×

Consensus of linear multi-agent systems with reduced-order observer-based protocols. (English) Zbl 1222.93013

Summary: This paper considers the consensus problems for both continuous- and discrete-time linear multi-agent systems with directed communication topologies. Distributed reduced-order observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct a reduced-order protocol, under which a continuous-time multi-agent system whose communication topology contains a directed spanning tree can reach consensus. This algorithm is further modified to achieve consensus with a prescribed convergence rate. These two algorithms have a favorable decoupling property. In light of the modified algebraic Riccati equation, an algorithm is then given to construct a reduced-order protocol for the discrete-time case.

MSC:

93A14 Decentralized systems
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems

Software:

SeDuMi
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Olfati-Saber, R.; Fax, J.; Murray, R., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138
[2] Ren, W.; Beard, R.; Atkins, E., Information consensus in multivehicle cooperative control, IEEE control systems magazine, 27, 2, 71-82, (2007)
[3] Fax, J.; Murray, R., Information flow and cooperative control of vehicle formations, IEEE transactions on automatic control, 49, 9, 1465-1476, (2004) · Zbl 1365.90056
[4] 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
[5] Su, H.; Wang, X.; Lin, Z., Flocking of multi-agents with a virtual leader, IEEE transactions on automatic control, 54, 2, 293-307, (2009) · Zbl 1367.37059
[6] Jadbabaie, A.; Lin, J.; Morse, A., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE transactions on automatic control, 48, 6, 988-1001, (2003) · Zbl 1364.93514
[7] 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)
[8] 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
[9] Ren, W.; Beard, R., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control, 50, 5, 655-661, (2005) · Zbl 1365.93302
[10] Rahmani, A.; Ji, M.; Mesbahi, M.; Egerstedt, M., Controllability of multi-agent systems from a graph-theoretic perspective, SIAM journal on control and optimization, 48, 1, 162-186, (2009) · Zbl 1182.93025
[11] Hong, Y.; Chen, G.; Bushnell, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850, (2008) · Zbl 1283.93019
[12] Cortés, J., Distributed algorithms for reaching consensus on general functions, Automatica, 44, 3, 726-737, (2008) · Zbl 1283.93016
[13] Lin, P.; Jia, Y., Distributed robust \(H_\infty\) consensus control in directed networks of agents with time-delay, Systems and control letters, 57, 8, 643-653, (2008) · Zbl 1140.93355
[14] Li, Z.; Duan, Z.; Huang, L., \(H_\infty\) control of networked multi-agent systems, Journal of systems science and complexity, 22, 1, 35-48, (2009) · Zbl 1178.93045
[15] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567
[16] Lin, P.; Jia, Y., Further results on decentralised coordination in networks of agents with second-order dynamics, IET control theory and applications, 3, 7, 957-970, (2009)
[17] Ren, W.; Moore, K.; Chen, Y., High-order and model reference consensus algorithms in cooperative control of multivehicle systems, ASME journal of dynamic systems, measurement, and control, 129, 5, 678-688, (2007)
[18] Jiang, F.; Wang, L., Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies, International journal of control, 85, 2, 404-420, (2010) · Zbl 1184.93008
[19] Cao, Y.; Ren, W., Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction, International journal of control, 83, 3, 506-515, (2010) · Zbl 1222.93146
[20] Gao, Y.; Wang, L.; Xie, G.; Wu, B., Consensus of multi-agent systems based on sampled-data control, International journal of control, 82, 12, 2193-2205, (2009) · Zbl 1178.93091
[21] Z. Li, X. Liu, P. Lin, W. Ren, Consensus of multi-Agent systems with general linear dynamics and reduced-order protocols, in: Proceedings of the Chinese Control Conference, Yantai, China, 2011.
[22] Tuna, S., Conditions for synchronizability in arrays of coupled linear systems, IEEE transactions on automatic control, 54, 10, 2416-2420, (2009) · Zbl 1367.93542
[23] Scardovi, L.; Sepulchre, R., Synchronization in networks of identical linear systems, Automatica, 45, 11, 2557-2562, (2009) · Zbl 1183.93054
[24] Seo, J.; Shim, H.; Back, J., Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach, Automatica, 45, 11, 2659-2664, (2009) · Zbl 1180.93005
[25] Li, Z.; Duan, Z.; Chen, G.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint, IEEE transactions on circuits and systems I: regular papers, 57, 1, 213-224, (2010)
[26] Li, Z.; Duan, Z.; Chen, G, On dynamic consensus of linear multi-agent systems, IET control theory and applications, 5, 1, 19-28, (2011)
[27] Agaev, R.; Chebotarev, P., On the spectra of nonsymmetric Laplacian matrices, Linear algebra and its applications, 399, 1, 157-178, (2005) · Zbl 1076.15012
[28] Chen, C., Linear system theory and design, (1999), Oxford University Press New York, NY
[29] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[30] Sturm, J., Using sedumi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization methods and software, 11, 1, 625-653, (1999) · Zbl 0973.90526
[31] Sinopoli, B.; Schenato, L; Franceschetti, M.; Poolla, K.; Jordan, M.; Sastry, S., Kalman filtering with intermittent observations, IEEE transactions on automatic control, 49, 9, 1453-1464, (2004) · Zbl 1365.93512
[32] Schenato, L.; Sinopoli, B.; Franceschetti, M.; Poolla, K.; Sastry, S., Foundations of control and estimation over lossy networks, Proceedings of the IEEE, 95, 1, 163-187, (2007)
[33] Zhou, K.; Doyle, J., Essentials of robust control, (1998), Prentice Hall Upper Saddle River, NJ
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.