Lobatto IIIA methods, direct transcription, and DAEs with delays

被引：5

作者：

Betts, John T. ^{[1
]}

Campbell, Stephen L. ^{[2
]}

Thompson, Karmethia ^{[2
]}

机构：

[1] Appl Math Anal LLC, Issaquah, WA 98027 USA

[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

来源：

NUMERICAL ALGORITHMS | 2015年 / 69卷 / 02期

基金：

美国国家科学基金会;

关键词：

Optimal control; Delays; Direct transcription; Numerical discretizations; Stability; DIFFERENTIAL-ALGEBRAIC EQUATIONS; ASYMPTOTIC STABILITY; SYSTEMS;

D O I：

10.1007/s11075-014-9896-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recent results in the literature have shown that LobattoIIIA methods may have some undesirable stability properties when used to numerically integrate differential algebraic equations (DAEs) which have delays. In these studies Lagrange interpolation was used to compute the delayed terms. Here we show that this undesirable behavior of LobattoIIIA methods reported in the literature is tied to the use of Lagrange interpolation and their use in an ODE integrator. With these and other natural interpolations some LobattoIIIA methods do not exhibit this undesirable behavior when used within a direct transcription framework.

引用

页码：291 / 300

页数：10

共 21 条

[1] THE NUMERICAL-SOLUTION OF DELAY-DIFFERENTIAL-ALGEBRAIC EQUATIONS OF RETARDED AND NEUTRAL TYPE [J].