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Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction. (English) Zbl 1222.93146

Summary: We study two sampled-data-based discrete-time coordination algorithms for multi-vehicle systems with double-integrator dynamics under dynamic directed interaction. For both algorithms, we derive sufficient conditions on the interaction graph, the damping gain and the sampling period to guarantee coordination by using the property of infinity products of stochastic matrices. When the conditions on the damping gain and the sampling period are satisfied, the first algorithm guarantees coordination on positions with a zero final velocity if the interaction graph has a directed spanning tree jointly while the second algorithm guarantees coordination on positions with a constant final velocity if the interaction graph has a directed spanning tree at each time interval. Simulation results are presented to show the effectiveness of the theoretical results.

MSC:

93C57 Sampled-data control/observation systems
93C55 Discrete-time control/observation systems
93A14 Decentralized systems
93C15 Control/observation systems governed by ordinary differential equations
05C90 Applications of graph theory
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References:

[1] DOI: 10.1016/j.laa.2004.09.003 · Zbl 1076.15012
[2] DOI: 10.1137/060657005 · Zbl 1157.93514
[3] DOI: 10.1109/TRA.2004.824698
[4] DOI: 10.1109/TAC.2004.834433 · Zbl 1365.90056
[5] Franklin GF, Digital Control of Dynamic Systems (2006)
[6] DOI: 10.1109/TAC.2003.812781 · Zbl 1364.93514
[7] DOI: 10.1016/j.sysconle.2005.02.004 · Zbl 1129.93303
[8] DOI: 10.1109/TRA.2003.819598
[9] DOI: 10.1109/TAC.2007.902752 · Zbl 1366.93503
[10] DOI: 10.1109/TAC.2004.825639 · Zbl 1365.93208
[11] DOI: 10.1109/TAC.2004.841888 · Zbl 1365.93268
[12] DOI: 10.1115/1.2766721
[13] DOI: 10.1109/TAC.2005.864190 · Zbl 1366.93391
[14] DOI: 10.1109/JPROC.2006.887293 · Zbl 1376.68138
[15] DOI: 10.1109/TAC.2004.834113 · Zbl 1365.93301
[16] DOI: 10.1109/TAC.2008.924961 · Zbl 1367.93567
[17] DOI: 10.1002/rnc.1147 · Zbl 1266.93010
[18] DOI: 10.1109/TAC.2005.846556 · Zbl 1365.93302
[19] DOI: 10.1109/MCS.2007.338264
[20] DOI: 10.1109/TAC.2007.895948 · Zbl 1366.93414
[21] DOI: 10.1109/TAC.1986.1104412 · Zbl 0602.90120
[22] Wolfowitz J, Proceedings of the American Mathematical Society 15 pp 733– (1963)
[23] DOI: 10.1002/rnc.1144 · Zbl 1266.93013
[24] DOI: 10.1109/TAC.2008.2006925 · Zbl 1367.93040
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