Geodesic
Distributed event-triggered algorithm for optimal resource allocation of multi-agent systems
Kybernetika, Tome 53 (2017) no. 5, pp. 747-764 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This paper is concerned with solving the distributed resource allocation optimization problem by multi-agent systems over undirected graphs. The optimization objective function is a sum of local cost functions associated to individual agents, and the optimization variable satisfies a global network resource constraint. The local cost function and the network resource are the private data for each agent, which are not shared with others. A novel gradient-based continuous-time algorithm is proposed to solve the distributed optimization problem. We take an event-triggered communication strategy and an event-triggered gradient measurement strategy into account in the algorithm. With strongly convex cost functions and locally Lipschitz gradients, we show that the agents can find the optimal solution by the proposed algorithm with exponential convergence rate, based on the construction of a suitable Lyapunov function. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed scheme.
This paper is concerned with solving the distributed resource allocation optimization problem by multi-agent systems over undirected graphs. The optimization objective function is a sum of local cost functions associated to individual agents, and the optimization variable satisfies a global network resource constraint. The local cost function and the network resource are the private data for each agent, which are not shared with others. A novel gradient-based continuous-time algorithm is proposed to solve the distributed optimization problem. We take an event-triggered communication strategy and an event-triggered gradient measurement strategy into account in the algorithm. With strongly convex cost functions and locally Lipschitz gradients, we show that the agents can find the optimal solution by the proposed algorithm with exponential convergence rate, based on the construction of a suitable Lyapunov function. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed scheme.
DOI : 10.14736/kyb-2017-5-0747
Classification : 37N40, 90C26, 93A14
Keywords: distributed optimization; event-triggered strategy; multi-agent systems; resource allocation 
@article{10_14736_kyb_2017_5_0747,
     author = {Yu, Weiyong and Deng, Zhenhua and Zhou, Hongbing and Zeng, Xianlin},
     title = {Distributed event-triggered algorithm for optimal resource allocation of multi-agent systems},
     journal = {Kybernetika},
     pages = {747--764},
     year = {2017},
     volume = {53},
     number = {5},
     doi = {10.14736/kyb-2017-5-0747},
     mrnumber = {3750101},
     zbl = {06861622},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0747/}
}
TY  - JOUR
AU  - Yu, Weiyong
AU  - Deng, Zhenhua
AU  - Zhou, Hongbing
AU  - Zeng, Xianlin
TI  - Distributed event-triggered algorithm for optimal resource allocation of multi-agent systems
JO  - Kybernetika
PY  - 2017
SP  - 747
EP  - 764
VL  - 53
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0747/
DO  - 10.14736/kyb-2017-5-0747
LA  - en
ID  - 10_14736_kyb_2017_5_0747
ER  - 
%0 Journal Article
%A Yu, Weiyong
%A Deng, Zhenhua
%A Zhou, Hongbing
%A Zeng, Xianlin
%T Distributed event-triggered algorithm for optimal resource allocation of multi-agent systems
%J Kybernetika
%D 2017
%P 747-764
%V 53
%N 5
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-5-0747/
%R 10.14736/kyb-2017-5-0747
%G en
%F 10_14736_kyb_2017_5_0747
Yu, Weiyong; Deng, Zhenhua; Zhou, Hongbing; Zeng, Xianlin. Distributed event-triggered algorithm for optimal resource allocation of multi-agent systems. Kybernetika, Tome 53 (2017) no. 5, pp. 747-764. doi: 10.14736/kyb-2017-5-0747

[1] Beck, A., Nedić, A., Ozdaglar, A., Teboulle, M.: An $O(1/k)$ gradient method for network resource allocation problems. IEEE Trans. Control Network Systems 1 (2014), 64-74. | DOI | MR

[2] Chen, W., Ren, W.: Event-triggered zero-gradient-sum distributed consensus optimization over directed networks. Automatica 65 (2016), 90-97. | DOI | MR | Zbl

[3] Deng, Z., Wang, X., Hong, Y.: Distributed optimization design with triggers for disturbed continuous-time multi-agent systems. IET Control Theory Appl. 11 (2017), 282-290. | DOI | MR

[4] Ghadimi, E., Shames, I., Johansson, M.: Multi-step gradient methods for networked optimization. IEEE Trans. Signal Processing 61 (2013), 5417-5429. | DOI

[5] Godsil, C., Royle, G.: Algebraic Graph Theory. Springer-Verlag, New York 2001. | DOI | MR | Zbl

[6] Gao, Y., Wang, L.: Sampled-data based consensus of continuous-time multi-agent systems with time-varying topology. IEEE Trans. Automat. Control 56 (2011), 1226-1231. | DOI | MR

[7] Ho, Y. C., Servi, L., Suri, R.: A class of center-free resource allocation algorithms. Large Scale Systems 1 (1980), 51-62. | MR

[8] Khalil, H. K.: Nonlinear Systems. Third edition. Prentice Hall, New Jersey 2002.

[9] Kia, S. S., Cortés, J., Martínez, S.: Distributed convex optimization via continuous-time coordinate alorithms with discrete-time communication. Automatica 55 (2015), 254-264. | DOI | MR

[10] Lehmann, D., Lunze, J.: Event-based control with communication delays and packet losses. Int. J. Control 85 (2012), 563-577. | DOI | MR

[11] Lakshmanan, H., Farias, D. P.: Decentralized resource allocation in dynamic networks of agents. SIAM J. Optim. 19 (2008), 911-940. | DOI | MR

[12] Hu, J., Chen, G., Li, H.: Distributed event-triggered tracking control of leader-follower multi-agent systems with communication delays. Kybernetika 47 (2011), 630-643. | MR | Zbl

[13] Nedić, A., Ozdaglar, A., Parrilo, P. A.: Constrained consensus and optimization in multi-agent networks. IEEE Trans. Automat. Control 55 (2010), 922-938. | DOI | MR

[14] Lou, Y., Shi, G., Johansson, K., Hong, Y.: Approximate projected consensus for convex interesection computation: convergence analysis and critical error angle. IEEE Trans. Automat. Control 59 (2014), 1722-1736. | DOI | MR

[15] Rockafellar, R. T.: Convex Analysis. Princeton University Press, Princeton 1972. | MR | Zbl

[16] Ruszczynski, A. P.: Nonlinear Optimization. Princeton University Press, Princeton 2006. | MR

[17] Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Automat. Control 52 (2007), 1680-1685. | DOI | MR

[18] Wang, X., Yi, P., Hong, Y.: Dynamic optimization for multi-agent systems with external disturbances. Control Theory Technol. 12 (2014), 132-138. | DOI | MR

[19] Wang, X., Deng, Z., Ma, S., Du, X.: Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems. Kybernetika 1 (2017), 179-194. | MR

[20] Xiao, L., Boyd, S.: Optimal scaling of a gradient method for distributed resource allocation. J. Optim. Theory and Appl. 129 (2006), 469-488. | DOI | MR

[21] Zhang, Y., Hong, Y.: Distributed event-triggered tracking control of multi-agent systems with active leader. In: Proc. 10th IEEE World Congress on Intelligent Control and Automation 2012, pp. 1453-1458. | DOI

[22] Zhang, Y., Lou, Y., Hong, Y., Xie, L.: Distributed projection-based algorithms for source localization in wireless sensor networks. IEEE Trans. Wireless Communications 14 (2015), 3131-3142. | DOI | MR

[23] Yi, P., Hong, Y., Liu, F.: Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems. Automatica 74 (2016), 259-269. | DOI | MR

Cité par Sources :