Abstract
In the past decades, extensive research has been conducted on the cooperative control of multi–agent systems with possible applications ranging from UAVs and sensor networks over transportation systems to micro–satellite clusters (see, e.g., [19] for a rather recent overview). Thereby, different analysis and design approaches have emerged depending on the available communication topology and the considered formation control task.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alvarez, L., Horowitz, R., Li, P.: Traffic flow control in automated highway systems. Control Eng. Practice 7, 1071–1078 (1999)
Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Physics Reports 469(3), 93–153 (2008)
Balch, T., Arkin, R.: Behavior–Based Formation Control for Multirobot Teams. IEEE Trans. Robotics Automat. 14(6), 926–939 (1998)
Barooah, P., Mehta, P., Hespanha, J.: Mistuning–Based Control Design to Improve Closed–Loop Stability Margin of Vehicular Platoons. IEEE Trans. Automat. Control 54(9), 2100–2113 (2009)
Bullo, F., Cortés, J., Martínez, S.: Distributed Control of Robotic Networks. Applied Mathematics Series. Princeton University Press (2009)
Cybenko, G.: Dynamic Load Balancing for Distributed Memory Multiprocessors. J. Parallel Distr. Com. 7, 279–301 (1989)
Dunbar, W., Murray, R.: Distributed Receding Horizon Control for Multi–Vehicle Formation Stabilization. Automatica 42(4), 549–558 (2006)
Ferrari-Trecate, G., Buffa, A., Gati, M.: Analysis and Coordination in Multi–Agent Systems Through Partial Difference Equations. IEEE Trans. Automat. Control 51(6), 1058–1063 (2006)
Frihauf, P., Krstic, M.: Rapidly convergent leader-enabled multi-agent deployment into planar curves. In: Proc. American Control Conference, St. Louis (MO), USA, pp. 1994–1999 (2009)
Frihauf, P., Krstic, M.: Leader–Enabled Deployment Onto Planar Curves: A PDE-Based Approach. IEEE Trans. Automat. Control 56(8), 1791–1806 (2011)
Helbing, D.: Traffic and related self–driven many-particle systems. Rev. Mod. Phys. 73(4), 1067–1141 (2001)
Jadbabaie, A., Lin, J., Morse, A.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)
Ji, M., Ferrari-Trecate, G., Egerstedt, M., Buffa, A.: Containment Control in Mobile Networks. IEEE Trans. Autom. Control 53(8), 1972–1975 (2008)
Kim, J., Kim, K.D., Natarajan, V., Kelly, S., Bentsman, J.: PdE–based model reference adaptive control of uncertain heterogeneous multiagent networks. Nonlinear Analysis: Hybrid Systems 2, 1152–1167 (2008)
Krstic, M., Smyshlyaev, A.: Boundary Control of PDEs: A Course on Backstepping Designs. SIAM, Philadelphia (2008)
Mesbahi, M., Egerstedt, M.: Graph Theoretic Methods in Multiagent Networks. Princeton Univeristy Press, Princeton (2010)
Meurer, T., Krstic, M.: Nonlinear PDE–based motion planning for the formation control of mobile agents. In: Proc (CD–ROM) 8th IFAC Symposium Nonlinear Control Systems (NOLCOS 2010), Bologna (I), pp. 599–604 (2010)
Meurer, T., Krstic, M.: Finite–time multi–agent deployment: A nonlinear PDE motion planning approach. Automatica 47(11), 2534–2542 (2011)
Murray, R.: Recent Research in Cooperative Control of Multivehicle Systems. J. Dyn. Meas. Contr. 129, 571–583 (2007)
Olfati-Saber, R.: Flocking for Multi–Agent Dynamic Systems: Algortihms and Theory. IEEE Trans. Automat. Control 51(3), 401–420 (2006)
Olfati-Saber, R., Murray, R.: Consensus Problems in Networks of Agents With Switching Topology and Time-Delays. IEEE Trans. Automat. Control 49(9), 1520–1533 (2004)
Ren, W., Beard, R.: Formation feedback control for multiple spacecraft via virtual structures. IEE Proceedings 151(3), 357–368 (2004)
Ren, W., Beard, R.: Distributed Consensus in Multi–vehicle Cooperative Control. Springer, London (2008)
Sarlette, A., Sepulchre, R.: A PDE viewpoint on basic properties of coordination algorithms with symmetries. In: Proc. IEEE Conference on Decision and Control (CDC), pp. 5139–5144 (2009)
Schwarz, H.: Numerische Mathematik. Teubner-Verlag, Stuttgart (1997)
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel Type of Phase Transition in a System of Self-Driven Particles. Phys. Rev. Lett. 75(6), 1226–1229 (1995)
Zhang, W., Hu, J.: Optimal multi–agent coordination under tree formation constraints. IEEE Trans. Automat. Control 53(3), 692–705 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Meurer, T. (2013). Model Equations for Multi–Agent Networks. In: Control of Higher–Dimensional PDEs. Communications and Control Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30015-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-30015-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30014-1
Online ISBN: 978-3-642-30015-8
eBook Packages: EngineeringEngineering (R0)