Asymptotics of the Optimal Time in a Singular Perturbed Linear Time-Optimal Problem

被引：1

作者：

Danilin, A. R. ^{[1
]}

Kovrizhnykh, O. O. ^{[1
]}

机构：

[1] Russian Acad Sci, Ural Div, Inst Math & Mech, Ekaterinburg 620990, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2010年 / 271卷

基金：

俄罗斯基础研究基金会;

关键词：

optimal control; time-optimal control problem; asymptotic expansion; singular perturbed problems; small parameter;

D O I：

10.1134/S0081543810070059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A time-optimal control problem is considered for a linear system with fast and slow variables and smooth geometric constraints on the control. For the optimal time and optimal control, asymptotic expansions in a small parameter at the derivatives in the equations of the system and a small perturbation of the initial conditions are constructed.

引用

页码：S53 / S65

页数：13

共 50 条

[21] On Singular Phenomena in Certain Time-Optimal Problem
Wladyslaw HEJMO
Jacenty KLOCH
Journal of Global Optimization, 1997, 10 : 327 - 349
[22] On singular phenomena in certain time-optimal problem
Hejmo, W
Kloch, J
JOURNAL OF GLOBAL OPTIMIZATION, 1997, 10 (03) : 327 - 349
[23] SINGULAR CONTROL ABSENCE IN THE TIME-OPTIMAL PROBLEM
BUGROV, DI
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1993, (06): : 52 - 55
[24] Asymptotic representation of a solution to a singular perturbation linear time-optimal problem
Danilin, A. R.
Kovrizhnykh, O. O.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 281 : S22 - S35
[25] Asymptotic representation of a solution to a singular perturbation linear time-optimal problem
Danilin, A. R.
Kovrizhnykh, O. O.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2012, 18 (02): : 67 - 79
[26] Asymptotic representation of a solution to a singular perturbation linear time-optimal problem
A. R. Danilin
O. O. Kovrizhnykh
Proceedings of the Steklov Institute of Mathematics, 2013, 281 : 22 - 35
[27] AN ALGORITHM FOR THE ASYMPTOTIC SOLUTION OF A SINGULARLY PERTURBED LINEAR TIME-OPTIMAL CONTROL PROBLEM
KALININ, AI
PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 1989, 53 (06): : 695 - 703
[28] SOME PROBLEM OF LINEAR TIME-OPTIMAL CONTROL
WALCZAK, S
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES TECHNIQUES, 1975, 23 (01): : 81 - 86
[29] Approximate solution of a linear time-optimal problem
Alexandrov, VM
AUTOMATION AND REMOTE CONTROL, 1998, 59 (12) : 1699 - 1707
[30] Time-optimal control problem with the linear terminal set
Kiselev, Yu.N.
Vestnik Moskovskogo Universiteta, Seriya 15: Matematika i Kibernetika, 1991, (04): : 39 - 43

← 1 2 3 4 5 →