Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5000032 | Automatica | 2017 | 4 Pages |
Abstract
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 Cesà ro convergence of the translates Skx0, kâ¥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(tâ1/2) as tââ. 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.
Related Topics
Physical Sciences and Engineering
Engineering
Control and Systems Engineering
Authors
Lassi Paunonen, David Seifert,