×

zbMATH — the first resource for mathematics

Stability analysis for multi-agent systems using the incidence matrix: quantized communication and formation control. (English) Zbl 1193.93059
Summary: The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.

MSC:
93A14 Decentralized systems
93C05 Linear systems in control theory
93D30 Lyapunov and storage functions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arcak, M., Passivity as a design tool for group coordination, IEEE transactions on automatic control, 52, 8, 1380-1390, (2007) · Zbl 1366.93563
[2] Baillieul, J., & Suri, A. (2004). Information patterns and hedging Brocketts theorem in controlling vehicle formations. In 43rd IEEE conf. decision and control (pp. 556-563).
[3] Cao, M., Anderson, B., Morse, A., & Yu, C. (2008). Control of acyclic formations of mobile autonomous agents. In 47th IEEE conf. on decision and control (pp. 1187-1192).
[4] Carli, R., Fagnani, F., & Zampieri, S. (2006). On the state agreement with quantized information. In 17th Intern. symp. networks and systems (pp. 1500-1508).
[5] Cortes, J.; Martinez, S.; Bullo, F., Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions, IEEE transactions on automatic control, 51, 8, 1289-1298, (2006) · Zbl 1366.93400
[6] Fax, J., & Murray, R. (2002). Graph {\scL}aplacians and stabilization of vehicle formations. In 15th IFAC world congress.
[7] Godsil, C.; Royle, G., ()
[8] Guattery, S.; Miller, G., Graph embeddings and Laplacian eigenvalues, SIAM journal of matrix analysis and applications, 21, 3, 703-723, (2000) · Zbl 0942.05040
[9] Hendrickx, J., Anderson, B., & Blondel, V. (2005). Rigidity and persistence of directed graphs. In 44th IEEE conf. decision and control (pp. 2176-2181).
[10] Horn, R.A.; Johnson, C.R., Matrix analysis, (1996), Cambridge University Press
[11] Johansson, K. H., Speranzon, A., & Zampieri, S. (2005). On quantization and communication topologies in multi-vehicle rendezvous. In 16th IFAC world congress (electronic proceedings).
[12] Kashyap, A.; Basar, T.; Srikant, R., Quantized consensus, Automatica, 43, 7, 1192-1203, (2007) · Zbl 1123.93090
[13] Lygeros, J.; Johansson, K.; Simic, S.; Zhang, J.; Sastry, S., Dynamical properties of hybrid automata, IEEE transactions on automatic control, 48, 1, 2-17, (2003) · Zbl 1364.93503
[14] Olfati-Saber, R.; Murray, R., Consensus problems in networks of agents with switching topology and time-delays, IEEE transactions on automatic control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301
[15] Olfati-Saber, R., & Shamma, J. (2005). Consensus filters for sensor networks and distributed sensor fusion. In 44th IEEE conference on decision and control (pp. 6698-6703).
[16] Zelazo, D., Rahmani, A., & Mesbahi, M. (2007). Agreement via the edge laplacian. In 46th IEEE conference on decision and control (pp. 2309-2314).
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.