from variational PDEs

IF 2.5 3区 数学 Q1 MATHEMATICS, APPLIED
V. Costanza, P. Rivadeneira
{"title":"Initial values for Riccati ODEs from variational PDEs","authors":"V. Costanza, P. Rivadeneira","doi":"10.1590/S1807-03022011000200005","DOIUrl":null,"url":null,"abstract":"The recently discovered variational PDEs (partial differential equations) for finding missing boundary conditions in Hamilton equations of optimal control are applied to the extended-space transformation of time-variant linear-quadratic regulator (LQR) problems. These problems become autonomous but with nonlinear dynamics and costs. The numerical solutions to the PDEs are checked against the analytical solutions to the original LQR problem. This is the first validation of the PDEs in the literature for a nonlinear context. It is also found that the initial value of the Riccati matrix can be obtained from the spatial derivative of the Hamiltonian flow, which satisfies the variational equation. This last result has practical implications when implementing two-degrees-of freedom control strategies for nonlinear systems with generalized costs.","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":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational & Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1590/S1807-03022011000200005","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 4

Abstract

The recently discovered variational PDEs (partial differential equations) for finding missing boundary conditions in Hamilton equations of optimal control are applied to the extended-space transformation of time-variant linear-quadratic regulator (LQR) problems. These problems become autonomous but with nonlinear dynamics and costs. The numerical solutions to the PDEs are checked against the analytical solutions to the original LQR problem. This is the first validation of the PDEs in the literature for a nonlinear context. It is also found that the initial value of the Riccati matrix can be obtained from the spatial derivative of the Hamiltonian flow, which satisfies the variational equation. This last result has practical implications when implementing two-degrees-of freedom control strategies for nonlinear systems with generalized costs.
由变分偏微分方程得到Riccati偏微分方程的初值
将最近发现的用于寻找Hamilton最优控制方程中缺失边界条件的变分偏微分方程应用于时变线性二次型调节器(LQR)问题的扩展空间变换。这些问题变得自治,但具有非线性动力学和成本。将微分方程的数值解与原LQR问题的解析解进行了对比。这是文献中首次对非线性环境下的偏微分方程进行验证。通过对哈密顿流的空间导数可以得到Riccati矩阵的初值,满足变分方程。最后的结果对于实现具有广义代价的非线性系统的二自由度控制策略具有实际意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Computational & Applied Mathematics
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信