Previous |  Up |  Next


multi-agent system; discrete-time system; distributed control; consensus; observer
In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.
[1] Cao, Y., Yu, W., Ren, W., Chen, G.: An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Industr. Informatics 9 (2013), 427-4384. DOI 10.1109/tii.2012.2219061
[2] Chen, C. T.: Linear System Theory and Design. Third edition. Oxford University Press, New York 1999.
[3] Franceschetti, M., Poolla, K., Jordan, M., Sastry, S.: Kalman filtering with intermittent observations. IEEE Trans. Automat. Control 49 (2004), 1453-1464. DOI 10.1109/tac.2004.834121 | MR 2086911
[4] Gao, L., Tang, Y., Chen, W., Zhang, H.: Consensus seeking in multi-agent systems with an active leader and communication delays. Kybernetika 47 (2011), 773-789. MR 2850463 | Zbl 1236.93006
[5] Gao, L., Tong, C., Wang, L.: $H_\infty$ dynamic output feedback consensus control for discrete-time multi-agent systems with switching topology. The Arabian J. Sci. Engrg. 39 (2014), 1477-1487. DOI 10.1007/s13369-013-0807-7 | MR 3158186
[6] Gao, Y., Wang, L.: Consensus of multiple dynamic agents with sampled information. IET Control Theory Appl. 4 (2010), 945-956. DOI 10.1049/iet-cta.2008.0565 | MR 2680775
[7] Gao, L., Xu, B., Li, J., Zhang, H.: Distributed reduced-order observer-based approach to consensus problems for linear multi-agent systems. IET Control Theory Appl. 9 (2015), 784-792. DOI 10.1049/iet-cta.2013.1104 | MR 3363254
[8] Gao, L., Zhu, X., Chen, W.: Leader-following consensus problem with an accelerated motion leader. Int. J. Control, Automation, and Systems 10 (2012), 5, 931-939. DOI 10.1007/s12555-012-0509-z
[9] Hengster-Movric, K., Lewis, F.: Cooperative observers and regulators for discrete-time multiagent systems. Int. J. Robust and Nonlinear Control 23 (2013), 1545-1562. DOI 10.1002/rnc.2840 | MR 3086126 | Zbl 1286.93039
[10] Hengster-Movric, K., You, K., Lewis, F. L., Xie, L.: Synchronization of discrete-time multi-agent systems on graphs using Riccati design. Automatica 49 (2013), 414-423. DOI 10.1016/j.automatica.2012.11.038 | MR 3004706 | Zbl 1259.93005
[11] Hong, Y., Hu, J., Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42 (2006), 1177-1182. DOI 10.1016/j.automatica.2006.02.013 | MR 2230987 | Zbl 1117.93300
[12] Hong, Y., Chen, G., Bushnell, L.: Distributed observers design for leader-following control of multi-agent networks. Automatica 44 (2008), 846-850. DOI 10.1016/j.automatica.2007.07.004 | MR 2527101
[13] Hong, Y., Wang, X.: Multi-agent tracking of a high-dimensional active leader with switching topology. J. Systems Science Complex. 22 (2009), 722-731. DOI 10.1007/s11424-009-9197-z | MR 2565265 | Zbl 1300.93014
[14] Hu, J., Geng, J., Zhou, H.: An observer-based consensus tracking control and application to event-triggered tracking. Comm. Nonlinear Sci. Numer. Simul. 20 (2015), 559-570. DOI 10.1016/j.cnsns.2014.06.002 | MR 3251515
[15] Hu, J., Zheng, W.: Adaptive tracking control of leader follower systems with unknown dynamics and partial measurements. Automatica 50 (2014), 1416-1423. DOI 10.1016/j.automatica.2014.02.037 | MR 3198780 | Zbl 1296.93085
[16] Jadbabaie, A., Lin, J., Morse, A. S.: Coordination of groups of mobile agents using nearest neighbor rules. IEEE Trans. Automat. Control 48 (2003), 988-1001. DOI 10.1109/tac.2003.812781 | MR 1986266
[17] Ke, Y., Xie, L.: Network topology and communication data rate for consensusability of discrete-time multi-agent systems. IEEE Trans. Automat. Control 56 (2011), 2262-2275. DOI 10.1109/tac.2011.2164017 | MR 2884153
[18] Li, Z., Duan, Z., Chen, G., Huang, L.: Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Trans. on Circuits and Systems I: Regular Papers 57 (2010), 213-224. DOI 10.1109/tcsi.2009.2023937 | MR 2729823
[19] Li, Z., Liu, X., Lin, P., Ren, W.: Consensus of linear multi-agent systems with reduced-order observer-based protocols. Systems Control Lett. 60 (2011), 510-516. DOI 10.1016/j.sysconle.2011.04.008 | MR 2849495 | Zbl 1222.93013
[20] Liu, Y., Ho, D. W. C., Wang, Z.: A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays. Int. J. Control 85 (2012), 1755-1765. DOI 10.1080/00207179.2012.703331 | MR 2980250 | Zbl 1253.93081
[21] Olfati-Saber, R., Murrary, R. M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Automat. Control. 49 (2004), 1520-1533. DOI 10.1109/tac.2004.834113 | MR 2086916
[22] Ren, W., Cao, Y.: Distributed Coordination of Multi-agent Networks. Springer-Verlag London Limited 2011. DOI 10.1007/978-0-85729-169-1 | Zbl 1225.93003
[23] Su, Y., Huang, J.: Two consensus problems for discrete-time multi-agent systems with switching network topology. Automatica 48 (2012), 1988-1997. DOI 10.1016/j.automatica.2012.03.029 | MR 2956875 | Zbl 1258.93015
[24] Xu, B., Gao, L., Zhang, Y., Xu, X.: Leader-following consensus stability of discrete-time linear multiagent systems with observer-based protocols. Abstract and Applied Analysis 2013 (2013), 1-10. DOI 10.1155/2013/357971 | MR 3111802 | Zbl 1291.93018
[25] Xu, B., Li, J., Gao, L.: Distributed reduced-order observer-based consensus control of discrete-time linear multi-agent system. In: Proc. 3rd IFAC International Conference on Intelligent Control and Automation Science, 2013, pp. 124-129. DOI 10.3182/20130902-3-cn-3020.00040
[26] Xu, X., Chen, S., Huang, W., Gao, L.: Leader-following consensus of discrete-time multi-agent systems with observer-based protocols. Neurocomputing 118 (2013), 334-341. DOI 10.1016/j.neucom.2013.02.023
[27] Xu, X., Chen, S., Gao, L.: Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design. Neurocomputing 156 (2015), 297-305. DOI 10.1016/j.neucom.2014.12.037
[28] Zhai, C.: Sweep coverage of discrete time multi-robot networks with general topologies. Kybernetika 50 (2014), 19-31. MR 3195002 | Zbl 1302.93225
[29] Zhang, H., Lewis, F. L., Das, A.: Optimal design for synchronization of cooperative systems: State feedback, observer and output feedback. IEEE Trans. Automat. Control 56 (2011), 1948-1952. DOI 10.1109/tac.2011.2139510 | MR 2856813
Partner of
EuDML logo