Singularly perturbed differential inclusions: An averaging approach

被引：31

作者：

Grammel, G ^{[1
]}

机构：

[1] UNIV S AUSTRALIA,SCH MATH,THE LEVELS,SA 5095,AUSTRALIA

来源：

SET-VALUED ANALYSIS | 1996年 / 4卷 / 04期

关键词：

differential inclusion; singular perturbation; averaging method; controlability; stability;

D O I：

10.1007/BF00436111

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider nonlinear, singularly perturbed differential inclusions and apply the averaging method in order to construct a limit differential inclusion for slow motion. The main approximation result states that the existence and regularity of the limit differential inclusion suffice to describe the limit behavior of the slow motion. We give explicit approximation rates for the uniform convergence on compact time intervals. The approach works under controllability or stability properties of fast motion.

引用

页码：361 / 374

页数：14

共 50 条

[21] Averaging and near viability of singularly perturbed control systems
Gaitsgory, V.
[J]. JOURNAL OF CONVEX ANALYSIS, 2006, 13 (02) : 329 - 352
[22] Closeness of Solutions for Singularly Perturbed Systems via Averaging
Deghat, Mohammad
Ahmadizadeh, Saeed
Nesic, Dragan
Manzie, Chris
[J]. 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2018, : 3110 - 3115
[23] ON THE AVERAGING OF DIFFERENTIAL INCLUSIONS WITH MAXIMA
Bar, Bachir
[J]. MATHEMATICA BOHEMICA, 2023, 148 (01): : 1 - 10
[24] Asymptotics for singularly perturbed differential games
Subbotina, NN
[J]. NONSMOOTH AND DISCONTINUOUS PROBLEMS OF CONTROL AND OPTIMIZATION (NDPCO'98), 1999, : 43 - 52
[25] A viability approach for an extension of Tikhonov theorem to singularly perturbed differential inclusion
Quincampoix, M
[J]. DOKLADY AKADEMII NAUK, 1998, 360 (03) : 309 - 312
[26] Renormalization group approach to a class of singularly perturbed delay differential equations
Xu, Lin
Xu, Zhiguo
Li, Wenlei
Shi, Shaoyun
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 103
[27] Stability of singularly perturbed differential-difference systems: A LMI approach
Fridman, E
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS, 2002, 9 (02): : 201 - 212
[28] Computing singularly perturbed differential equations
Chatterjee, Sabyasachi
Acharya, Amit
Arstein, Zvi
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 354 : 417 - 446
[29] Decomposition of singularly perturbed differential systems
Voropaeva N.V.
Sobolev V.A.
[J]. Computational Mathematics and Modeling, 1998, 9 (1) : 28 - 37
[30] Existence of limit occupational measures set used for averaging of singularly perturbed controlled stochastic differential equations
Borkar, Vivek
Gaitsgory, Vladimir
[J]. PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2006, : 326 - 331

← 1 2 3 4 5 →