DocumentCode :
2633061
Title :
Time optimal synthesis for a so(3)-left-invariant control system on a sphere
Author :
Boscain, Ugo ; Chitour, Yacine
Author_Institution :
SISSA-ISAS, Trieste, Italy
Volume :
3
fYear :
2003
fDate :
9-12 Dec. 2003
Firstpage :
2740
Abstract :
Consider the control system (Σ) given by x˙ = x(f + ug) where x ∈ SO(3), |u| ≤ 1 and f, g ∈ so(3) define two perpendicular left-invariant vector fields normalized so that ||f|| = cos(α) and ||g|| = sin(α), α ∈ (0, π/4). In this paper, we provide an upper bound and a lower bound for N(α), the maximum number of switchings for time-optimal trajectories of (Σ). More precisely, we show that NS(α) ≤ N(α) ≤ NS(α) ≤+4, where NS(a) is a suitable integer function of α such that NS(α) α→0. The result is obtained by studying the time optimal synthesis of a projected control problem on RP2, where the projection is defined by an appropriate Hopf fibration.
Keywords :
computational complexity; control system synthesis; invariance; optimal control; Hopf fibration; perpendicular left-invariant vector fields; so(3)-left-invariant control system; sphere; time optimal synthesis; time-optimal trajectories; Control system synthesis; Control systems; Control theory; H infinity control; Lighting control; Optimal control; Portable media players; Testing; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
ISSN :
0191-2216
Print_ISBN :
0-7803-7924-1
Type :
conf
DOI :
10.1109/CDC.2003.1273038
Filename :
1273038
Link To Document :
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