Reply to “Comments on “Consensus and Cooperation in Networked Multi-Agent Systems””

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Information Theory and Cooperative Control in Networked Multi-Agent Systems with Applications to Smart Grid

This dissertation focuses on information theoretic aspects of and cooperative control techniques in networked multi-agent systems (NMAS) with communication constraints. In the first part of the dissertation, information theoretic limitations of tracking problems in networked control systems, especially leader-follower systems with communication constraints, are studied. Necessary conditions on the data rate of each communication link for tracking of the leader-follower systems are provided. By considering the forward and feedback channels as one cascade channel, we also provide a lower bound for the data rate of the cascade channel for the system to track a reference signal such that the tracking error has finite second moment. Finally, the aforementioned results are extended to the case in which the leader system and follower system have different system models. In the second part, we propose an easily scalable hierarchical decision-making and control architecture for smart grid with communication constraints in which distributed customers equipped with renewable distributed generation (RDG) interact and trade energy in the grid. We introduce the key components and their interactions in the proposed control architecture and discuss the design of distributed controllers which deal with short-term and long-term grid stability, power load balancing and energy routing. At microgrid level, under the assumption of user cooperation and inter-user communications, we propose a distributed networked control strategy to solve the demand-side management problem in microgrids. Moreover, by considering communication delays between users and microgrid central controller, we propose a distributed networked control strategy with prediction to solve the demand-side management problem with communication delays. In the third part, we consider the disturbance attenuation and stabilization problem in networked control systems. To be specific, we consider the string stability in a large group of interconnected systems over a communication network. Its potential applications could be found in formation tracking control in groups of robots, as well as uncertainty reduction and disturbance attenuation in smart grid. We propose a leader-following consensus protocol for such interconnected systems and derive the sufficient conditions, in terms of communication topology and control parameters, for string stability. Simulation results and performance in terms of disturbance propagation are also given. In the fourth part, we consider distributed tracking and consensus in networked multi-agent systems with noisy time-varying graphs and incomplete data. In particular, a distributed tracking with consensus algorithm is developed for the space-object tracking with a satellite surveillance network. We also intend to investigate the possible application of such methods in smart grid networks. Later, conditions for achieving distributed consensus are discussed and the rate of convergence is quantified for noisy time-varying graphs with incomplete data. We also provide detailed simulation results and performance comparison of the proposed distributed tracking with consensus algorithm in the case of space-object tracking problem and that of distributed local Kalman filtering with centralized fusion and centralized Kalman filter. The information theoretic limitations developed in the first part of this dissertation provide guildlines for design and analysis of tracking problems in networked control systems. The results reveal the mutual interaction and joint application of information theory and control theory in networked control systems. Second, the proposed architectures and approaches enable scalability in smart grid design and allow resource pooling among distributed energy resources (DER) so that the grid stability and optimality is maintained. The proposed distributed networked control strategy with prediction provides an approach for cooperative control at RDG-equipped customers within a self-contained microgrid with different feedback delays. Our string stability analysis in the third part of this dissertation allows a single networked control system to be extended to a large group of interconnected subsystems while system stability is still maintained. It also reveals the disturbance propagation through the network and the effect of disturbance in one subsystem on other subsystems. The proposed leader-following consensus protocol in the constrained communication among users reveals the effect of communication in stabilization of networked control systems and the interaction between communication and control over a network. Finally, the distributed tracking and consensus in networked multi-agent systems problem shows that information sharing among users improves the quality of local estimates and helps avoid conflicting and inefficient distributed decisions. It also reveals the effect of the graph topologies and incomplete node measurements on the speed of achieving distributed decision and final consensus accuracy

Implementing MAS agreement processes based on consensus networks

[EN] Consensus is a negotiation process where agents need to agree upon certain quantities of interest. The theoretical framework for solving consensus problems in dynamic networks of agents was formally introduced by Olfati-Saber and Murray, and is based on algebraic graph theory, matrix theory and control theory. Consensus problems are usually simulated using mathematical frameworks. However, implementation using multi-agent system platforms is a very difficult task due to problems such as synchronization, distributed finalization, and monitorization among others. The aim of this paper is to propose a protocol for the consensus agreement process in MAS in order to check the correctness of the algorithm and validate the protocol. © Springer International Publishing Switzerland 2013.This work is supported by ww and PROMETEO/2008/051 projects of the Spanish government, CONSOLIDER-INGENIO 2010 under grant CSD2007-00022, TIN2012-36586-C03-01 and PAID-06-11-2084.Palomares Chust, A.; Carrascosa Casamayor, C.; Rebollo Pedruelo, M.; Gómez, Y. (2013). Implementing MAS agreement processes based on consensus networks. Distributed Computing and Artificial Intelligence. 217:553-560. https://doi.org/10.1007/978-3-319-00551-5_66S553560217Argente, E.: et al: An Abstract Architecture for Virtual Organizations: The THOMAS approach. Knowledge and Information Systems 29(2), 379–403 (2011)Búrdalo, L.: et al: TRAMMAS: A tracing model for multiagent systems. Eng. Appl. Artif. Intel. 24(7), 1110–1119 (2011)Fogués, R.L., et al.: Towards Dynamic Agent Interaction Support in Open Multiagent Systems. In: Proc. of the 13th CCIA, vol. 220, pp. 89–98. IOS Press (2010)Luck, M., et al.: Agent technology: Computing as interaction (a roadmap for agent based computing). Eng. Appl. Artif. Intel. (2005)Mailler, R., Lesser, V.: Solving distributed constraint optimization problems using cooperative mediation. In: AAMAS 2004, pp. 438–445 (2004)Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE 95(1), 215–233 (2007)Pujol-Gonzalez, M.: Multi-agent coordination: Dcops and beyond. In: Proc. of IJCAI, pp. 2838–2839 (2011)Such, J.: et al: Magentix2: A privacy-enhancing agent platform. Eng. Appl. Artif. Intel. 26(1), 96–109 (2013)Vinyals, M., et al.: Constructing a unifying theory of dynamic programming dcop algorithms via the generalized distributive law. Autonomous Agents and Multi-Agent Systems 22, 439–464 (2011

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