Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems

Wang, Xue-Fang ; Deng, Zhenhua ; Ma, Song ; Du, Xian

Kybernetika, Tome 53 (2017) no. 1, pp. 179-194

Abstract (VO)

In this paper, a distributed optimal consensus problem is investigated to achieve the optimization of the sum of local cost function for a group of agents in the Euler-Lagrangian (EL) system form. We consider that the local cost function of each agent is only known by itself and cannot be shared with others, which brings challenges in this distributed optimization problem. A novel gradient-based distributed continuous-time algorithm with the parameters of EL system is proposed, which takes the distributed event-triggered control mechanism into account. A sufficient condition is given to show that the performance of the global convergence to the optimal point can be guaranteed under the proposed method. Moreover, the Zeno behavior of triggering time can be excluded. Finally, to show the effectiveness of the presented algorithm, an example is given along with simulation results.

Détail

DOI : 10.14736/kyb-2017-1-0179

Classification : 34H05, 34K35, 49K35, 65K10, 90C25
Keywords: optimal consensus; multi-agent system; Euler–Lagrangian system; event-triggered control

Bibliographie

[1] Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Trans. Automat. Control 54 (2009), 48-61. | DOI | MR

[2] Shi, G., Johansson, K. H., Hong, Y.: Reaching an optimal consensus: dynamical systems that compute intersections of convex sets. IEEE Trans. Automat. Control 58 (2013), 610-622. | DOI | MR

[3] Bose, S., Low, S. H., Teeraratkul, T., Hassibi, B.: Equivalent relaxations of optimal power flow. IEEE Trans. Automat. Control 60 (2015), 729-742. | DOI | MR

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

[5] Liu, Q., Wang, J.: A second-order multi-agent network for bound-constrained distributed optimization. IEEE Trans. Automat. Control 60 (2015), 3310-3315. | DOI | MR

[6] Yi, P., Hong, Y., Liu, F.: Distributed gradient algorithm for constrained optimization with application to load sharing in power systems. Systems Control Lett. 83 (2015), 45-52. | DOI | MR | Zbl

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

[8] Wang, X., Hong, Y., Ji, H.: Distributed optimization for a class of nonlinear multiagent systems With disturbance rejection. IEEE Trans. Cybernet. 46 (2016), 1655-1666. | DOI

[9] Zhang, Y., Deng, Z., Hong, Y.: Distributed optimal coordination for multiple heterogenous Euler-Lagrangian systems. Automatica 79 (2017), 207-213. | DOI | MR

[10] Yi, P., Hong, Y.: Stochastic sub-gradient algoirthm for distributed optimization with random sleep scheme. Control Theory Technol. 13 (2015), 333-347. | DOI | MR

[11] 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

[12] Deng, Z., Hong, Y.: Distributed event-triggered optimization for multi-agent systems with disturbance rejection. In: 12th IEEE Int. Conf. Control and Autom., Kathmandu 2016, pp 13-18. | DOI

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

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

[15] Deng, Z., Wang, X., Hong, Y.: Distributed optimization design with triggers for disturbed continuous-time multi-agent systems. IET Control Theory Appl. 11 (2017), 2, 282-290. | DOI

[16] Kia, S. S., Cortes, J., Martinez, S.: Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication. Automatica 55 (2015), 254-264. | DOI | MR

[17] Cai, H., Huang, J.: Leader-following consensus of multiple uncertain Euler-Lagrange systems under switching network topology. Int. J. Gene. Sys., 43 (2014), 294-304. | DOI | MR | Zbl

[18] Chung, S. J., Slotine, J. J. E.: Cooperative robot control and concurrent synchronization of lagrangian systems. IEEE Trans. Robotics 25 (2009), 686-700. | DOI

[19] Dixon, W. E.: Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach. Birkhäuser, Boston 2003. | Zbl

[20] Kim, C. Y., Song, D. Z., Xu, Y. L., Yi, J. G., Wu, X. Y.: Cooperative search of multiple unknown transient radio sources using multiple paired mobile robots. IEEE Trans. Rob. 30 (2014), 1161-1173. | DOI

[21] Deng, Z., Hong, Y.: Multi-agent optimization design for autonomous lagrangian systems. Unmanned Systems 4 (2016), 5-13. | DOI

[22] Spong, M., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. John Wiley and Sons, Hoboken 2006. | DOI

[23] Meng, Z., Yang, T., Shi, G., Dimarogonas, D. V., Hong, Y., Johansson, K. H.: Set target aggregation of multiple mechanical systems. In: IEEE 53rd Ann. Conf. Decision and Control (CDC), Los Angeles 2014, pp. 6830-6835. | DOI

[24] Rockafellar, R.: Convex Analysis. Princeton University Press, Princeton 1970. | DOI | MR | Zbl

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

[26] Zhu, W., Jiang, Z. P.: Event-based leader-following consensus of multi-agent systems with input time delay. IEEE Trans. Automat. Control 60 (2015), 1362-1367. | DOI | MR