Summary
The presence of communication networks in the feedback path of a control system has led to new problems for control designers. Meanwhile, physicists, computer scientists, and mathematicians have been studying the formation and properties of physical networks under the heading of complex networks. Control engineers use a network model to facilitate controller design, while complex network theorists investigate networks to model their dynamics and growth. Despite the use of distinct analysis tools, network properties such as connectivity, efficiency, and robustness are common to both control and complex networks research. A question that naturally arises is whether ideas used by the complex network community can suggest new control design directions. In this chapter we review the tools from the network theoristÕs arsenal to make them available to control engineers, and describe how ideas developed for complex network research can be exploited within a control systems framework.
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References
Walsh, G., Ye, H., Bushnell, L.: Stability analysis of networked control systems. IEEE Transactions on Control Systems Technology 10(3), 438–445 (2002)
Zhang, W., Branicky, M.S., Phillips, S.M.: Stability of networked control systems. IEEE Control Systems Magazine 21(1), 84–99 (2001)
Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45, 167–256 (2003)
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 (2002)
Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control 50(2), 169–182 (2005)
Ren, W., Beard, R.W.: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control 50(5), 655–661 (2005)
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49(9), 1520–1533 (2004)
Tanner, H.G., Jadbabaie, A., Pappas, G.J.: Stable flocking of mobile agents, part ii: Dynamic topology. In: Proc. of the 44th IEEE Conference on Decision and Control, pp. 2016–2021 (2003)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. Computer Communications Review 29, 251–262 (1999)
Bollobás, B.: Random graphs. Academic Press, London (1995)
Clauset, A., Moore, C.: How do networks become navigable? e-print arXiv:cond-mat/0309415 (2003)
Stanley, H.E.: Introduction to Phase Transition and Critical Phenomena. Oxford University Press, Oxford (1983)
Cohen, R., Erez, K., ben Avraham, D., Havlin, S.: Resilience of the internet to random breakdowns. Physical Review Letters 85, 4626 (2000)
Link, H., LaViolette, R.A., Saia, J., Lane, T.: Parameters affecting the resilience of scale-free networks to random failures. e-print arXiv:cs.LG/0511012 (2005)
Gallos, L.K., Cohen, R., Argyrakis, P., Bunde, A., Havlin, S.: Stability and topology of scale-free networks under attack. Physical Review Letters 94, 188701 (2005)
Guillaume, J.L., Latapy, M., Magnien, C.: Comparison of failures and attacks on random and scale-free networks. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 186–196. Springer, Heidelberg (2004)
Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. Journal of the ACM 27(22), 228–234 (1980)
Ben-Or, M., Canetti, R., Goldreich, O.: Asynchronous secure computation. In: Proc. 25th ACM Symposium on Theory of Computing, pp. 52–61 (1993)
Internet Engineering Task Force. Rfc 1247 (open shortest path first), http://www.ietf.org/rfc/rfc1247.txt
Internet Engineering Task Force. Rfc 1771 (border gateway protocol), http://www.ietf.org/rfc/rfc1771.txt
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440 (1998)
Kleinberg, J.: The small-world phenomenon: An algorithmic perspective. Technical Report 99-1776, Computer Science Department, Cornell University (1999)
Şimşek, Ö., Jensen, D.: Decentralized search in networks using homophily and degree disparity. In: Proc. 19th International Joint Conference on Artificial Intelligence, pp. 304–310 (2005)
Tanner, H.G., Jadbabaie, A., Pappas, G.J.: Stable flocking of mobile agents, part i: Fixed topology. In: Proc. of the 44th IEEE Conference on Decision and Control, pp. 2010–2015 (2003)
Xue, F., Kumar, P.R.: The number of neighbors needed for connectivity of wireless networks. Wireless Networks 10(2), 169–181 (2004)
Bettstetter, C.: On the minimum node degree and connectivity of a wireless multihop network. In: Proc.3rd ACM Int. Symp. on Mobile Ad Hoc Net. and Comp. (MobiHoc 2002), pp. 80–91 (2002)
Santi, P., Blough, D.M.: The critical transmitting range for connectivity in sparse wireless ad hoc networks. IEEE Transactions on Mobile Computing 2(1), 25–39 (2003)
Angeli, D., Bliman, P.A.: Extension of a result by Moreau on stability of leaderless multi-agent systems. In: Proc. of the 44th IEEE Conference on Decision and Control, ECC-CDC 2005, pp. 759–764 (2005)
Hidaka, Y.S., Mourikis, A.I., Roumeliotis, S.I.: Optimal formations for cooperative localization of mobile robots. In: Proc. of the International Conference on Robotics and Automation, pp. 4137–4142 (2005)
Mourikis, A., Roumeliotis, S.: Performance bounds for cooperative simultaneous localization and mapping. In: Thrun, S., Sukhatme, G., Schaal, S., Brock, O. (eds.) Robotics: Science and Systems I, pp. 73–80. MIT Press, Cambridge (2005)
Byrne, R., Feddema, J., Abdallah, C.: Algebraic connectivity and graph robustness. Technical report Sandia National Laboratories (2005)
Fiedler, M.: Algebraic connectivity of graphs. Czechoslovak Mathematical Journal 23(98), 298–305 (1973)
Olfati-Saber, R.: Ultra-fast consensus in small-world networks. In: Proc. of the American Control Conference, pp. 2371–2378 (2005)
Nordstrom, O., Dovrolis, C.: Beware of bgp attacks. SIGCOMM Comput. Commun. Rev. 34(2) (2004)
Swaroop, D.: A note about the stability of a string of lti systems. ASME Journal of Dynamic Systems, Measurement and Control 124, 472–475 (2002)
Pant, A., Seiler, P., Hedrick, K.: Mesh stability of look-ahead interconnected systems. IEEE Transactions on Automatic Control 47, 403–407 (2002)
Tanner, H.G., Pappas, G.J., Kumar, V.: Leader-to-formation stability. IEEE Transactions on Robotics and Automation 20(3), 433–455 (2004)
Wong, W., Brockett, R.: Systems with finite communication bandwidth constraints i: State estimation problems. IEEE Transactions on Automatic Control 42(9), 1294–1299 (1997)
Wong, W., Brockett, R.: Systems with finite communication bandwidth constraints ii: Stabilization with limited information feedback. IEEE Transactions on Automatic Control 44(5), 1049–1053 (1999)
Nair, G., Evans, R.: Stabilization with data-rate-limited feedback: Tightest attainable bounds. Systems and Control Letters 41, 49–76 (2000)
Ballieul, J.: Feedback designs in information-based control. In: Pasik-Duncan, B. (ed.) Stochastic Theory and Control. Proceedings of Workshop held at the University of Kansas. LNCIS, pp. 35–57. Springer, New York (2002)
Brockett, R., Liberzon, D.: Quantized feedback stabilization of linear systems. IEEE Transactions on Automatic Control 45(7), 1279–1289 (2000)
Tatikonda, S., Elia, N.: Communication requirements for networked systems. In: Chiasson, J., Trabouriech, S., Abdallah, C.T. (eds.) Advances in Communication Control Networks. LNCIS, pp. 303–326. Springer, New York (2005)
Martins, N.C., Dahleh, M.A.: Fundamental limitations of performance in the presence of finite capacity feedback. In: Proc. of the American Control Conference, pp. 79–86 (2005)
Tanner, H.G., Christodoulakis, D.: Discrete time flocking with time delays. In: Proc. of the 44th IEEE Conference on Decision and Control, pp. 4945–4950 (2005)
Morse, A.S.: Lecture Notes on Logically Switched Dynamical Systems. Springer, Heidelberg (2006)
Abdallah, C.T., Dorato, P., Benitez-Read, J., Byrne, R.: Delayed positive feedback can stabilize oscillatory systems. In: Proc. of the American Control Conference, pp. 3106–3107 (1993)
Khoury, J., Abdallah, C.T.: Identifier-based discovery mechanism design in large-scale networks. In: Future-Net 2009: Proceedings of the International Workshop on the Network of the Future - IEEE ICC 2009, Dresden, Germany (2009)
Kleinberg, J.: Complex networks and decentralized search algorithms. In: Proceedings of the International Congress of Mathematicians, ICM (2006)
Kleinberg, J., Kempe, D., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005)
Kempe, D., Kleinberg, J., Demers, A.: Spatial gossip and resource location protocols. In: Proc. ACM Symposium on Theory of Computing, pp. 163–172 (2001)
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Clauset, A., Tanner, H.G., Abdallah, C.T., Byrne, R.H. (2009). Controlling Across Complex Networks: Emerging Links Between Networks and Control. In: Loiseau, J.J., Michiels, W., Niculescu, SI., Sipahi, R. (eds) Topics in Time Delay Systems. Lecture Notes in Control and Information Sciences, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02897-7_28
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