Maximizing Convergence Speed for Second Order Consensus in Leaderless Multi-Agent Systems

Gianvito Difilippo; Maria Pia Fanti; Agostino Marcello Mangini

doi:10.1109/JAS.2021.1004320

Volume 9 Issue 2

Feb. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(2): 259-269

G. Difilippo, M. P. Fanti, and A. M. Mangini, “Maximizing convergence speed for second order consensus in leaderless multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 2, pp. 259–269, Feb. 2022. doi: 10.1109/JAS.2021.1004320

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G. Difilippo, M. P. Fanti, and A. M. Mangini, “Maximizing convergence speed for second order consensus in leaderless multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 2, pp. 259–269, Feb. 2022. doi: 10.1109/JAS.2021.1004320

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Maximizing Convergence Speed for Second Order Consensus in Leaderless Multi-Agent Systems

doi: 10.1109/JAS.2021.1004320

Department of Electrical and Information Engineering, Polytechnic University of Bari, Bari 70125, Italy

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Author Bio:
Gianvito Difilippo received the master degree in automation engineering with honors from the Polytechnic University of Bari (Italy) in 2019. He worked in the same university as Research Assistant in Laboratory of Control and Automation in 2018 for the H2020 project OptiTruck and for AutoLogS s.r.l., an engineering and logistics company based in the Polytechnic University of Bari. He currently works for Code Architects, an automation software company, and is a Ph.D. candidate at Polytechnic University of Bari, in the Laboratory of Control and Automation. His research activity is mainly focused on consensus algorithms and autonomous driving

Maria Pia Fanti (Fellow, IEEE) received the laurea degree in electronic engineering from the University of Pisa, Italy, in 1983. She was a Visiting Researcher at the Rensselaer Polytechnic Institute of Troy, USA, in 1999. Since 1983, she has been with the Department of Electrical and Information Engineering of the Polytechnic University of Bari, Italy, where she is currently a Full Professor of system and control engineering and Chair of the Laboratory of Automation and Control. Her research interests include management and modeling of complex systems, such as transportation and logistics systems; discrete event systems; Petri nets; consensus protocols; fault detection. Prof. Fanti has published more than +310 papers and two textbooks on her research topics. She was Editor of the IEEE Trans. on Automation Science and Engineering and she is Associate Editor of the IEEE Trans. on Systems, Man, and Cybernetics: Systems. She was Member at large of the Board of Governors of the IEEE Systems, Man, and Cybernetics Society, and actually she is Member of the AdCom of the IEEE Robotics and Automaton Society, and Chair of the Technical Committee on Automation in Logistics of the IEEE Robotics and Automation Society. Prof. Fanti was General Chair of the 2011 IEEE Conference on Automation Science and Engineering, the 2017 IEEE International Conference on Service Operations and logistics, and Informatics and the 2019 Systems, Man, and Cybernetics Conference

Agostino Marcello Mangini (Member, IEEE) received the laurea degree in electronics engineering and the Ph.D. degree in electrical engineering from the Polytechnic of Bari, Italy, in 2003 and 2008, respectively. He has been a Visiting Scholar with the University of Zaragoza, Spain. He is currently an Assistant Professor with the Department of Electrical and Information Engineering, Polytechnic University of Bari. He has authored or co-authored over 100 printed publications. His current research interests include modeling, simulation, and control of discrete-event systems, Petri nets, optimization, consensus, urban traffic networks, distribution and internal logistics, management of drug distribution systems, and healthcare systems. Dr. Mangini was on the program committees of the 2007–2021 IEEE International Conference on Systems, Man, and Cybernetics, the 2018–2020 Workshop on Discrete Event Systems (WODES), the 2016–2021 IEEE Conference on Automation Science and Engineering (CASE), and the 2009 IFAC Workshop on Dependable Control of Discrete Systems (DCDS). He was on the Editorial Board of the 2017 IEEE Conference on Automation Science and Engineering. Finally, Dr. Mangini was Publication Chair of the 2017 IEEE International Conference on Service Operations and Logistics, and Informatics (SOLI 2017) and the 2019 IEEE International Conference on Systems, Man, and Cybernetics Conference (SMC 2019)
Corresponding author: Maria Pia Fanti, e-mail: mariapia.fanti@poliba.it
Received Date: 2021-08-09
Accepted Date: 2021-09-01

Available Online: 2023-03-29

Abstract

Abstract

The paper deals with the consensus problem in a leaderless network of agents that have to reach a common velocity while forming a uniformly spaced string. Moreover, the final common velocity (reference velocity) is determined by the agents in a distributed and leaderless way. Then, the consensus protocol parameters are optimized for networks characterized by a communication topology described by a class of directed graphs having a directed spanning tree, in order to maximize the convergence rate and avoid oscillations. The advantages of the optimized consensus protocol are enlightened by some simulation results and comparison with a protocol proposed in the related literature. The presented protocol can be applied to coordinate agents such as mobile robots, automated guided vehicles (AGVs) and autonomous vehicles that have to move with the same velocity and a common inter-space gap.
- Consensus protocols,
- directed spanning tree,
- multi-agent systems,
- networked systems,
- second-order consensus

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References(42)

References

[1]	Y. Cao, W. Yu, W. Ren, and G. Chen, “An overview of recent progress in the study of distributed multi-agent coordination,” IEEE Trans. Industrial Informatics, vol. 9, no. 1, pp. 427–438, 2013. doi: 10.1109/TII.2012.2219061
[2]	R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Trans. Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004. doi: 10.1109/TAC.2004.834113
[3]	F. Xiao and L. Wang, “Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays,” IEEE Trans. Automatic Control, vol. 53, no. 8, pp. 1804–1816, 2008. doi: 10.1109/TAC.2008.929381
[4]	F. Xiao, T. Chen, and H. Gao, “Synchronous hybrid event- and time-driven consensus in multiagent networks with time delays,” IEEE Trans. Cybernetics, vol. 46, no. 5, pp. 1165–1174, 2016. doi: 10.1109/TCYB.2015.2428056
[5]	Y. G. Sun and L. Wang, “Consensus of multi-agent systems in directed networks with nonuniform time-varying delays,” IEEE Trans. Automatic Control, vol. 54, no. 7, pp. 1607–1613, 2009. doi: 10.1109/TAC.2009.2017963
[6]	P. Lin and Y. Jia, “Multi-agent consensus with diverse timedelays and jointly-connected topologies,” Automatica, vol. 47, no. 4, pp. 848–856, 2011. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0005109811000689
[7]	C. Z. X. Yu, F. Yang, and L. Ou, “Stabilization parametric region of distributed PID controllers for general first-order multi-agent systems with time delay,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1555–1564, 2020. doi: 10.1109/JAS.2019.1911627
[8]	Z. Meng, W. Ren, Y. Cao, and Z. You, “Leaderless and leader-following consensus with communication and input delays under a directed network topology,” IEEE Trans. Systems,Man,and Cybernetics,Part B (Cybernetics), vol. 41, no. 1, pp. 75–88, 2011. doi: 10.1109/TSMCB.2010.2045891
[9]	C. Huang, G. Zhai, and G. Xu, “Necessary and sufficient conditions for consensus in third order multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 5, pp. 1044–1053, 2018. doi: 10.1109/JAS.2018.7511222
[10]	Y. G. Sun and L. Wang, “Consensus problems in networks of agents with double-integrator dynamics and time-varying delays,” Int. Journal of Control, vol. 82, no. 10, pp. 1937–1945, 2009. [Online]. Available: https://doi.org/10.1080/00207170902838269
[11]	P. Lin and Y. Jia, “Consensus of a class of second-order multiagent systems with time-delay and jointly-connected topologies,” IEEE Trans. Automatic Control, vol. 55, no. 3, pp. 778–784, 2010. doi: 10.1109/TAC.2010.2040500
[12]	K. Liu, Z. Ji, and W. Ren, “Necessary and sufficient conditions for consensus of second-order multiagent systems under directed topologies without global gain dependency,” IEEE Trans. Cybernetics, vol. 47, no. 8, pp. 2089–2098, 2017. doi: 10.1109/TCYB.2016.2616020
[13]	W. Ren, R. W. Beard, and E. M. Atkins, “Information consensus in multivehicle cooperative control,” IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71–82, 2007. doi: 10.1109/MCS.2007.338264
[14]	W. Ren, “On consensus algorithms for double-integrator dynamics,” IEEE Trans. Automatic Control, vol. 53, no. 6, pp. 1503–1509, 2008. doi: 10.1109/TAC.2008.924961
[15]	W. Yu, G. Chen, and M. Cao, “Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, 2010. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0005109810001251
[16]	J. Qin, W. X. Zheng, and H. Gao, “Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology,” Automatica, vol. 47, no. 9, pp. 1983–1991, 2011. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0005109811002871
[17]	S. Santini, A. Salvi, A. S. Valente, A. Pescapè, M. Segata, and R. L. Cigno, “Platooning maneuvers in vehicular networks: A distributed and consensus-based approach,” IEEE Trans. Intelligent Vehicles, vol. 4, no. 1, pp. 59–72, 2019. doi: 10.1109/TIV.2018.2886677
[18]	M. Lv, W. Yu, J. Cao, and S. Baldi, “Consensus in high-power multiagent systems with mixed unknown control directions via hybrid nussbaum-based control,” IEEE Trans. Cybernetics, pp. 1–13, 2020. DOI: 10.1109/TCYB.2020.3028171
[19]	M. Lv, W. Yu, J. Cao, and S. Baldi, “A separation-based methodology to consensus tracking of switched high-order nonlinear multiagent systems,” IEEE Trans. Neural Networks and Learning Systems, pp. 1–13, 2021. DOI: 10.1109/TNNLS.2021.3070824
[20]	Y. Liu, D. Yao, H. Li, and R. Lu, “Distributed cooperative compound tracking control for a platoon of vehicles with adaptive NN,” IEEE Trans. Cybernetics, pp. 1–10, 2021. DOI: 10.1109/TCYB.2020.3044883
[21]	Z. Meng, Z. Zhao, and Z. Lin, “On global leader-following consensus of identical linear dynamic systems subject to actuator saturation,” Systems & Control Letters, vol. 62, no. 2, pp. 132–142, 2013. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0167691112002150
[22]	J. Fu, a. W. Y. G. Wen, T. Huang, and X. Yu, “Consensus of second-order multiagent systems with both velocity and input constraints,” IEEE Trans. Industrial Electronics, vol. 66, no. 10, pp. 7946–7955, 2019. doi: 10.1109/TIE.2018.2879292
[23]	M. Jafarian and C. De Persis, “Formation control using binary information,” Automatica, vol. 53, pp. 125–135, 2015. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0005109814005950
[24]	Q. Wei, X. Wang, X. Zhong, and N. Wu, “Consensus control of leader-following multi-agent systems in directed topology with heterogeneous disturbances,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 423–431, 2021. doi: 10.1109/JAS.2021.1003838
[25]	D. Yao, H. Li, R. Lu, and Y. Shi, “Distributed sliding-mode tracking control of second-order nonlinear multiagent systems: An event-triggered approach,” IEEE Trans. Cybernetics, vol. 50, no. 9, pp. 3892–3902, 2020. doi: 10.1109/TCYB.2019.2963087
[26]	R. Palmieri, “Leaderless consensus: The state of the art,” in Proc. IEEE Int. Parallel and Distributed Processing Symposium Workshops, 2016, pp. 1307–1310.
[27]	H. Rezaee and F. Abdollahi, “Adaptive leaderless consensus control of strict-feedback nonlinear multiagent systems with unknown control directions,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 51, no. 10, pp. 6435–6444, 2021.
[28]	Y. Kim and M. Mesbahi, “On maximizing the second smallest eigenvalue of a state-dependent graph laplacian,” IEEE Trans. Automatic Control, vol. 51, no. 1, pp. 116–120, 2006. doi: 10.1109/TAC.2005.861710
[29]	J. Sheng and Z. Ding, “Optimal consensus control of linear multiagent systems with communication time delay,” IET Control Theory Applications, vol. 7, no. 15, pp. 1899–1905, 2013. doi: 10.1049/iet-cta.2013.0478
[30]	W. Yang, X. Wang, and H. Shi, “Optimal second order consensus protocol with time delay,” in Proc. 50th IEEE Decision and Control and European Control Conf., 2011, pp. 3470–3475.
[31]	J. Zhu, “Maximum consensus speed of second-order multi-agent network systems under a kind of dynamic consensus protocols,” in Proc. 29th Chinese Control Conf., 2010, pp. 796–800.
[32]	Z. Yu and L. Xie, “Convergence rate of distributed consensus for second-order multi-agent systems,” in Proc. IEEE ICCA, 2010, pp. 2284–2289.
[33]	W. Xing, Y. Zhao, and H. Karimi, “Convergence analysis on multi-AUV systems with leader-follower architecture,” IEEE Access, vol. 5, pp. 853–868, 2017. doi: 10.1109/ACCESS.2017.2651048
[34]	A. Eichler and H. Werner, “Closed-form solution for optimal convergence speed of multi-agent systems with discrete-time double-integrator dynamics for fixed weight ratios,” Systems & Control Letters, vol. 71, pp. 7–13, 2014. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0167691114001509
[35]	A. Eichler and H. Werner, “Optimal convergence speed with constrained damping of double-integrator multi-agent systems with undirected topology,” in Proc. 54th IEEE Conf. Decision and Control, 2015, pp. 2211–2216.
[36]	W. Ren and E. Atkins, “Distributed multi-vehicle coordinated control via local information exchange,” Int. Journal of Robust and Nonlinear Control, vol. 17, no. 10–11, pp. 1002–1033, 2007. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.1147
[37]	Y. Zu, C. Liu, and R. Dai, “Distributed traffic speed control for improving vehicle throughput,” IEEE Intelligent Transportation Systems Magazine, vol. 11, no. 3, pp. 56–68, 2019. doi: 10.1109/MITS.2019.2919621
[38]	C. Godsil and G. Royle, Algebraic Graph Theory. New York: SpringerVerlag, 2001.
[39]	E. Seneta, Non-Negative Matrices and Markov Chains. New York: Springer-Verlag, 2010.
[40]	E. Tegling and H. Sandberg, “On the coherence of large-scale networks with distributed PI and PD control,” IEEE Control Systems Letters, vol. 1, no. 1, pp. 170–175, 2017. doi: 10.1109/LCSYS.2017.2711781
[41]	W. Ren, “Consensus based formation control strategies for multi-vehicle systems,” in Proc. American Control Conf., 2006.
[42]	W.-C. Yueh, “Eigenvalues of several tridiagonal matrices,” in Applied Mathematics E-notes, 2005, pp. 5–66.

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Highlights

The presented consensus protocol allows to the agents to form a uniformly spaced string
The agents decide a non-predetermined common reference velocity and reach the common velocity
The conditions ensuring that the proposed second order consensus is achieved are proved
Protocol parameters to obtain the fastest convergence avoiding oscillations are optimized

Maximizing Convergence Speed for Second Order Consensus in Leaderless Multi-Agent Systems

doi: 10.1109/JAS.2021.1004320

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