Abstract
This paper extends the event-triggered communication in consensus problems of multi-agent systems to the case of distributed continuous-time convex optimization over weight-balanced digraphs. We address problems whose global objective functions are a sum of local functions associated to each agent. We utilize the event-triggered communication technique to reduce the communication load and avoid Zeno behavior meanwhile. Based on Lyapunov approach, we prove that the Zero-Gradient-Sum (ZGS) algorithm combined with the event-triggered communication makes all agents’ states converge to the optimal solution of the global objective function exponentially fast.
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References
Rabbat M, Nowak R (2004) Distributed optimization in sensor networks. In: International symposium on information processing in sensor networks. IEEE, pp 20–27
Tsianos KI, Lawlor S, Rabbat M (2012) Consensus-based distributed optimization: practical issues and applications in large scale machine learning. Commun Control Comput:1543–1550
Ram S Sundhar, Veeravalli Venugopal V, Nedic Angelia (2010) Distributed and recursive parameter estimation in parametrized linear state-space models. IEEE Trans Autom Control 55(2):488–492
Nedic Angelia, Ozdaglar Asuman (2009) Distributed subgradient methods for multi-agent optimization. IEEE Trans Autom Control 54(1):48–61
Lobel Ilan, Ozdaglar Asuman (2011) Distributed subgradient methods for convex optimization over random networks. IEEE Trans Autom Control 56(6):1291–1306
Yanhui Yin, Zhongxin Liu, Zengqiang Chen (2015) Distributed subgradient algorithm for multi-agent optimization with directed communication topology. IFAC Papersonline 48(28):863–868
Nedic Angelia, Ozdaglar Asuman, Parrilo Pablo A (2010) Constrained consensus and optimization in multi-agent networks. IEEE Trans Autom Control 55(4):922–938
Duchi John C, Agarwal Alekh, Wainwright Martin J (2012) Dual averaging for distributed optimization: convergence analysis and network scaling. IEEE Trans Autom Control 57(3):592–606
Lee Soomin, Nedic Angelia (2013) Distributed random projection algorithm for convex optimization. IEEE J Sel Top Signal Process 7(2):221–229
Jie Lu, Tang Choon Yik (2012) Zero-gradient-sum algorithms for distributed convex optimization: the continuous-time case. IEEE Trans Autom Control 57(9):2348–2354
Gharesifard Bahman, Cortes Jorge (2014) Distributed continuous-time convex optimization on weight-balanced digraphs. IEEE Trans Autom Control 59(3):781–786
Lin P, Ren W, Song Y, Farrell JA (2014) Distributed optimization with the consideration of adaptivity and finite-time convergence. In: American Control Conference – ACC, pp 3177–3182
Yuheng Z, Yiguang H (2015) Distributed optimization design for high-order multi-agent systems. In: Proceedings of the 34th Chinese control conference, pp 7251–7256
Dimarogonas Dimos V, Frazzoli Emilio, Johansson Karl Henrik (2012) Distributed event-triggered control for multi-agent systems. IEEE Trans Autom Control 57(5):1291–1297
Liu Zhongxin, Chen Zengqiang, Yuan Zhuzhi (2012) Event-triggered average-consensus of multi-agent systems with weighted and direct topology. J Syst Sci Complex 25(5):845–855
Nowzari Cameron, Cortes Jorge (2016) Distributed event-triggered coordination for average consensus on weight-balanced digraphs. Automatica 68:237–244
Yi X, Lu W, Chen T Distributed event-triggered consensus for multi-agent systems with directed topologies. http://arxiv.org/abs/1407.3075
Zhong Minyi, Cassandras Christos G (2010) Asynchronous distributed optimization with event-driven communication. IEEE Trans Autom Control 55(12):2735–2750
Kia Solmaz S, Cortes Jorge, Martinez Sonia (2015) Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication. Automatica 55:254–264
Chen Weisheng, Ren Wei (2016) Event-triggered zero-gradient-sum distributed consensus optimization over directed networks. Automatica 65:90–97
Liu J, Chen W (2016) Distributed convex optimization with event-triggered communication in networked systems. Int J Syst Sci:1–12
Nesterov Yurii (2004) Introductory lectures on convex optimization: a basic course. Kluwer, Norwell, MA
Boyd Stephen, Vandenberghe Lieven (2004) Convex optimization. Cambridge University Press, New York, NY
Hardy Godfrey H, Littlewood John E, PĂłlya George (1952) Inequalities. Cambridge University Press, Cambridge, UK
Acknowledgments
This research is supported by the National Natural Science Foundation of China (Grant No. 61573200, 61273138), and the Tianjin Natural Science Foundation of China (Grant No. 14JCYBJC18700, 14JCZDJC39300).
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Pan, X., Liu, Z., Chen, Z. (2016). Distributed Optimization Over Weight-Balanced Digraphs with Event-Triggered Communication. In: Jia, Y., Du, J., Zhang, W., Li, H. (eds) Proceedings of 2016 Chinese Intelligent Systems Conference. CISC 2016. Lecture Notes in Electrical Engineering, vol 405. Springer, Singapore. https://doi.org/10.1007/978-981-10-2335-4_45
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DOI: https://doi.org/10.1007/978-981-10-2335-4_45
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