Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T08:51:43.224Z Has data issue: false hasContentIssue false
  • English
  • Français

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. ,
P. DeLELLIS  and
M. diBERNARDO
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
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

91B69: Heterogeneous agent models05C82: Complex networks93C40: Adaptive control
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Special Issue 6: Network Analysis and Modelling , December 2016 , pp. 923 - 940
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. (2011) Controllability of complex networks. Nature 473, 167–173.CrossRefGoogle ScholarPubMed
[2] Leonard, N.-E. (2011) Multi-agent system dynamics: Bifurcation and behavior of animal groups. Annu. Rev. Control 38 (2), 171–183.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), 1289–1298.Google Scholar
[5] Egerstedt, M. & Hu, X. (2001) Formation constrained multi-agent control. IEEE Trans. Robot. Autom. 17 (6), 947–951.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), 1616–1642.Google Scholar
[7] Olfati-Saber, R. (2006) Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Trans. Autom. Control 51 (3), 401–420.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), 462–470.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), 427–438.Google Scholar
[10] Strogatz, S. (2001) Exploring complex networks. Nature 410, 268–276.Google Scholar
[11] Thattai, M. & van Oudenaarden, A. (2001) Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. 98 (15), 8614–8619.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), 1574–1580.Google Scholar
[14] Xiang, J. & Chen, G. (2007) On the V-stability of complex dynamical networks. Automatica 43 (6), 1049–1057.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), 1–11.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), 154–163.Google Scholar
[18] Burbano, D. A. & di Bernardo, M. (2015) Multiplex PI-control for consensus in networks of heterogeneous linear agents. Automatica 67 (3), 310–320.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), 1750–1764.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, 2557–2562.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), 1068–1074.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), 3128–3134.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), 2603–2611.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), 56–77.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), 175–308.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), 521–531.Google Scholar
[34] Porfiri, M. & di Bernardo, M. (2008) Criteria for global pinning controllability of complex networks. Automatica 44 (12), 3100–3106.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), 339–341.CrossRefGoogle Scholar
[37] Nepusz, T. & Vicsek, T. (2012) Controlling edge dynamics in complex networks. Nature Phys. 8 (7), 568–573.Google Scholar
[38] DeLellis, P., di Bernardo, M. & Garofalo, F. (2009) Novel decentralized adaptive strategies for the synchronization of complex networks. Automatica 45 (5), 1312–1318.Google Scholar
[39] Radenkovic, M. & Bose, T. (2015) On multi-agent self-tuning consensus. Automatica 55 (5), 46–54.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), 64–82.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), 2132–2143.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), 214–230.Google Scholar
[43] Poole, G. & Boullion, T. (1974) A survey on M-matrices. SIAM Rev. 16 (4), 419–427.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), 215–233.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