Abstract: The consensus problem for general linear multi-agent systems (MASs) under directed topology is investigated. First, a novel consensus protocol based on proportional-integral-derivative (PID) control is proposed. Second, the consensus problem is converted into an asymptotic stability problem through transformations. Third, through a state projection method the consensus condition is proved and the explicit expression of the consensus function is given. Then, a Lyapunov function is constructed and the gain matrices of the protocol are given based on the linear matrix inequality. Finally, two experiments are conducted to explain the advantages of the method. Simulation results show the effectiveness of the proposed algorithm.

一种新型的有向拓扑条件下普通线性多智能体系统的一致性协议

[1]Andreasson, M., Sandberg, H., Dimarogonas, D.V., et al., 2012. Distributed integral action: stability analysis and frequency control of power systems. 51st Proc. IEEE Conf. on Decision and Control, p.2077-2083.

[2]Cai, H., Huang, J., 2014. The leader-following attitude control of multiple rigid spacecraft systems. Automatica, 50(4):1109-1115.

[3]Chen, K.R., Wang, J.W., Zhang, Y., et al., 2015. Consensus of second-order nonlinear multi-agent systems under state-controlled switching topology. Nonl. Dynam., 81(4):1871-1878.

[4]Cheng, L., Wang, Y., Ren, W., et al., 2015. Containment control of multiagent systems with dynamic leaders based on a PIⁿ type approach. IEEE Trans. Cybern., 46(12):3004-3017.

[5]Daniel, B., Mario, D., 2014. Distributed PID control for consensus of homogeneous and heterogeneous networks. IEEE Trans. Contr. Netw. Syst., 22(2):154-163.

[6]Fax, J.A., Murray, R.M., 2004. Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Contr., 49(9):1465-1476.

[7]Ji, L., Liao, X., 2013. Consensus problems of first-order dynamic multi-agent systems with multiple time delays. Chin. Phys. B, 4(22):040203.

[8]Li, Z.K., Ren, W., Liu, X.D., et al., 2013. Distributed consensus of linear multi-agent systems with adaptive dynamic protocols. Automatica, 49(7):1986-1995.

[9]Lin, Z.J., Hong, T., Liu, H., 2015. Consensus based on learning game theory with a UAV rendezvous application. Chin. J. Aeronaut., 28(1):191-199.

[10]Liu, Y.F., Geng, Z.Y., 2015. Finite-time formation control for linear multi-agent systems: a motion planning approach. Syst. Contr. Lett., 85(9):54-60.

[11]Lombana, D.A.B., di Bernardo, M., 2015. Distributed PID control for consensus of homogeneous and heterogeneous networks. IEEE Trans. Contr. Netw. Syst., 2(2):154-163.

[12]Mu, X.W., Yang, Z., Liu, K., et al., 2015. Containment control of general multi-agent systems with directed random switching topology. J. Franklin Inst., 352(10):4067-4080.

[13]Olfati-Saber, R., 2006. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Contr., 51(3):401-420.

[14]Olfati-Saber, R., Fax, J.A., Murray, R.M., 2007. Consensus and cooperation in networked multi-agent systems. Proc. IEEE, 95(1):215-233.

[15]Ren, W., Beard, R.W., 2005. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Contr., 50(5):655-661.

[16]Ren, W., Beard, R., Atkins, E., 2007. Information consensus in multivehicle cooperative control. IEEE Contr. Syst., 27(2):71-82.

[17]Ruggero, C., Edoardo, D., Sandro, Z., 2011. A PI controller based on asymmetric gossip communications for clocks synchronization in wireless sensors networks. 50th IEEE Conf. on Decision and Control and European Control, p.7512-7517.

[18]Sam, S., Khan, U.A., 2015. Leader-follower consensus in mobile sensor networks. IEEE Signal Process. Lett., 22(12):2249-2253.

[19]Su, H.S., Zhang, W., 2008. Second-order consensus of multiple agents with coupling delay. 7th World Congress on Intelligent Control and Automation, p.7181-7186.

[20]Sun, G., 2012. Second-order consensus of multiple agents with bounded control inputs and preserved network connectivity. Commun. Theor. Phys., 57(4):624-628.

[21]Wang, Y., Cheng, L., Hou, Z., et al., 2015. Coordinated transportation of a group of unmanned ground vehicles. 34th Chinese Control Conf., p.7027-7032.

[22]Yang, C.X., Hong, W.X., Huang, L.Y., et al., 2014. Fast consensus tracking of multiagent systems with diverse communication delays and input delays. Math. Probl. Eng., 2014:1-10.

[23]Yang, X.G., Xi, J.X., Wu, J.Y., et al., 2015. Consensus transformation for multi-agent systems with topology variances and time-varying delays. Neurocomputing, 168(5):1059-1064.

[24]Zhang, H., Yang, R., Yan, H., et al., 2015. H_infty consensus of event-based multi-agent systems with switching topology. Inform. Sci., 370(24):623-635.

[25]Zhang, H.T., Cheng, Z.M., Chen, G.R., 2015. Model predictive flocking control for second-order multi-agent systems with input constraints. IEEE Trans. Circ. Syst. I, 62(6):1599-1606.