Asymptotic tracking of periodic trajectories for a particle in an elliptical billiards

被引：0

作者：

Galeani, S. ^{[1
]}

Menini, L. ^{[1
]}

Potini, A. ^{[1
]}

Tornambe, A. ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Informat Sistemi & Prod, I-00133 Rome, Italy

来源：

2007 AMERICAN CONTROL CONFERENCE, VOLS 1-13 | 2007年

关键词：

elliptical billiards; trajectory tracking; LMI; nonsmooth impact;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

An infinitely rigid unitary mass (particle) is considered, moving on a planar region delimited by a rigid elliptical barrier (elliptical billiards) under the action of proper control forces. A class of periodic trajectories, involving an infinite sequence of nonsmooth impacts between the mass and the barrier at fixed times, is found by using an LMIs based procedure and a tracking problem is stated and solved by means of a controller whose state is subject to jumps.

引用

页码：1882 / 1887

页数：6

共 50 条

[1] Robust asymptotic tracking of periodic trajectories in elliptical billiards
Galeani, S.
Menini, L.
Potini, A.
Tornambe, A.
PROCEEDINGS OF THE 46TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14, 2007, : 919 - 924
[2] Trajectory tracking for a particle in elliptical billiards
Galeani, S.
Menini, L.
Potini, A.
Tornambe, A.
INTERNATIONAL JOURNAL OF CONTROL, 2008, 81 (02) : 189 - 213
[3] Counting Periodic Trajectories of Finsler Billiards
Blagojevi, Pavle V. M.
Harrison, Michael
Tabachnikov, Serge
Ziegler, Guenter M.
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2020, 16
[4] PERIODIC TRAJECTORIES IN RIGHT-TRIANGLE BILLIARDS
CIPRA, B
HANSON, RM
KOLAN, A
PHYSICAL REVIEW E, 1995, 52 (02): : 2066 - 2071
[5] PERIODIC TRAJECTORIES OF BIRKHOFF'S BILLIARDS.
Treshchev, D.V.
Moscow University mechanics bulletin, 1987, 42 (05) : 35 - 39
[6] Correlations for pairs of periodic trajectories for open billiards
Petkov, Vesselin
Stoyanov, Luchezar
NONLINEARITY, 2009, 22 (11) : 2657 - 2679
[7] Classification of symmetric periodic trajectories in ellipsoidal billiards
Casas, Pablo S.
Ramirez-Ros, Rafael
CHAOS, 2012, 22 (02)
[8] VARIATIONAL PRINCIPLE FOR PERIODIC TRAJECTORIES OF HYPERBOLIC BILLIARDS
BUNIMOVICH, LA
CHAOS, 1995, 5 (02) : 349 - 355
[9] PERIODIC TRAJECTORIES IN 3-DIMENSIONAL BIRKHOFF BILLIARDS
BABENKO, IK
MATHEMATICS OF THE USSR-SBORNIK, 1992, 71 (01): : 1 - 13
[10] Periodic trajectories in 3-dimensional convex billiards
Farber, M
Tabachnikov, S
MANUSCRIPTA MATHEMATICA, 2002, 108 (04) : 431 - 437

← 1 2 3 4 5 →