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Event-triggered zero-gradient-sum distributed consensus optimization over directed networks. (English) Zbl 1328.93167

Summary: This paper focuses on the event-triggered zero-gradient-sum algorithms for a distributed convex optimization problem over directed networks. The communication process is driven by trigger conditions monitored by nodes. The proposed trigger conditions are decentralized and just depend on each node’s own state. In the continuous-time case, we propose an algorithm based on a sample-based monitoring scheme. In the discrete-time case, we propose a new event-triggered zero-gradient-sum algorithm which is suitable for more general network models. It is proved that two proposed event-triggered algorithms are exponentially convergent if the design parameters are chosen properly and the network topology is strongly connected and weight-balanced. Finally, we illustrate the advantages of the proposed algorithms by numerical simulation.

MSC:

93C65 Discrete event control/observation systems
93A14 Decentralized systems
93B40 Computational methods in systems theory (MSC2010)
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[1] Dimarogonas, D. V.; Frazzoli, E.; Johansson, K. H., Distributed event-triggered conrol for multi-agent systems, IEEE Transactions on Automatic Control, 57, 5, 1291-1297, (2012) · Zbl 1369.93019
[2] Duchi, J. C.; Agarwal, A.; Wainwright, M. J., Dual averaging for distributed optimization: convergence analysis and network scaling, IEEE Transactions on Automatic Control, 57, 3, 592-606, (2012) · Zbl 1369.90156
[3] Fan, Y.; Feng, G.; Wang, Y.; Song, C., Distributed event-triggered control of multi-agent systems with combinational measurements, Automatica, 49, 2, 671-675, (2013) · Zbl 1258.93004
[4] Gharesifard, B.; Cortés, J., Distributed continuous-time convex optimization on weight-balanced digraphs, IEEE Transactions on Automatic Control, 59, 3, 781-786, (2014) · Zbl 1360.90257
[5] Jakovetic, D.; Xavier, J.; Moura, J. M.F., Cooperative convex optimization in networked systems: augmented Lagrangian algorithms with directed gossip communication, IEEE Transactions on Signal Processing, 59, 8, 3889-3902, (2011) · Zbl 1392.94018
[6] Lee, S.; Nedić, A., Distributed random projection algorithm for convex optimization, IEEE Journal of Selected Topics in Signal Processing, 7, 2, 221-229, (2013)
[7] Li, N.; Marden, J. R., Designing games for distributed optimization, IEEE Journal of Selected Topics in Signal Processing, 7, 2, 230-242, (2013)
[8] Lobel, I.; Ozdaglar, A., Distributed subgradient methods for convex optimization over random networks, IEEE Transactions on Automatic Control, 56, 6, 1291-1306, (2011) · Zbl 1368.90125
[9] Lu, J.; Tang, C. Y., Zero-gradient-sum algorithms for distributed convex optimization: the continuous-time case, IEEE Transactions on Automatic Control, 56, 12, 2348-2354, (2012) · Zbl 1369.90122
[10] Lu, J.; Tang, C. Y.; Regier, P. R.; Bow, T. D., Gossip algorithms for convex consensus optimization over networks, IEEE Transactions on Automatic Control, 56, 12, 2917-2923, (2011) · Zbl 1368.90023
[11] Matei, I.; Baras, J. S., Performance evaluation of the consensus-based distributed subgradient method under random communication topologies, IEEE Journal of Selected Topics in Signal Processing, 5, 4, 754-771, (2011)
[12] Matei, I., & Baras, J. (2013). Distributed algorithms for optimization problems with equality constraints. TR-2013-5. http://hdl.handle.net/1903/13672.
[13] Mazo, M.; Tabuada, P., Decentralized event-triggered control over wireless sensor/actuator networks, IEEE Transactions on Automatic Control, 56, 10, 2456-2461, (2011) · Zbl 1368.93358
[14] Meng, X.; Chen, T., Event based agreement protocols for multi-agent networks, Automatica, 49, 7, 2125-2132, (2013) · Zbl 1364.93476
[15] Nedić, A., Asynchronous broadcast-based convex optimization over a network, IEEE Transactions on Automatic Control, 56, 6, 1337-1351, (2011) · Zbl 1368.90126
[16] Nedić, A.; Ozdaglar, A., Distributed subgradient methods for multi-agent optimization, IEEE Transactions on Automatic Control, 54, 1, 48-61, (2009) · Zbl 1367.90086
[17] Nedić, A.; Ozdaglar, A.; Parrilo, P. A., Constrained consensus and optimization in multi-agent networks, IEEE Transactions on Automatic Control, 55, 4, 922-938, (2010) · Zbl 1368.90143
[18] Rabbat, M. G., & Nowak, R. D. (2004). Distriuted optimization in sensor networks. In Proceeding of int. symp. inform. precessing sens. netw., Berkeley, CA (pp. 20-27).
[19] Ram, S. S., Nedić, A., & Veeravalli, V. V. (2009). Asynchronous gossip algorithms for stochastic optimization. In Proc. 48th IEEE CDC (pp. 3581-3586).
[20] Ram, S. S.; Nedić, A.; Veeravalli, V. V., Distributed stochastic subgradient projection algorithms for convex optimization, Journal of Optimization Theory and Applications, 147, 3, 516-545, (2010) · Zbl 1254.90171
[21] Seyboth, G. S.; Dimarognas, D. V.; Johansson, K. H., Event-triggered broadcasting for multi-agent average consensus, Automatica, 49, 1, 245-252, (2013) · Zbl 1257.93066
[22] Srivastava, K.; Nedić, A., Distributed asynchronous constrained stochastic optimization, IEEE Journal of Selected Topics in Signal Processing, 5, 4, 772-790, (2011)
[23] Wan, P., & Lemmon, M. D. (2009). Event-triggered distributed optimization in sensor networks. In Proceeding of IPSN’09, San Francisco, USA (pp. 49-60).
[24] Wang, X.; Lemmon, M. D., Event-triggered in distributed networked control system, IEEE Transactions on Automatic Control, 56, 3, 586-601, (2011) · Zbl 1368.93211
[25] Yuan, D.; Xu, S.; Zhao, H.; Rong, L., Distributed primal-dual stochastic subgradient algorithms for multi-agent optimization under inequality constraints, International Journal of Robust and Nonlinear Control, 23, 16, 1846-1868, (2013) · Zbl 1285.93105
[26] Zhu, W.; Jiang, Z.; Feng, G., Event-based consensus of multi-agent systems with general linear models, Automatica, 50, 2, 552-558, (2014) · Zbl 1364.93489
[27] Zhu, M.; Martinez, S., On distributed convex optimization under inequality and equality constraints, IEEE Transactions on Automatic Control, 57, 1, 151-164, (2012) · Zbl 1369.90129
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