Matches in SemOpenAlex for { <https://semopenalex.org/work/W2950847168> ?p ?o ?g. }
Showing items 1 to 92 of
92
with 100 items per page.
- W2950847168 abstract "For $alphain(0,pi/2)$, let $(Sigma)_alpha$ be the control system $dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $uin [-1,1]$ and $F,G$ are $3times3$ skew-symmetric matrices generating rotations with perpendicular axes of respective length $cos(alpha)$ and $sin(alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(Sigma)_alpha$, as the parameter $alpha$ tends to zero. We first prove that the TOS is characterized by a ``two-snakes'' configuration on the whole $S^2$, except for a neighborhood $U_alpha$ of the south pole $(0,0,-1)^T$ of diameter at most $O(alpha)$. We next show that, inside $U_alpha$, the TOS depends on the relationship between $r(alpha):=pi/2alpha-[pi/2alpha]$ and$alpha$. More precisely, we characterize three main relationships, by considering sequences $(alpha_k)_{kgeq 0}$ satisfying $(a)$$r(alpha_k)=bar{r}$; $(b)$ $r(alpha_k)=Calpha_k$ and $(c)$ $r(alpha_k)=0$, where $bar{r}in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $alpha$ tends to zero, of the corresponding TOS inside $U_alpha$." @default.
- W2950847168 created "2019-06-27" @default.
- W2950847168 creator A5000279658 @default.
- W2950847168 creator A5012657462 @default.
- W2950847168 creator A5061850292 @default.
- W2950847168 creator A5073564675 @default.
- W2950847168 date "2006-11-27" @default.
- W2950847168 modified "2023-10-01" @default.
- W2950847168 title "Limit Time Optimal Synthesis for a Control-Affine System on $S^2$" @default.
- W2950847168 cites W1595765050 @default.
- W2950847168 cites W1970654756 @default.
- W2950847168 cites W2004953010 @default.
- W2950847168 cites W2023024274 @default.
- W2950847168 cites W2034793951 @default.
- W2950847168 cites W2056700074 @default.
- W2950847168 cites W2971463487 @default.
- W2950847168 hasPublicationYear "2006" @default.
- W2950847168 type Work @default.
- W2950847168 sameAs 2950847168 @default.
- W2950847168 citedByCount "0" @default.
- W2950847168 crossrefType "posted-content" @default.
- W2950847168 hasAuthorship W2950847168A5000279658 @default.
- W2950847168 hasAuthorship W2950847168A5012657462 @default.
- W2950847168 hasAuthorship W2950847168A5061850292 @default.
- W2950847168 hasAuthorship W2950847168A5073564675 @default.
- W2950847168 hasConcept C105795698 @default.
- W2950847168 hasConcept C114614502 @default.
- W2950847168 hasConcept C121332964 @default.
- W2950847168 hasConcept C127413603 @default.
- W2950847168 hasConcept C134306372 @default.
- W2950847168 hasConcept C138885662 @default.
- W2950847168 hasConcept C151201525 @default.
- W2950847168 hasConcept C153294291 @default.
- W2950847168 hasConcept C171606756 @default.
- W2950847168 hasConcept C188198153 @default.
- W2950847168 hasConcept C188721877 @default.
- W2950847168 hasConcept C2524010 @default.
- W2950847168 hasConcept C2778049214 @default.
- W2950847168 hasConcept C2780813799 @default.
- W2950847168 hasConcept C33923547 @default.
- W2950847168 hasConcept C41895202 @default.
- W2950847168 hasConcept C49453240 @default.
- W2950847168 hasConcept C62520636 @default.
- W2950847168 hasConcept C64943373 @default.
- W2950847168 hasConcept C78519656 @default.
- W2950847168 hasConceptScore W2950847168C105795698 @default.
- W2950847168 hasConceptScore W2950847168C114614502 @default.
- W2950847168 hasConceptScore W2950847168C121332964 @default.
- W2950847168 hasConceptScore W2950847168C127413603 @default.
- W2950847168 hasConceptScore W2950847168C134306372 @default.
- W2950847168 hasConceptScore W2950847168C138885662 @default.
- W2950847168 hasConceptScore W2950847168C151201525 @default.
- W2950847168 hasConceptScore W2950847168C153294291 @default.
- W2950847168 hasConceptScore W2950847168C171606756 @default.
- W2950847168 hasConceptScore W2950847168C188198153 @default.
- W2950847168 hasConceptScore W2950847168C188721877 @default.
- W2950847168 hasConceptScore W2950847168C2524010 @default.
- W2950847168 hasConceptScore W2950847168C2778049214 @default.
- W2950847168 hasConceptScore W2950847168C2780813799 @default.
- W2950847168 hasConceptScore W2950847168C33923547 @default.
- W2950847168 hasConceptScore W2950847168C41895202 @default.
- W2950847168 hasConceptScore W2950847168C49453240 @default.
- W2950847168 hasConceptScore W2950847168C62520636 @default.
- W2950847168 hasConceptScore W2950847168C64943373 @default.
- W2950847168 hasConceptScore W2950847168C78519656 @default.
- W2950847168 hasLocation W29508471681 @default.
- W2950847168 hasOpenAccess W2950847168 @default.
- W2950847168 hasPrimaryLocation W29508471681 @default.
- W2950847168 hasRelatedWork W1487408709 @default.
- W2950847168 hasRelatedWork W1801609781 @default.
- W2950847168 hasRelatedWork W1985517542 @default.
- W2950847168 hasRelatedWork W1995278146 @default.
- W2950847168 hasRelatedWork W2056455920 @default.
- W2950847168 hasRelatedWork W2074534265 @default.
- W2950847168 hasRelatedWork W2208931740 @default.
- W2950847168 hasRelatedWork W2286364186 @default.
- W2950847168 hasRelatedWork W2288095102 @default.
- W2950847168 hasRelatedWork W2288291856 @default.
- W2950847168 hasRelatedWork W2299952715 @default.
- W2950847168 hasRelatedWork W2521533236 @default.
- W2950847168 hasRelatedWork W2741269571 @default.
- W2950847168 hasRelatedWork W2947395724 @default.
- W2950847168 hasRelatedWork W2951011656 @default.
- W2950847168 hasRelatedWork W2951106463 @default.
- W2950847168 hasRelatedWork W2955698430 @default.
- W2950847168 hasRelatedWork W3008396445 @default.
- W2950847168 hasRelatedWork W3027390247 @default.
- W2950847168 hasRelatedWork W3143130018 @default.
- W2950847168 isParatext "false" @default.
- W2950847168 isRetracted "false" @default.
- W2950847168 magId "2950847168" @default.
- W2950847168 workType "article" @default.