Synchronization of multi-agent systems with heterogeneous controllers. (English) Zbl 1384.34065
Summary: This paper studies synchronization in a multi-agent system, which is defined as a situation where all the agents in a group are required to achieve a common velocity direction. The agents are assumed to be coupled through controller gains that are not necessarily identical or homogeneous, which addresses a practical scenario where the gains may vary nominally due to minor implementation errors or drastically due to major faults or errors. The paper analyzes the effect of heterogeneous gains on the common velocity direction at which the system of agents synchronizes. Conditions under which heterogeneous controller gains result in a synchronized formation are derived and it is shown that the resulting common velocity direction lies in the conic hull of the initial velocity vectors of agents. A detailed analysis of the two agents system shows that there exists a less restrictive condition on heterogeneous gains that results in synchronization. Effect of saturation is also studied for two cases when the controller gains are bounded and when the control efforts are bounded. Both all-to-all and limited communication topologies are considered. Simulations are given to support the theoretical findings.
MSC:
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
| 93D20 | Asymptotic stability in control theory |
Keywords:
cooperative control; consensus; nonlinear systems; stabilization; heterogeneous controller gainsReferences:
| [1] | Ren, W., Beard, R.W.: Distributive Consensus in Multi-Vehicle Cooperative Control: Theory and Applications. Springer-Verlag, London (2008) · Zbl 1144.93002 · doi:10.1007/978-1-84800-015-5 |
| [2] | Mesbahi, M., Egerstedt, M.: Graph Theoretical Methods in Multiagent Networks. Princeton University Press, Princeton (2010) · Zbl 1203.93001 · doi:10.1515/9781400835355 |
| [3] | Rezaee, H., Abdollahi, F.: Motion synchronization in unmanned aircrafts formation control with communication delays. Commun. Nonlinear Sci. Numer. Simulat. 18, 744-756 (2013) · Zbl 1277.93006 · doi:10.1016/j.cnsns.2012.08.015 |
| [4] | Sahoo, S.R., Banavar, R.N.: Attitude synchronization of satellites with internal actuation. Eur. J. Control 20, 152-161 (2014) · Zbl 1293.93057 · doi:10.1016/j.ejcon.2014.03.003 |
| [5] | Yu, W., Chen, G., Lü, J.: On pinning synchronization of complex dynamical networks. Automatica 45(2), 429-435 (2009) · Zbl 1158.93308 · doi:10.1016/j.automatica.2008.07.016 |
| [6] | Zhang, H., Lewis, F.L., Das, A.: Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Trans. Autom. Control 56(8), 1948-1952 (2011) · Zbl 1368.93265 · doi:10.1109/TAC.2011.2139510 |
| [7] | Li, Z.K., Duan, Z.S., Lewis, F.L.: Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties. Automatica 50(3), 883-889 (2014) · Zbl 1298.93026 · doi:10.1016/j.automatica.2013.12.008 |
| [8] | Su, S., Lin, Z., Garcia, A.: Distributed synchronization control of multiagent systems with unknown nonlinearities. IEEE Trans. Cybern. 46(1), 325-338 (2016) · doi:10.1109/TCYB.2015.2402192 |
| [9] | Strogatz, S.H.: From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Phys. D: Nonlinear Phenom. 143(1-4), 1-20 (2000) · Zbl 0983.34022 · doi:10.1016/S0167-2789(00)00094-4 |
| [10] | Sepulchre, R., Paley, D.A., Leonard, N.E.: Stabilization of planar collective motion: all-to-all communication. IEEE Trans. Autom. Control 52(5), 811-824 (2007) · Zbl 1366.93527 · doi:10.1109/TAC.2007.898077 |
| [11] | Mei, J., Ren, W., Chen, J.: Consensus of second-order heterogeneous multi-agent systems under a directed graph. In: Proc. American Control Conference, Portland, Oregon, USA, 802-807 (2014) |
| [12] | Sinha, A., Ghose, D.: Generalization of linear cyclic pursuit with application to rendezvous of multiple autonomous agents. IEEE Trans. Autom. Control 51(11), 1819-1824 (2006) · Zbl 1366.93063 · doi:10.1109/TAC.2006.883033 |
| [13] | Seyboth, G.S., Wu, J., Qin, J., Yu, C., Allgöwer, F.: Collective circular motion of unicycle type vehicles with nonidentical constant velocities. IEEE Trans. Control Netw. Syst. 1(2), 167-176 (2014) · Zbl 1370.93183 · doi:10.1109/TCNS.2014.2316995 |
| [14] | Chen, Z., Zhang, H.-T.: A remark on collective circular motion of heterogeneous multi-agents. Automatica 49(5), 1236-1241 (2013) · Zbl 1337.93006 · doi:10.1016/j.automatica.2013.01.017 |
| [15] | Kim, H., Shim, H., Seo, J.H.: Output consensus of heterogeneous uncertain linear multi-agent systems. IEEE Trans. Autom. Control 56(1), 200-206 (2011) · Zbl 1368.93378 · doi:10.1109/TAC.2010.2088710 |
| [16] | Choi, Y.H., Yoo, S.J.: Adaptive synchronized tracking of heterogeneous spherical robots using distributed hierarchical sliding surfaces under a directed graph. Nonlinear Dyn. 85, 913-922 (2016) · Zbl 1355.93128 · doi:10.1007/s11071-016-2732-2 |
| [17] | Zhai, S., Li, Q.: Practical bipartite synchronization via pinning control on a network of nonlinear agents with antagonistic interactions. Nonlinear Dyn. 87, 207-218 (2016). doi:10.1007/s11071-016-3036-2 · Zbl 1371.34076 · doi:10.1007/s11071-016-3036-2 |
| [18] | Xi, J., He, M., Liu, H., Zheng, J.: Admissible output consensualization control for singular multi-agent systems with time delays. J. Franklin Inst. 353, 4074-4090 (2016) · Zbl 1347.93032 · doi:10.1016/j.jfranklin.2016.07.021 |
| [19] | Wu, Y., Su, H., Shi, P., Shu, Z., Wu, Z.-G.: Consensus of multiagent systems using aperiodic sampled-data control. IEEE Trans. Cybern. 46(9), 2132-2143 (2016) · doi:10.1109/TCYB.2015.2466115 |
| [20] | Wu, Y., Lu, R., Shi, P., Su, H., Wu, Z.-G.: Adaptive output synchronization of heterogeneous network with an uncertain leader. Automatica 76, 183-192 (2017) · Zbl 1352.93013 · doi:10.1016/j.automatica.2016.10.020 |
| [21] | Wu, Y., Meng, X., Xie, L., Lu, R., Su, H., Wu, Z.-G.: An input-based triggering approach to leader-following problems. Automatica 75, 221-228 (2017) · Zbl 1351.93091 · doi:10.1016/j.automatica.2016.09.040 |
| [22] | Wu, Y., Su, H., Shi, P., Lu, R., Wu, Z.-G.: Output synchronization of non-identical linear multi-agent systems. IEEE Trans. Cybern. 47(1), 130-141 (2017) · doi:10.1109/TCYB.2015.2508604 |
| [23] | Jain, A, Ghose, D.: Collective behavior with heterogeneous controllers. In: American Control Conference, Washington, DC, USA, 4636-4641 (2013) · Zbl 1337.93006 |
| [24] | Dorfler, F., Bullo, F.: Synchronization in complex networks of phase oscillators: a survey. Automatica 50, 1539-1564 (2014) · Zbl 1296.93005 · doi:10.1016/j.automatica.2014.04.012 |
| [25] | Dong, J.-G., Xue, X.: Finite-time synchronization of Kuramoto-type oscillators. Nonlinear Anal Real world Appl 26, 133-149 (2015) · Zbl 1356.34041 · doi:10.1016/j.nonrwa.2015.05.006 |
| [26] | Hong, H., Strogatz, S.H.: Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. Phys. Rev. Lett. 106(5), 1-4 (2011) · doi:10.1103/PhysRevLett.106.054102 |
| [27] | Jadbabaie, A., Motee, N., Barahona, M.: On the stability of the Kuramoto model of coupled nonlinear oscillators. In: American Control Conference, Boston, MA, 4296-4301 (2004) · Zbl 1366.93527 |
| [28] | Chopra, N., Spong, M.W.: On exponential synchronization of Kuramoto oscillators. IEEE Trans. Autom. Control 54(2), 353-357 (2009) · Zbl 1367.34076 · doi:10.1109/TAC.2008.2007884 |
| [29] | Tousi, M., Moghaddam, R.K., Pariz, N.: Synchronization in oscillator networks with time delay and limited non-homogeneous coupling strength. Nonlinear Dyn. 82, 1-8 (2015) · Zbl 1348.34093 · doi:10.1007/s11071-015-2133-y |
| [30] | Cai, N., Cao, J.-W., Ma, H.-Y., Wang, C.-X.: Swarm stability analysis of nonlinear dynamical multi-agent systems via relative Lyapunov function. Arab. J. Sci. Eng. 39(3), 2427-2434 (2014) · Zbl 1390.93657 |
| [31] | Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Upper Saddle River, NJ (2000) · Zbl 0973.93010 |
| [32] | Strang, G.: Linear Algebra and its Applications, 4th edn. Cengage Learning, Boston (2007) · Zbl 1329.15004 |
| [33] | Bai, H., Arcak, M., Wen, J.: Cooperative Control Design: A Systematic, Passivity-based Approach. Springer-Verlag, New York (2011) · Zbl 1228.93001 · doi:10.1007/978-1-4614-0014-1 |
| [34] | Sepulchre, R., Paley, D.A., Leonard, N.E.: Stabilization of planar collective motion with limited communication. IEEE Trans. Autom. Control 53(3), 706-719 (2008) · Zbl 1367.93145 · doi:10.1109/TAC.2008.919857 |
| [35] | Barvinok, A.: A Course in Convexity, Graduate Studies in Mathematics. American Mathematical Soc, Providence, Rhode Island (2002) · Zbl 1014.52001 |
| [36] | Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, NJ (1972) · Zbl 0224.49003 |
| [37] | Nef, W.: Linear Algebra, Euro. Mathematics Series. Dover Publications Inc, Mineola (1988) · Zbl 0694.15001 |
| [38] | Marshall, J.A., Broucke, M.E., Francis, B.A.: Formations of vehicles in cyclic pursuit. IEEE Trans. Autom. Control 49(11), 1963-1974 (2004) · Zbl 1366.91027 · doi:10.1109/TAC.2004.837589 |
| [39] | Lee, T.-C., Song, K.-T., Lee, C.-H., Teng, C.-C.: Tracking control of unicycle-modeled mobile robots using a saturation feedback controller. IEEE Trans. Control Sys. Tech. 9(2), 305-318 (2001) · doi:10.1109/87.911382 |
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