eISSN: 3087-4289 editor@aimjournals.com
All Journals
Submit your article

International Journal of Modern Computer Science and IT Innovations

Open Access Peer Review International
Open Access

LOCAL NODE COMPENSATION FOR ENHANCED STABILITY IN DISTRIBUTED SIGNED NETWORKS

DOI https://doi.org/10.55640/ijmcsit-v02i04-02
pdf
Pedro C. Almeida 1 , Prof. Laura B. Heinrich 1 ,
4 Department of Electrical and Computer Engineering, University of Porto, Portugal
4 Institute of Networked Systems, RWTH Aachen University, Germany

Abstract

Multi-agent systems exhibiting both cooperative and antagonistic interactions, often modeled as signed networks, present unique challenges for achieving system stability and desired collective behaviors. Traditional consensus algorithms, primarily designed for purely cooperative networks, often fail in the presence of negative links, leading to phenomena like polarization or divergence. This article introduces a novel distributed stabilization strategy for signed networks based on local node compensation, effectively adding self-loops to individual agents. By leveraging this compensatory mechanism at each node, agents can autonomously adjust their dynamics to counteract the destabilizing effects of antagonistic connections, thereby promoting system stability. We detail the theoretical framework for incorporating self-loop compensation into standard agent dynamics and analyze its impact on the network's spectral properties. Hypothetical results demonstrate that this localized intervention significantly enhances the stability margin and convergence characteristics, offering a scalable and implementable solution for maintaining coherent behavior in complex signed multi-agent environments.

Keywords

Distributed signed networks, local node compensation, network stability, consensus algorithms

References

📄 M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks. Princeton, NJ, USA: Princeton Univ. Press, 2010.
📄 S. S. Kia, B. Van Scoy, J. Cortes, R. A. Freeman, K. M. Lynch, and S. Martinez, “Tutorial on dynamic average consensus: The problem, its applications, and the algorithms,” IEEE Control Syst. Mag., vol. 39, no. 3, pp. 40–72, Jun. 2019.
📄 J. Qin, Q. Ma, Y. Shi, and L. Wang, “Recent advances in consensus of multi-agent systems: A brief survey,” IEEE Trans. Ind. Electron., vol. 64, no. 6, pp. 4972–4983, Jun. 2017.
📄 R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1520–1533, Sep. 2004.
📄 C. D. Godsil, G. Royle, and C. Godsil, Algebraic Graph Theory, vol. 207. New York, NY, USA : Springer, 2001.
📄 A. Ortega, P. Frossard, J. Kovačević, J. M. Moura, and P. Vandergheynst, “Graph signal processing: Overview, challenges, and applications,” Proc. IEEE, vol. 106, no. 5, pp. 808–828, May 2018.
📄 Y. Cao, W. Yu, W. Ren, and G. Chen, “An overview of recent progress in the study of distributed multi-agent coordination,” IEEE Trans. Ind. Informat., vol. 9, no. 1, pp. 427–438, Feb. 2013.
📄 Y. Song, D. J. Hill, and T. Liu, “On extension of effective resistance with application to graph Laplacian definiteness and power network stability,” IEEE Trans. Circuits Syst. I: Regular Papers, vol. 5, no. 3, pp. 901–912, Mar. 2017.
📄 Y. Song, D. J. Hill, and T. Liu, “Network-based analysis of small-disturbance angle stability of power systems,” IEEE Trans. Control Netw. Syst., vol. 5, no. 3, pp. 901–912, Sep. 2017.
📄 T. Ding, C. Li, Y. Yang, R. Bo, and F. Blaabjerg, “Negative reactance impacts on the eigenvalues of the jacobian matrix in power flow and type-1 low-voltage power-flow solutions,” IEEE Trans. Power Syst., vol. 32, no. 5, pp. 3471–3481, Sep. 2017.
📄 A. V. Proskurnikov, A. S. Matveev, and M. Cao, “Opinion dynamics in social networks with hostile camps: Consensus vs. polarization,” IEEE Trans. Autom. Control, vol. 61, no. 6, pp. 1524–1536, Jun. 2016.
📄 D. Meng, Z. Meng, and Y. Hong, “Uniform convergence for signed networks under directed switching topologies,” Automatica, vol. 90, pp. 8–15, 2018.
📄 W. Chen, “On spectral properties of signed Laplacians with connections to eventual positivity,” IEEE Trans. Autom. Control, vol. 66, no. 5, pp. 2177–2190, May 2021.
📄 C. Altafini, “Consensus problems on networks with antagonistic interactions,” IEEE Trans. Autom. Control, vol. 58, no. 4, pp. 935–946, Apr. 2013.
📄 W. Xia and M. Cao, “Clustering in diffusively coupled networks,” Automatica, vol. 47, no. 11, pp. 2395–2405, 2011.
📄 G. Shi, C. Altafini, and J. S. Baras, “Dynamics over signed networks,” SIAM Rev., vol. 61, no. 2, pp. 229–257, 2019.
📄 L. Pan, H. Shao, Y. Xi, and D. Li, “Bipartite consensus problem on matrix-valued weighted directed networks,” Sci. China Inf. Sci., vol. 64, no. 4, pp. 1–3, 2021.
📄 L. Pan, H. Shao, M. Mesbahi, Y. Xi, and D. Li, “Bipartite consensus on matrix-valued weighted networks,” IEEE Trans. Circuits Syst. II: Exp. Briefs, vol. 66, no. 8, pp. 1441–1445, Aug. 2019.
📄 L. Pan, H. Shao, M. Mesbahi, Y. Xi, and D. Li, “Consensus on matrix-weighted switching networks,” IEEE Trans. Autom. Control, vol. 66, no. 12, pp. 5990–5996, Dec. 2021.
📄 C. Wang, L. Pan, H. Shao, D. Li, and Y. Xi, “Characterizing bipartite consensus with balancing set on signed matrix-weighted networks,” Automatica, vol. 141, 2022, Art. no. 110237.
📄 Y. Cheng, L. Shi, J. Shao, and W. X. Zheng, “Seeking tracking consensus for general linear multiagent systems with fixed and switching signed networks,” IEEE Trans. Cybern., vol. 52, no. 7, pp. 6697–6706, Jul. 2022.
📄 L. Shi, W. X. Zheng, J. Shao, and Y. Cheng, “Sub-super-stochastic matrix with applications to bipartite tracking control over signed networks,” SIAM J. Control Optim., vol. 59, no. 6, pp. 4563–4589, 2021.
📄 J. Shao, L. Shi, Y. Cheng, and T. Li, “Asynchronous tracking control of leader-follower multiagent systems with input uncertainties over switching signed digraphs,” IEEE Trans. Cybern., vol. 52, no. 7, pp. 6379–6390, Jul. 2022.
📄 T. Vicsek and A. Zafeiris, “Collective motion,” Phys. Rep., vol. 517, no. 3/4, pp. 71–140, 2012.
📄 V. Gazi and K. M. Passino, “Stability analysis of swarms,” IEEE Trans. Autom. Control, vol. 48, no. 4, pp. 692–697, Apr. 2003.
📄 L. Pan, H. Shao, and M. Mesbahi, “Laplacian dynamics on signed networks,” in Proc. IEEE 55th Conf. Decis. Control, 2016, pp. 891–896.
📄 J. C. Bronski and L. DeVille, “Spectral theory for dynamics on graphs containing attractive and repulsive interactions,” SIAM J. Appl. Math., vol. 74, no. 1, pp. 83–105, 2014.
📄 D. Zelazo and M. Bürger, “On the robustness of uncertain consensus networks,” IEEE Trans. Control Netw. Syst., vol. 4, no. 2, pp. 170–178, Jun. 2017.
📄 W. Chen, D. Wang, J. Liu, T. Başar, and L. Qiu, “On spectral properties of signed Laplacians for undirected graphs,” in Proc. IEEE 56th Annu. Conf. Decis. Control, 2017, pp. 1999–2002.
📄 W. Chen, “Characterizing the positive semidefiniteness of signed Laplacians via effective resistances,” in Proc. IEEE 55th Conf. Decis. Control, 2016, pp. 985–990.

Similar Articles

1-10 of 25

You may also start an advanced similarity search for this article.