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Self-tuning proportional integral control for consensus in heterogeneous multi-agent systems

Published online by Cambridge University Press:  13 September 2016

D. A. BURBANO L.
Affiliation:
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, Italy email: danielalberto.burbanolombana@unina.it, pietro.delellis@unina.it
P. DeLELLIS
Affiliation:
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, Italy email: danielalberto.burbanolombana@unina.it, pietro.delellis@unina.it
M. diBERNARDO
Affiliation:
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, Italy email: danielalberto.burbanolombana@unina.it, pietro.delellis@unina.it Department of Engineering Mathematics, University of Bristol, Bristol, UK email: mario.dibernardo@unina.it
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Abstract

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In this paper, we present a distributed Proportional-Integral (PI) strategy with self-tuning adaptive gains for reaching asymptotic consensus in networks of non-identical linear agents under constant disturbances. Alternative adaptive strategies are presented, based on global or local measures of the agents' disagreement. The proposed approaches are validated on a representative numerical example. Preliminary analytical results further confirm the viability of the self-tuning strategies.

Type
Papers
Copyright
Copyright © Cambridge University Press 2016 

References

[1] Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. (2011) Controllability of complex networks. Nature 473, 167173.CrossRefGoogle ScholarPubMed
[2] Leonard, N.-E. (2011) Multi-agent system dynamics: Bifurcation and behavior of animal groups. Annu. Rev. Control 38 (2), 171183.Google Scholar
[3] Liu, Y.-Y. & Barabási, A.-L. (2016) Control principles of complex networks. URL: http://arxiv.org/abs/1508.05384.Google Scholar
[4] Cortés, J., Martnez, S. & Bullo, F. (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans. Autom. Control 51 (8), 12891298.Google Scholar
[5] Egerstedt, M. & Hu, X. (2001) Formation constrained multi-agent control. IEEE Trans. Robot. Autom. 17 (6), 947951.Google Scholar
[6] Dörfler, F. & Bullo, F. (2012) Synchronization and transient stability in power networks and nonuniform kuramoto oscillators. SIAM J. Control Optim. 50 (3), 16161642.Google Scholar
[7] Olfati-Saber, R. (2006) Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Trans. Autom. Control 51 (3), 401420.Google Scholar
[8] Swaroop, D. & Hedrick, J. K. (1999) Constant spacing strategies for platooning in automated highway systems. J. Dyn. Syst. Meas. Control 121 (3), 462470.Google Scholar
[9] Cao, Y., Yu, W., Ren, W. & Chen, G. (2013) An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Indust. Inform. 9 (1), 427438.Google Scholar
[10] Strogatz, S. (2001) Exploring complex networks. Nature 410, 268276.Google Scholar
[11] Thattai, M. & van Oudenaarden, A. (2001) Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. 98 (15), 86148619.Google Scholar
[12] Kim, M., Sterh, M.-O., Kim, J. & Ha, S. (2010) An application framework for loosely coupled networked cyber-physical systems. Proceedings of IEEE/IFIP 8th International Conference on Embedded and Ubiquitous Computing (EUC), pp.144–153, Hong Kong, 11–13 Dec.Google Scholar
[13] Hill, D. J. & Zhao, J. (2012). Synchronization of dynamical networks by network control. IEEE Trans. Autom. Control 57 (6), 15741580.Google Scholar
[14] Xiang, J. & Chen, G. (2007) On the V-stability of complex dynamical networks. Automatica 43 (6), 10491057.Google Scholar
[15] DeLellis, P., di Bernardo, M. & Liuzza, D. (2015) Convergence and synchronization in heterogeneous networks of smooth and piecewise smooth systems. Automatica 56 (6), 111.CrossRefGoogle Scholar
[16] Dorf, R. C. & Bishop, R. H. (2011). Modern Control Systems. Pearson, New York.Google Scholar
[17] Burbano, D. A. & di Bernardo, M. (2015) Distributed PID control for consensus of homogeneous and heterogeneous networks. IEEE Trans. Control Netw. Syst. 2 (2), 154163.Google Scholar
[18] Burbano, D. A. & di Bernardo, M. (2015) Multiplex PI-control for consensus in networks of heterogeneous linear agents. Automatica 67 (3), 310320.CrossRefGoogle Scholar
[19] Andreasson, M., Dimarogonas, D. V., Sandberg, H. & Johansson, K. H. (2014) Distributed control of networked dynamical systems: Static feedback, integral action and consensus. IEEE Trans. Autom. Control 59 (7), 17501764.Google Scholar
[20] Freeman, R. A., Peng, Y. & Lynch, K. M. (2006) Stability and convergence properties of dynamic average consensus estimators. Proceedings of 45th IEEE Conference on Decision and Control (CDC), pp. 338–343, 13–15 Dec, San Diego, CA.Google Scholar
[21] Scardovi, L. & Sepulchre, R. (2009) Synchronization in networks of identical linear systems. Automatica 34, 25572562.Google Scholar
[22] Seyboth, G. & Allgöwer, F. (2015) Output synchronization of linear multi-agent systems under constant disturbances via distributed integral action. Proc. American Control Conference (ACC). Chicago, IL, USA, pp. 62–67.Google Scholar
[23] Wieland, P., Sepulchre, R. & Allgöwer, F. (2011) An internal model principle is necessary and sufficient for linear output synchronization. Automatica 47 (5), 10681074.Google Scholar
[24] Bai, H., Freeman, R. A. & Lynch, K. M. (2010) Robust dynamic average consensus of time-varying inputs. Proceedings of 49th IEEE Conference on Decision and Control (CDC), pp. 3104–3109, 15–17 Dec, Atlanta, GA.Google Scholar
[25] Sarlette, A., Dai, J., Phulpin, Y. & Ernst, D. (2012) Cooperative frequency control with a multi-terminal high-voltage DC network. Automatica 48 (12), 31283134.Google Scholar
[26] Simpson-Porco, J. W., Dörfler, F. & Bullo, F. (2013) Synchronization and power sharing for droop-controlled inverters in islanded microgrids. Automatica 49 (9), 26032611.Google Scholar
[27] Bidram, A., Lewis, F. L. & Davoudi, A. (2013) Distributed control systems for small-scale power networks: Using multiagent cooperative control theory. IEEE Control Syst. Mag. 34 (6), 5677.Google Scholar
[28] Carli, R., Chiuso, A., Schenato, L. & Zampieri, S. (2008) A PI consensus controller for networked clocks synchronization. Proceedings of the 17th IFAC World Congress, Vol. 17, pp. 10289–10294, July 6–11, Seoul, Korea.CrossRefGoogle Scholar
[29] Xuan, Z. & Papachristodoulou, A. (2014) A distributed PID controller for network congestion control problems. Proceedings of American Control Conference (ACC), pp. 0743–1619, 4–6 June, Portland, OR.Google Scholar
[30] Cheng, L., Wang, Y., Ren, W., Hou, Z.-G. & Tan, M. (2015) Containment control of multiagent systems with dynamic leaders based on a PIn -type approach. IEEE Trans. Cybern., forthcoming issue.Google Scholar
[31] Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D. U. (2006) Complex networks: Structure and dynamics. Phys. Rep. 424 (4–5), 175308.CrossRefGoogle Scholar
[32] Lo Iudice, F., Garofalo, F. & Sorrentino, F. (2015) Structural permeability of complex networks to control signals. Nature Commun. 6, 8349.CrossRefGoogle ScholarPubMed
[33] Wang, X. F. & Chen, G. (2002) Pinning control of scale-free dynamical networks. Physica A 310 (3–4), 521531.Google Scholar
[34] Porfiri, M. & di Bernardo, M. (2008) Criteria for global pinning controllability of complex networks. Automatica 44 (12), 31003106.Google Scholar
[35] Cornelius, S. P., Kath, W. L. & Motter, A. E. (2013) Realistic control of network dynamics. Nature Commun. 4, 1942.Google Scholar
[36] Lai, Y. C. (2014) Controlling complex, non-linear dynamical networks. Natl. Sci. Rev. 1 (3), 339341.CrossRefGoogle Scholar
[37] Nepusz, T. & Vicsek, T. (2012) Controlling edge dynamics in complex networks. Nature Phys. 8 (7), 568573.Google Scholar
[38] DeLellis, P., di Bernardo, M. & Garofalo, F. (2009) Novel decentralized adaptive strategies for the synchronization of complex networks. Automatica 45 (5), 13121318.Google Scholar
[39] Radenkovic, M. & Bose, T. (2015) On multi-agent self-tuning consensus. Automatica 55 (5), 4654.Google Scholar
[40] DeLellis, P., di Bernardo, M., Gorochowski, T. E. & Russo, G. (2010) Synchronization and control of complex networks via contraction, adaptation and evolution. IEEE Circuits Syst. Mag. 10 (3), 6482.CrossRefGoogle Scholar
[41] DeLellis, P., di Bernardo, M., Garofalo, F. & Porfiri, M. (2010) Evolution of complex networks via edge snapping. IEEE Trans. Circuits Syst. I: Regular Papers 57 (8), 21322143.Google Scholar
[42] Lu, W. & Chen, T. (2006) New approach to synchronization analysis of linearly coupled ordinary differential systems. Physica D: Nonlinear Phenom. 213 (2), 214230.Google Scholar
[43] Poole, G. & Boullion, T. (1974) A survey on M-matrices. SIAM Rev. 16 (4), 419427.Google Scholar
[44] Olfati-Saber, R., Fax, J. A. & Murray, R. M. (2007) Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95 (1), 215233.Google Scholar
[45] Burbano Lombana, D. A. (2015) Distributed PID Control for Synchronization and Consensus in Multi-agent Networks, PhD Thesis, University of Naples Federico II.Google Scholar
[46] Bernstein, D. S. (2009) Matrix Mathematics: Theory, Facts, and Formulas, 2nd ed., Princeton University Press, New Jersey.Google Scholar
[47] Khalil, H. K. & Grizzle, J. W. (2001) Nonlinear Systems, 3rd ed., Prentice Hall, New Jersey.Google Scholar