Time Optimal Synthesis for Left--Invariant Control Systems on SO(3)
| dc.creator | Boscain, Ugo | |
| dc.creator | Chitour, Yacine | |
| dc.date | 2005-02-23 | |
| dc.date.accessioned | 2026-07-07T05:17:24Z | |
| dc.date.available | 2026-07-07T05:17:24Z | |
| dc.description | Consider the control system given by $\dot x=x(f+ug)$, where $x\in SO(3)$, $|u|\leq 1$ and $f,g\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\|f\|=\cos(\al)$ and $\|g\|=\sin(\al)$, $\al\in ]0,π/4[$. In this paper, we provide an upper bound and a lower bound for $N(α)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\al)\leq N(\al)\leq N_S(\al)+4$, where $N_S(\al)$ is a suitable integer function of $\al$ which for $\al\to 0$ is of order $π/(4α).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations. | |
| dc.identifier | https://arxiv.org/abs/math/0502483 | |
| dc.identifier | http://arxiv.org/abs/math/0502483 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74290 | |
| dc.subject | Optimization and Control | |
| dc.subject | 49k15 | |
| dc.title | Time Optimal Synthesis for Left--Invariant Control Systems on SO(3) | |
| dc.type | text |