Matrix-scaled resilient consensus of discrete-time and continuous-time networks
Author:
Yilun Shang
Journal:
Quart. Appl. Math. 81 (2023), 777-800
MSC (2020):
Primary 93B70, 93C10, 93E03
DOI:
https://doi.org/10.1090/qam/1662
Published electronically:
March 13, 2023
Full-text PDF
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References |
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Additional Information
Abstract: This paper studies the matrix-scaled resilient consensus problems over multi-agent networks as occurring in computer science and distributed control. Unlike existing works on consensus problems, where the states of agents converge to a common value or reach some prescribed proportions, we take a more general matrix-scaled approach to accommodate the interdependence of multi-dimensional states. We develop a unified analytical framework to deal with matrix-scaled resilient consensus of discrete-time and continuous-time dynamical agents, where the underlying communication network is modeled as a generic directed time-dependent random graph. We propose new distributed protocols to guarantee the matrix-scaled consensus of cooperative agents in the network in the presence of Byzantine agents, who have full knowledge of the system and pose a severe security threat to the collective consensus objective. The cooperative agents feature multiple input and multiple output, and the number and identities of Byzantine agents are not available to the cooperative ones. Our mathematical approach capitalizes on matrix analysis, control theory, graph theory, and martingale convergence. Some numerical examples are presented to demonstrate the effectiveness of our theoretical results.
References
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- Yilun Shang, $L^1$ group consensus of multi-agent systems with switching topologies and stochastic inputs, Phys. Lett. A 377 (2013), no. 25-27, 1582–1586. MR 3062208, DOI 10.1016/j.physleta.2013.04.054
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- Y. Shang, Consensus of hybrid multi-agent systems with malicious nodes, IEEE Trans. Circuits Syst. Express Briefs 67 (2020), no. 4, 685–689.
- Yilun Shang, Resilient consensus in multi-agent systems with state constraints, Automatica J. IFAC 122 (2020), 109288, 7. MR 4161366, DOI 10.1016/j.automatica.2020.109288
- Y. Shang, Resilient consensus for expressed and private opinions, IEEE Trans. Cybernet. 51 (2021), no. 1, 318–331.
- Yilun Shang, Resilient group consensus in heterogeneously robust networks with hybrid dynamics, Math. Methods Appl. Sci. 44 (2021), no. 2, 1456–1469. MR 4185326, DOI 10.1002/mma.6844
- Yilun Shang, A system model of three-body interactions in complex networks: consensus and conservation, Proc. A. 478 (2022), no. 2258, Paper No. 20210564, 19. MR 4395551, DOI 10.1098/rspa.2021.0564
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- Y. Shang, Resilient tracking consensus over dynamic random graphs: A linear system approach, Eur. J. Appl. Math. 34 (2023), no. 2, 408–423, DOI: 10.1017/S0956792522000225.
- Yilun Shang, On connectivity and robustness of random graphs with inhomogeneity, J. Appl. Probab. 60 (2023), no. 1, 284–294. MR 4546123, DOI 10.1017/jpr.2022.32
- P. Shi and B. Yan, A survey on intelligent control for multiagent systems, IEEE Trans. Syst. Man Cybernet. Syst. 51 (2021), no. 1, 161–175.
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References
- Waseem Abbas, Mudassir Shabbir, Jiani Li, and Xenofon Koutsoukos, Resilient distributed vector consensus using centerpoint, Automatica J. IFAC 136 (2022), Paper No. 110046, 8. MR 4343617, DOI 10.1016/j.automatica.2021.110046
- A. Amirkhani and A. H. Barshooi, Consensus in multi-agent systems: a review, Artif. Intell. Rev. 55 (2022), 3897–3935.
- Y. Bai and J. Wang, Resilient consensus of continuous-time linear networked systems, IEEE Trans. Circuits Syst. Express Briefs 69 (2022), no. 8, 3500–3504.
- F. Battiston, E. Amico, A. Barrat, G. Bianconi, G. F. de Arruda, B. Franceschiello, I. Iacopini, S. Kefi, V. Latora, Y. Moreno, M. M. Murray, T. P. Peixoto, F. Vaccarino, and G. Petri, The physics of higher-order interactions in complex systems, Nat. Phys. 17 (2021), 1093–1098.
- S. Bouraga, A taxonomy of blockchain consensus protocols: A survey and classification framework, Expert Syst. Appl. 168 (2021), 114384.
- Nicolas Broutin, Thomas Duquesne, and Minmin Wang, Limits of multiplicative inhomogeneous random graphs and Lévy trees: the continuum graphs, Ann. Appl. Probab. 32 (2022), no. 4, 2448–2503. MR 4474511, DOI 10.1214/21-aap1737
- C.-T. Chen, Linear system theory and design, Oxford University Press, 1998.
- Seyed Mehran Dibaji and Hideaki Ishii, Resilient consensus of second-order agent networks: asynchronous update rules with delays, Automatica J. IFAC 81 (2017), 123–132. MR 3654593, DOI 10.1016/j.automatica.2017.03.008
- M. Drobyshevskly and D. Turdakov, Random graph modeling: A survey of the concepts, ACM Comput. Surv. 52 (2020), no. 6, 131.
- Rick Durrett, Probability—theory and examples, Cambridge Series in Statistical and Probabilistic Mathematics, vol. 49, Cambridge University Press, Cambridge, 2019. Fifth edition of [MR1068527]. MR 3930614, DOI 10.1017/9781108591034
- Alan Frieze and MichałKaroński, Introduction to random graphs, Cambridge University Press, Cambridge, 2016. MR 3675279, DOI 10.1017/CBO9781316339831
- W. Fu, J. Qin, W. X. Zheng, Y. Chen, and Y. Kang, Resilient cooperative source seeking of double-integrator multi-robot systems under deception attacks, IEEE Trans. Ind. Elect. 68 (2021), no. 5, 4218–4227.
- H. Hassani, R. Razavi-Far, M. Saif, F. Chiclana, O. Krejcar, and E. Herrera-Viedma, Classical dynamic consensus and opinion dynamics models: A survey of recent trends and methodologies, Inf. Fusion 88 (2022), 22–40.
- Hideaki Ishii, Yuan Wang, and Shuai Feng, An overview on multi-agent consensus under adversarial attacks, Annu. Rev. Control 53 (2022), 252–272. MR 4426981, DOI 10.1016/j.arcontrol.2022.01.004
- Zhong-Ping Jiang and Yuan Wang, Input-to-state stability for discrete-time nonlinear systems, Automatica J. IFAC 37 (2001), no. 6, 857–869. MR 1834595, DOI 10.1016/S0005-1098(01)00028-0
- H. J. LeBlanc, H. Zhang, X. Koutsoukos, and S. Sundaram, Resilient asymptotic consensus in robust networks, IEEE J. Select. Areas Commun. 31 (2013), no. 4, 766–781.
- David G. Luenberger, Canonical forms for linear multivariable systems, IEEE Trans. Automatic Control AC-12 (1967), no. 3, 290–293. MR 0441429, DOI 10.1109/tac.1967.1098584
- D. Meng and Y. Jia, Robust consensus algorithms for multiscale coordination control of multivehicle systems with disturbances, IEEE Trans. Ind. Elect. 63 (2016), no. 2, 1107–1119.
- R. Olfati-Saber, J. A. Fax, and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proc. IEEE 95 (2007), 215–233.
- M. Papadopoulou, H. Hildenbrandt, D. W. E. Sankey, S. J. Portugal, and C. K. Hemelrijk, Self-organization of collective escape in pigeon flocks, PLoS Comput. Biol. 18 (2022), no. 1, e1009772.
- J. Qin, Q. Ma, Y. Shi, and L. Wang, Recent advances in consensus of multi-agent systems: a brief survey, IEEE Trans. Ind. Elect. 64 (2017), no. 6, 4972–4983.
- Q. I. Rahman and G. Schmeisser, Analytic theory of polynomials, London Mathematical Society Monographs. New Series, vol. 26, The Clarendon Press, Oxford University Press, Oxford, 2002. MR 1954841
- Daniel Revuz and Marc Yor, Continuous martingales and Brownian motion, 3rd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 293, Springer-Verlag, Berlin, 1999. MR 1725357, DOI 10.1007/978-3-662-06400-9
- Hamed Rezaee, Thomas Parisini, and Marios M. Polycarpou, Almost sure resilient consensus under stochastic interaction: links failure and noisy channels, IEEE Trans. Automat. Control 66 (2021), no. 12, 5727–5741. MR 4349153
- Sandip Roy, Scaled consensus, Automatica J. IFAC 51 (2015), 259–262. MR 3284775, DOI 10.1016/j.automatica.2014.10.073
- Yilun Shang, $L^1$ group consensus of multi-agent systems with switching topologies and stochastic inputs, Phys. Lett. A 377 (2013), no. 25-27, 1582–1586. MR 3062208, DOI 10.1016/j.physleta.2013.04.054
- Yilun Shang, Resilient consensus of switched multi-agent systems, Systems Control Lett. 122 (2018), 12–18. MR 3872601, DOI 10.1016/j.sysconle.2018.10.001
- Y. Shang, Consensus of hybrid multi-agent systems with malicious nodes, IEEE Trans. Circuits Syst. Express Briefs 67 (2020), no. 4, 685–689.
- Yilun Shang, Resilient consensus in multi-agent systems with state constraints, Automatica J. IFAC 122 (2020), 109288, 7. MR 4161366, DOI 10.1016/j.automatica.2020.109288
- Y. Shang, Resilient consensus for expressed and private opinions, IEEE Trans. Cybernet. 51 (2021), no. 1, 318–331.
- Yilun Shang, Resilient group consensus in heterogeneously robust networks with hybrid dynamics, Math. Methods Appl. Sci. 44 (2021), no. 2, 1456–1469. MR 4185326, DOI 10.1002/mma.6844
- Yilun Shang, A system model of three-body interactions in complex networks: consensus and conservation, Proc. A. 478 (2022), no. 2258, Paper No. 20210564, 19. MR 4395551, DOI 10.1098/rspa.2021.0564
- Yilun Shang, On the tree-depth and tree-width in heterogeneous random graphs, Proc. Japan Acad. Ser. A Math. Sci. 98 (2022), no. 9, 78–83. MR 4505377, DOI 10.3792/pjaa.98.015
- Y. Shang, Resilient tracking consensus over dynamic random graphs: A linear system approach, Eur. J. Appl. Math. 34 (2023), no. 2, 408–423, DOI: 10.1017/S0956792522000225.
- Yilun Shang, On connectivity and robustness of random graphs with inhomogeneity, J. Appl. Probab. 60 (2023), no. 1, 284–294. MR 4546123, DOI 10.1017/jpr.2022.32
- P. Shi and B. Yan, A survey on intelligent control for multiagent systems, IEEE Trans. Syst. Man Cybernet. Syst. 51 (2021), no. 1, 161–175.
- Srdjan S. Stanković, Marko Beko, and Miloš S. Stanković, Nonlinear robustified stochastic consensus seeking, Systems Control Lett. 139 (2020), 104667, 9. MR 4080747, DOI 10.1016/j.sysconle.2020.104667
- Yongzheng Sun, Wang Li, Hongjun Shi, Donghua Zhao, and Sandro Azaele, Finite-time and fixed-time consensus of multiagent networks with pinning control and noise perturbation, SIAM J. Appl. Math. 79 (2019), no. 1, 111–130. MR 3904439, DOI 10.1137/18M1174143
- Fenglan Sun, Xiaogang Liao, and Jürgen Kurths, Mean-square consensus for heterogeneous multi-agent systems with probabilistic time delay, Inform. Sci. 543 (2021), 112–124. MR 4130037, DOI 10.1016/j.ins.2020.07.021
- Leo Torres, Ann S. Blevins, Danielle Bassett, and Tina Eliassi-Rad, The why, how, and when of representations for complex systems, SIAM Rev. 63 (2021), no. 3, 435–485. MR 4296737, DOI 10.1137/20M1355896
- M. H. Trinh, D. V. Vu, Q. V. Tran, and H.-S. Ahn, Matrix-scaled consensus, arXiv:2204.10723.
- T. Vicsek and A. Zafeiris, Collective motion, Phys. Rep. 517 (2012), 71–140.
- Chengjie Xu, Haichuan Xu, Housheng Su, and Chen Liu, Adaptive bipartite consensus of competitive linear multi-agent systems with asynchronous intermittent communication, Internat. J. Robust Nonlinear Control 32 (2022), no. 9, 5120–5140. MR 4423300, DOI 10.1002/rnc.6086
- Jiaqi Yan, Xiuxian Li, Yilin Mo, and Changyun Wen, Resilient multi-dimensional consensus in adversarial environment, Automatica J. IFAC 145 (2022), Paper No. 110530, 12. MR 4469589, DOI 10.1016/j.automatica.2022.110530
- J. Yu and Y. Shi, Scaled group consensus in multiagent systems with first/second-order continuous dynamics, IEEE Trans. Cybernet. 48 (2018), no. 8, 2259–2271.
- Haotian Zhang, Elaheh Fata, and Shreyas Sundaram, A notion of robustness in complex networks, IEEE Trans. Control Netw. Syst. 2 (2015), no. 3, 310–320. MR 3401191, DOI 10.1109/TCNS.2015.2413551
- P. Zhang, D. C. Schmidt, J. White, and A. Dubey, Consensus mechanisms and information security technologies, Advances in Computers, Vol. 115, Elsevier, 2019, pp. 181–209.
- Dan Zhao, Yuezu Lv, Xinghuo Yu, Guanghui Wen, and Guanrong Chen, Resilient consensus of higher order multiagent networks: an attack isolation-based approach, IEEE Trans. Automat. Control 67 (2022), no. 2, 1001–1007. MR 4376138
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Additional Information
Yilun Shang
Affiliation:
Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom
MR Author ID:
867738
ORCID:
0000-0002-2817-3400
Email:
yilun.shang@northumbria.ac.uk
Received by editor(s):
December 18, 2022
Received by editor(s) in revised form:
January 24, 2023
Published electronically:
March 13, 2023
Article copyright:
© Copyright 2023
Brown University
