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Asymptotic behaviour in the robot rendezvous problem

Tutkimustuotos: vertaisarvioituArtikkeli

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut127-130
Sivumäärä4
JulkaisuAutomatica
Vuosikerta79
DOI - pysyväislinkit
TilaJulkaistu - 1 toukokuuta 2017
OKM-julkaisutyyppiA1 Alkuperäisartikkeli

Tiivistelmä

This paper presents a natural extension of the results obtained by Feintuch and Francis in (2012a,b) concerning the so-called robot rendezvous problem. In particular, we revisit a known necessary and sufficient condition for convergence of the solution in terms of Cesàro convergence of the translates Skx0, k≥0, of the sequence x0 of initial positions under the right-shift operator S, thus shedding new light on questions left open in Feintuch and Francis (2012a,b). We then present a new proof showing that a certain stronger ergodic condition on x0 ensures that the corresponding solution converges to its limit at the optimal rate O(t−1/2) as t→∞. After considering a natural two-sided variant of the robot rendezvous problem already studied in Feintuch and Francis (2012a) and in particular proving a new quantified result in this case, we conclude by relating the robot rendezvous problem to a more realistic model of vehicle platoons.

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