×

zbMATH — the first resource for mathematics

State estimation of heterogeneous oscillators by means of proximity measurements. (English) Zbl 1309.93006
Summary: In this paper, we aim at estimating the state of an ensemble of mobile agents. Specifically, each agent is an oscillator which moves along a circle at a given time-varying angular velocity. We assume that an agent can measure the distance from the other oscillators only when they are in its proximity. We propose a recursive algorithm which, based on these intermittent and uncertain measurements, is capable of estimating in real-time the relative angular position of the agents. The algorithm combines the information coming from the collected measures with the information on the agents’ dynamics, and its convergence is proved by means of interval analysis. The theoretical analysis is complemented with extensive numerical simulations.

MSC:
93A14 Decentralized systems
93E10 Estimation and detection in stochastic control theory
68T42 Agent technology and artificial intelligence
93B07 Observability
93C10 Nonlinear systems in control theory
Software:
Boids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bornholdt, S.; Schuster, H. G., Handbook of graphs and networks, (2003), Wiley-VHC, Weinheim Germany
[2] Chen, Z.; Zhang, H.-T., No-beacon collective circular motion of jointly connected multi-agents, Automatica, 47, 9, 1929-1937, (2011) · Zbl 1227.93005
[3] DeLellis, P.; diBernardo, M.; Garofalo, F., Novel decentralized adaptive strategies for the synchronization of complex networks, Automatica, 45, 5, 1312-1318, (2009) · Zbl 1162.93361
[4] DeLellis, P.; diBernardo, M.; Garofalo, F.; Porfiri, M., Evolution of complex networks via edge snapping, IEEE Transactions on Circuits and Systems I, 57, 8, 2132-2143, (2010)
[5] DeLellis, P.; Porfiri, M.; Bollt, E. M., Topological analysis of group fragmentation in multi-agent systems, Physical Review E, 87, 2, 022818, (2013)
[6] Fan, Y.; Feng, G.; Wang, Y.; Qiu, J., A novel approach to coordination of multiple robots with communication failures via proximity graph, Automatica, 47, 8, 1800-1805, (2011) · Zbl 1226.68117
[7] Hajimiri, A., A general theory of phase noise in electrical oscillators, IEEE Journal of Solid-State Circuits, 33, 2, 179-194, (2002)
[8] Hardy, G. H.; Wright, E. M., An introduction to the theory of numbers. kronecker’s theorem, 501-522, (2008), Oxford University Press New York, (Chapter XXIII)
[9] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 6, 988-1001, (2003) · Zbl 1364.93514
[10] Jaulin, L.; Kieffer, M.; Braems, I.; Walter, E., Guaranteed non-linear estimation using constraint propagation on sets, International Journal of Control, 74, 18, 1772-1782, (2010) · Zbl 1023.93020
[11] Jaulin, L.; Kieffer, M.; Didrit, O.; Walter, E., Applied interval analysis, (2001), Springer
[12] Jeanson, R., Long-term dynamics in proximity networks in ants, Animal Behavior, 83, 4, 915-923, (2012)
[13] Kulakowski, P.; Vales-Alonso, J.; Egea-López, E.; Ludwin, W.; Garcia-Haro, J., Angle-of-arrival localization based on antenna arrays for wireless sensor networks, Computers & Electrical Engineering, 36, 6, 1181-1186, (2010) · Zbl 1202.94152
[14] Le Bars, F.; Sliwka, J.; Jaulin, L.; Reynet, O., Set-membership state estimation with fleeting data, Automatica, 48, 2, 381-387, (2012) · Zbl 1260.93153
[15] Mao, G.; Fidan, B.; Anderson, B. D.O., Sensor networks and configuration: fundamentals, standards, platforms, and applications, 2281-2315, (2007), Springer Berlin, chapter Localisation
[16] Moore, R. E.; Kearfott, R. B.; Cloud, M. J., Introduction to interval analysis. the interval number system, (2009), Society for Industrial and Applied Mathematics, (Chapter 2) · Zbl 1168.65002
[17] Nassreddine, G.; Abdallah, F.; Denoeux, T., State estimation using interval analysis and belief-function theory: application to dynamic vehicle localization, IEEE Transactions on Systems, Man and Cybernetics, Part B, 40, 5, 1205-1218, (2009)
[18] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE Transactions on Automatic Control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[19] Paley, D. A.; Leonard, N. E.; Sepulchre, R.; Grünbaum, D., Oscillator models and collective motion, IEEE Control Systems Magazine, 27, 4, 89-105, (2007)
[20] Piovan, G.; Shames, I.; Fidan, B.; Bullo, F.; Anderson, B. D.O., On frame and orientation localization for relative sensing networks, Automatica, 49, 1, 206-213, (2013) · Zbl 1258.93012
[21] Reynolds, C. W. (1987). Flocks, herds, and schools: a distributed behavioral model. In SIGGRAPH ’87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques, Vol. 21. (pp. 25-34). New York.
[22] Sepulchre, R.; Paley, D. A.; Leonard, N. E., Stabilization of planar collective motion with limited communication, IEEE Transactions on Automatic Control, 53, 3, 706-719, (2008) · Zbl 1367.93145
[23] Shames, I.; Fidan, B.; Anderson, B. D.O., Minimization of the effect of noisy measurements on localization of multi-agent autonomous formations, Automatica, 45, 4, 1058-1065, (2009) · Zbl 1162.93307
[24] Shan, G., Baoming, Y., & Qiang, Ye (2010). Interval analysis and its applications to control problems. In Int. Conf. on Educ. and Inform. Tech., Vol. 1. (pp. 213-218). Chongqing.
[25] Strogatz, S. H., From Kuramoto to crawford: exploring the onset of synchronization in populations of coupled oscillators, Physica D, 143, 1-4, 1-20, (2000) · Zbl 0983.34022
[26] Toner, J.; Tu, Y., Flocks, herds, and schools: A quantitative theory of flocking, Physical Review E, 58, 4, 4828-4858, (1998)
[27] Toroczkai, Z.; Guclu, H., Proximity networks and epidemics, Physica A, 378, 1, 68-75, (2007)
[28] Vicsek, T.; Czirók, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 75, 6, 1226-1229, (1995)
[29] Yu, W.; Chen, G.; Lü, J., On pinning synchronization of complex dynamical networks, Automatica, 45, 2, 429-435, (2009) · Zbl 1158.93308
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.