{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:06:50Z","timestamp":1787321210716,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>In this paper we consider ad-hoc networks of robotic agents with double integrator dynamics. For such networks, the connectivity maintenance problems are as follows: (i) Do there exist control inputs for each agent to maintain network connectivity, and (ii) given desired controls for each agent, can we compute the closest connectivity-maintaining controls in a distributed fashion? The proposed solution is based on three contributions. First, we define and characterize admissible sets for double integrators to remain inside disks. Second, we establish an existence theorem for the connectivity maintenance problem by introducing a novel state-dependent graph, called the double-integrator disk graph. Specifically, we show that one can always maintain connectivity by maintaining a spanning tree of this new graph, but one will not always maintain connectivity of a particular agent pair that happens to be connected at one instant of time. Finally, we design a distributed \u201cflow-control\u201d algorithm for distributed computation of connectivity-maintaining controls.<\/jats:p>","DOI":"10.1137\/060674971","type":"journal-article","created":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T23:04:59Z","timestamp":1234393499000},"page":"187-205","source":"Crossref","is-referenced-by-count":45,"title":["Maintaining Limited-Range Connectivity Among Second-Order Agents"],"prefix":"10.1137","volume":"48","author":[{"given":"Ketan","family":"Savla","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giuseppe","family":"Notarstefano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Bullo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"G. Notarstefano, K. Savla, F. Bullo, and A. Jadbabaie,\n                      Maintaining limited-range connectivity among second-order agents\n                      , in Proceedings of the IEEE American Control Conference (Minneapolis, MN), 2006, pp. 2124\u20132129.","DOI":"10.1109\/ACC.2006.1656533"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1109\/70.795787"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"J. Lin, A. S. Morse, and B. D. O. Anderson,\n                      The multi-agent rendezvous problem\n                      , in Proceedings of the 42nd IEEE Conference on Decision and Control (Maui, HI), 2003, pp. 1508\u20131513.","DOI":"10.1109\/CDC.2003.1272825"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2006.878713"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"A. Ganguli, J. Cort\u00e9s, and F. Bullo,\n                      On rendezvous for visually-guided agents in a nonconvex polygon\n                      , in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (Seville, Spain), 2005, pp. 5686\u20135691.","DOI":"10.1109\/CDC.2005.1583069"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"D. P. Spanos and R. M. Murray,\n                      Motion planning with wireless network constraints\n                      , in Proceedings of the IEEE American Control Conference (Portland, OR), 2005, pp. 87\u201392.","DOI":"10.1109\/ACC.2005.1469913"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"M. M. Zavlanos and G. J. Pappas,\n                      Controlling connectivity of dynamic graphs\n                      , in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (Seville, Spain), 2005, pp. 6388\u20136393.","DOI":"10.1109\/CDC.2005.1583186"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.895948"},{"key":"R9","unstructured":"Z. Gao,\n                      On discrete time optimal control: A closed-form solution\n                      , in Proceedings of the IEEE American Control Conference (Boston, MA), 2004, pp. 52\u201358."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0209063"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2004.03.009"},{"key":"R12","unstructured":"D. P. Bertsekas and J. N. Tsitsiklis,\n                      Parallel and Distributed Computation: Numerical Methods\n                      , Athena Scientific, Belmont, MA, 1997."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060674971","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:09:07Z","timestamp":1787317747000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060674971"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1137\/060674971"],"URL":"https:\/\/doi.org\/10.1137\/060674971","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,1]]}}}