Supportive consensus

[EN] The paper is concerned with the consensus problem in a multi-agent system such that each agent has boundary constraints. Classical Olfati-Saber's consensus algorithm converges to the same value of the consensus variable, and all the agents reach the same value. These algorithms find an equality solution. However, what happens when this equality solution is out of the range of some of the agents? In this case, this solution is not adequate for the proposed problem. In this paper, we propose a new kind of algorithms called supportive consensus where some agents of the network can compensate for the lack of capacity of other agents to reach the average value, and so obtain an acceptable solution for the proposed problem. Supportive consensus finds an equity solution. In the rest of the paper, we define the supportive consensus, analyze and demonstrate the network's capacity to compensate out of boundaries agents, propose different supportive consensus algorithms, and finally, provide some simulations to show the performance of the proposed algorithms.The author(s) received specific funding for this work from the Valencian Research Institute for Artificial Intelligence (VRAIN) where the authors are currently working. This work is partially supported by the Spanish Government project RTI2018-095390-B-C31, GVA-CEICE project PROMETEO/2018/002, and TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No 952215. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Palomares Chust, A.; Rebollo Pedruelo, M.; Carrascosa Casamayor, C. (2020). Supportive consensus. PLoS ONE. 15(12):1-30. https://doi.org/10.1371/journal.pone.0243215S1301512Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and Cooperation in Networked Multi-Agent Systems. Proceedings of the IEEE, 95(1), 215-233. doi:10.1109/jproc.2006.887293Pérez, I. J., Cabrerizo, F. J., Alonso, S., Dong, Y. C., Chiclana, F., & Herrera-Viedma, E. (2018). On dynamic consensus processes in group decision making problems. Information Sciences, 459, 20-35. doi:10.1016/j.ins.2018.05.017Fischbacher, U., & Gächter, S. (2010). Social Preferences, Beliefs, and the Dynamics of Free Riding in Public Goods Experiments. American Economic Review, 100(1), 541-556. doi:10.1257/aer.100.1.541Du, S., Hu, L., & Song, M. (2016). Production optimization considering environmental performance and preference in the cap-and-trade system. Journal of Cleaner Production, 112, 1600-1607. doi:10.1016/j.jclepro.2014.08.086Alfonso, B., Botti, V., Garrido, A., & Giret, A. (2013). A MAS-based infrastructure for negotiation and its application to a water-right market. Information Systems Frontiers, 16(2), 183-199. doi:10.1007/s10796-013-9443-8Rebollo M, Carrascosa C, Palomares A. Consensus in Smart Grids for Decentralized Energy Management. In: Highlights of Practical Applications of Heterogeneous Multi-Agent Systems. The PAAMS Collection. Springer; 2014. p. 250–261.Zhao, T., & Ding, Z. (2018). Distributed Agent Consensus-Based Optimal Resource Management for Microgrids. IEEE Transactions on Sustainable Energy, 9(1), 443-452. doi:10.1109/tste.2017.2740833Qiu, Z., Liu, S., & Xie, L. (2018). Necessary and sufficient conditions for distributed constrained optimal consensus under bounded input. International Journal of Robust and Nonlinear Control, 28(6), 2619-2635. doi:10.1002/rnc.4040Wei Ren, & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655-661. doi:10.1109/tac.2005.846556Ren, W., & Beard, R. W. (2008). Distributed Consensus in Multi-vehicle Cooperative Control. Communications and Control Engineering. doi:10.1007/978-1-84800-015-5Knorn F, Corless MJ, Shorten RN. A result on implicit consensus with application to emissions control. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference; 2011. p. 1299–1304.Roy, S. (2015). Scaled consensus. Automatica, 51, 259-262. doi:10.1016/j.automatica.2014.10.073Mo, L., & Lin, P. (2018). Distributed consensus of second-order multiagent systems with nonconvex input constraints. International Journal of Robust and Nonlinear Control, 28(11), 3657-3664. doi:10.1002/rnc.4076Wang, Q., Gao, H., Alsaadi, F., & Hayat, T. (2014). An overview of consensus problems in constrained multi-agent coordination. Systems Science & Control Engineering, 2(1), 275-284. doi:10.1080/21642583.2014.897658Xi, J., Yang, J., Liu, H., & Zheng, T. (2018). Adaptive guaranteed-performance consensus design for high-order multiagent systems. Information Sciences, 467, 1-14. doi:10.1016/j.ins.2018.07.069Fontan A, Shi G, Hu X, Altafini C. Interval consensus: A novel class of constrained consensus problems for multiagent networks. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC); 2017. p. 4155–4160.Hou, W., Wu, Z., Fu, M., & Zhang, H. (2018). Constrained consensus of discrete-time multi-agent systems with time delay. International Journal of Systems Science, 49(5), 947-953. doi:10.1080/00207721.2018.1433899Elhage N, Beal J. Laplacian-based consensus on spatial computers. In: AAMAS; 2010. p. 907–914.Cavalcante R, Rogers A, Jennings N. Consensus acceleration in multiagent systems with the Chebyshev semi-iterative method. In: Proc. of AAMAS’11; 2011. p. 165–172.Hu, H., Yu, L., Zhang, W.-A., & Song, H. (2013). Group consensus in multi-agent systems with hybrid protocol. Journal of the Franklin Institute, 350(3), 575-597. doi:10.1016/j.jfranklin.2012.12.020Ji, Z., Lin, H., & Yu, H. (2012). Leaders in multi-agent controllability under consensus algorithm and tree topology. Systems & Control Letters, 61(9), 918-925. doi:10.1016/j.sysconle.2012.06.003Li, Y., & Tan, C. (2019). A survey of the consensus for multi-agent systems. Systems Science & Control Engineering, 7(1), 468-482. doi:10.1080/21642583.2019.1695689Salazar, N., Rodriguez-Aguilar, J. A., & Arcos, J. L. (2010). Robust coordination in large convention spaces. AI Communications, 23(4), 357-372. doi:10.3233/aic-2010-0479Pedroche F, Rebollo M, Carrascosa C, Palomares A. On the convergence of weighted-average consensus. CoRR. 2013;abs/1307.7562

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In this paper, we consider an output consensus problem for a general class of nonlinear multi-agent systems without a prior knowledge of the agents' control directions. Two distributed Nussbaumtype control laws are proposed to solve the leaderless and leader-following adaptive consensus for heterogeneous multiple agents. Examples and simulations are given to verify their effectivenessComment: 10 pages;2 figure