On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs

References

• Adibzadeh, A., Suratgar, A. A., Menhaj, M. B., & Zamani, M. (2018). Constrained optimal consensus in multi-agent systems with single- and double-integrator dynamics. International Journal of Control, 1–13. doi:10.1080/00207179.2018.1481299
   Web of Science ®Google Scholar
• Andrieu, V., Praly, L., & Astolfi, A. (2008). Homogeneous approximation, recursive observer design, and output feedback. SIAM Journal on Control and Optimization, 47(4), 1814–1850. doi: 10.1137/060675861
   Web of Science ®Google Scholar
• Bacciotti, A., & Rosier, L. (2006). Liapunov functions and stability in control theory. London: Springer Science & Business Media.
   Google Scholar
• Bhat, S. P., & Bernstein, D. S. (2000). Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization, 38(3), 751–766. doi: 10.1137/S0363012997321358
   Web of Science ®Google Scholar
• Bhat, S. P., & Bernstein, D. S. (2005). Geometric homogeneity with applications to finite-time stability. Mathematics of Control, Signals and Systems, 17(2), 101–127. doi: 10.1007/s00498-005-0151-x
   Web of Science ®Google Scholar
• Brunner, D., & Uhl, A. (1999). Optimal multipliers for linear congruential pseudo-random number generators with prime moduli: Parallel computation and properties. BIT Numerical Mathematics, 39(2), 193–209. doi: 10.1023/A:1022333627834
   Web of Science ®Google Scholar
• Cai, K. (2012, December). Averaging over general random networks. IEEE Transactions on Automatic Control, 57(12), 3186–3191. doi: 10.1109/TAC.2012.2199181
   Web of Science ®Google Scholar
• Cai, K., & Ishii, H. (2014, April). Average consensus on arbitrary strongly connected digraphs with time-varying topologies. IEEE Transactions on Automatic Control, 59(4), 1066–1071. doi: 10.1109/TAC.2014.2305952
   Web of Science ®Google Scholar
• Cao, Y., & Ren, W. (2014). Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics. Automatica, 50(10), 2648–2656. doi: 10.1016/j.automatica.2014.08.028
   Web of Science ®Google Scholar
• Cao, Y., Ren, W., & Meng, Z. (2010). Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking. Systems & Control Letters, 59, 522–529. doi: 10.1016/j.sysconle.2010.06.002
   Web of Science ®Google Scholar
• Center, M. K., & Kawski, M. (1995). Geometric homogeneity and stabilization. In In preprints of ifac nonlinear control systems design symposium (pp. 164–169).
   Google Scholar
• Chen, X., Hao, F., & Shao, M. (2015). Event-triggered consensus of multi-agent systems under jointly connected topology. IMA Journal of Mathematical Control and Information, 32(3), 537–556. doi: 10.1093/imamci/dnu009
   Web of Science ®Google Scholar
• Chen, G., Lewis, F. L., & Xie, L. (2011). Finite-time distributed consensus via binary control protocols. Automatica, 47, 1962–1968. doi: 10.1016/j.automatica.2011.05.013
   Web of Science ®Google Scholar
• Chen, Y., Lu, J., Yu, X., & Hill, D. (2013, thirdquarter). Multi-agent systems with dynamical topologies: Consensus and applications. IEEE Circuits and Systems Magazine, 13(3), 21–34. doi: 10.1109/MCAS.2013.2271443
   Web of Science ®Google Scholar
• Cortés, J. (2006). Finite-time convergent gradient flows with applications to network consensus. Automatica, 42(11), 1993–2000. doi: 10.1016/j.automatica.2006.06.015
   Web of Science ®Google Scholar
• Dai, J., & Guo, G. (2017). Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and markovian switching topologies. Jornal of the Franklin Institue, 354, 6098–6118. doi: 10.1016/j.jfranklin.2017.07.011
   Web of Science ®Google Scholar
• Defoort, M., Polyakov, A., Demesure, G., Djemai, M., & Veluvolu, K. (2015). Leader-follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics. IET Control Theory & Applications, 9(14), 2165–2170. doi: 10.1049/iet-cta.2014.1301
   Web of Science ®Google Scholar
• Eriksson, K., Estep, D., & Johnson, C. (2013). Applied mathematics: Body and soul: Volume 1: Derivatives and geometry in IR3. Berlin: Springer Science & Business Media.
   Google Scholar
• Franceschelli, M., Giua, A., & Pisano, A. (2017). Finite-time consensus on the median value with robustness properties. IEEE Transactions on Automatic Control, 62(4), 1652–1667. doi: 10.1109/TAC.2016.2590602
   Web of Science ®Google Scholar
• Franceschelli, M., Giua, A., Pisano, A., & Usai, E. (2013). Finite-time consensus for switching network topologies with disturbances. Nonlinear Analysis: Hybrid Systems, 10, 83–93.
   Web of Science ®Google Scholar
• Franceschelli, M., Pisano, A., Giua, A., & Usai, E. (2015). Finite-time consensus with disturbance rejection by discontinuous local interactions in directed graphs. IEEE Transactions on Automatic Control, 60(4), 1133–1138. doi: 10.1109/TAC.2014.2351431
   Web of Science ®Google Scholar
• Godsil, C., & Royle, G. (2001). Algebraic graph theory (Vol. 8). New York: Springer-Verlag.
   Google Scholar
• Gómez-Gutiérrez, D., Ruiz-León, J., Celikovsky, S., & Sánchez-Torres, J. D. (2018). A finite-time consensus algorithm with simple structure for fixed networks. Computación y Sistemas, 22(2), 547–556.
   Web of Science ®Google Scholar
• Guan, Z. H., Sun, F. L., Wang, Y. W., & Li, T. (2012). Finite-time consensus for leader-following second-order multi-agent networks. IEEE Transactions on Circuits and Systems, 59, 2646–2654. doi: 10.1109/TCSI.2012.2190676
   Google Scholar
• Hermes, H. (1991). Homogeneous coordinates and continuous asymptotically stabilizing feedback controls. Differential Equations Stability and Control, 109, 249–260.
   Google Scholar
• Hong, H., Yu, W., Wen, G., & Yu, X. (2017, July). Distributed robust fixed-time consensus for nonlinear and disturbed multiagent systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(7), 1464–1473. doi: 10.1109/TSMC.2016.2623634
   Web of Science ®Google Scholar
• Hui, Q., Haddad, W. M., & Bhat, S. P. (2008). Finite-time semistability and consensus for nonlinear dynamical networks. IEEE Transactions on Automatic Control, 53(8), 1887–1900. doi: 10.1109/TAC.2008.929392
   Web of Science ®Google Scholar
• Hui, Q., Haddad, W. M., & Bhat, S. P. (2010). Finite-time semistability, filippov systems, and consensus protocols for nonlinear dynamical networks with switching topologies. Nonlinear Analysis: Hybrid Systems, 4(3), 557–573.
   Web of Science ®Google Scholar
• Jiang, F., & Wang, L. (2009). Finite-time information consensus for multi-agent systems with fixed and switching topologies. Physica D: Nonlinear Phenomena, 238(16), 1550–1560. doi: 10.1016/j.physd.2009.04.011
   Web of Science ®Google Scholar
• Khalil, H. K., & Grizzle, J. (2002). Nonlinear systems (Vol. 3). Upper Saddle River: Prentice Hall.
   Google Scholar
• Khoo, S., Xie, L., & Man, Z. (2009). Consensus tracking algorithm for multirobot systems. IEEE/ASME Transactions on Mechatronic Systems, 14, 219–228. doi: 10.1109/TMECH.2009.2014057
   Web of Science ®Google Scholar
• Levant, A. (2005). Homogeneity approach to high-order sliding mode design. Automatica, 41(5), 823–830. doi: 10.1016/j.automatica.2004.11.029
   Web of Science ®Google Scholar
• Lewis, F. L., Zhang, H., Hengster-Movric, K., & Das, A. (2014). Algebraic graph theory and cooperative control consensus. In Cooperative control of multi-agent systems: Optimal and adaptive design approaches (pp. 23–71). London: Springer.
   Google Scholar
• Li, S., Du, H., & Lin, X. (2011). Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica, 47, 1706–1712. doi: 10.1016/j.automatica.2011.02.045
   Web of Science ®Google Scholar
• Li, Z., Duan, Z., Chen, G., & Huag, L. (2010). Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Transactions on Circuits and Systems, 57, 213–224. doi: 10.1109/TCSI.2009.2023937
   Google Scholar
• Li, C., & Qu, Z. (2014). Distributed finite-time consensus of nonlinear systems under switching topologies. Automatica, 50(6), 1626–1631. doi: 10.1016/j.automatica.2014.04.002
   Web of Science ®Google Scholar
• Li, S., & Wang, X. (2013). Finite-time consensus and collision avoidance control algorithms for multiple AUVs. Automatica, 49(11), 3359–3367. doi: 10.1016/j.automatica.2013.08.003
   Web of Science ®Google Scholar
• Liberzon, D. (2003). Switching in systems and control. Boston: Birkhäuser.
   Google Scholar
• Lin, P., Qin, K., Zhao, H., & Sun, M. (2012). A new approach to average consensus problems with multiple time-delays and jointly-connected topologies. Journal of the Franklin Institute, 349(1), 293–304. doi: 10.1016/j.jfranklin.2011.11.002
   Web of Science ®Google Scholar
• Liu, X., Lam, J., Yu, W., & Chen, G. (2016). Finite-time consensus of multiagent systems with a switching protocol. IEEE Transactions on Neural Networks and Learning Systems, 27(4), 853–862. doi: 10.1109/TNNLS.2015.2425933
   PubMed Web of Science ®Google Scholar
• Liu, B., Lu, W., & Chen, T. (2015). Consensus in continuous-time multiagent systems under discontinuous nonlinear protocols. IEEE Transactions on Neural Networks and Learning Systems, 26(2), 290–301. doi: 10.1109/TNNLS.2014.2314699
   PubMed Web of Science ®Google Scholar
• Liu, Y., Zhao, Y., Ren, W., & Chen, G. (2018). Appointed-time consensus: Accurate and practical designs. Automatica, 89, 425–429. doi: 10.1016/j.automatica.2017.12.030
   Web of Science ®Google Scholar
• Meng, D., & Jia, Y. (2016). Robust consensus algorithms for multiscale coordination control of multivehicle systems with disturbances. IEEE Transactions on Industrial Electronics, 63(2), 1107–1119. doi: 10.1109/TIE.2015.2478740
   Web of Science ®Google Scholar
• Meng, D., & Zuo, Z. (2016, July 01). Signed-average consensus for networks of agents: a nonlinear fixed-time convergence protocol. Nonlinear Dynamics, 85(1), 155–165. doi: 10.1007/s11071-016-2675-7
   Web of Science ®Google Scholar
• Mondal, S., & Su, R. (2016, May). Finite-time tracking control of high order nonlinear multi agent systems with actuator saturation. In 2016 14th ifac symposium on control in transportation systems (pp. 165–170).
   Google Scholar
• Mu, X., Xiao, X., Liu, K., & Zhang, J. (2014). Leader-following consensus of multi-agent systems with jointly connected topology using distributed adaptive protocols. Journal of the Franklin Institute, 351, 5399–5410. doi: 10.1016/j.jfranklin.2014.09.018
   Web of Science ®Google Scholar
• Ning, B., Jin, J., & Zheng, J. (2017). Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology. International Journal of Systems Science, 48(10), 2023–2032. doi: 10.1080/00207721.2017.1308579
   Web of Science ®Google Scholar
• Ning, B., Jin, J., Zheng, J., & Man, Z. (2018). Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics. International Journal of Control, 91(6), 1259–1270. doi: 10.1080/00207179.2017.1313453
   Web of Science ®Google Scholar
• Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007, January). Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1), 215–233. doi: 10.1109/JPROC.2006.887293
   Web of Science ®Google Scholar
• Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533. doi: 10.1109/TAC.2004.834113
   Web of Science ®Google Scholar
• Orlov, Y. (2004). Finite time stability and robust control synthesis of uncertain switched systems. SIAM Journal on Control and Optimization, 43(4), 1253–1271. doi:10.1137/S0363012903425593
   Web of Science ®Google Scholar
• Parsegov, S., Polyakov, A., & Shcherbakov, P. (2013). Fixed-time consensus algorithm for multi-agent systems with integrator dynamics. In IFAC workshop on distributed estimation and control in networked systems (pp. 110–115).
   Google Scholar
• Perruquetti, W., Floquet, T., & Moulay, E. (2008). Finite-time observers : Application to secure communication. IEEE Transactions on Automatic Control, 53(1), 356–360. doi: 10.1109/TAC.2007.914264
   Web of Science ®Google Scholar
• Polyakov, A., Efimov, D., & Perruquetti, W. (2016). Robust stabilization of MIMO systems in finite/fixed time. International Journal of Robust and Nonlinear Control, 26(1), 69–90. doi: 10.1002/rnc.3297
   Web of Science ®Google Scholar
• Qin, J., & Yu, C. (2014). Exponential consensus of general linear multi-agent systems under directed dynamic topology. Automatica, 50, 2327–2333. doi: 10.1016/j.automatica.2014.07.009
   Web of Science ®Google Scholar
• Ren, W., Beard, R. W., & Atkins, E. M. (2005). A survey of consensus problems in multi-agent coordination. In American control conference, 2005. Proceedings of the 2005 (pp. 1859–1864), Portland, USA.
   Google Scholar
• Rosier, L. (1992). Homogeneous lyapunov function for homogeneous continuous vector field. Systems & Control Letters, 19(6), 467–473. doi: 10.1016/0167-6911(92)90078-7
   Web of Science ®Google Scholar
• Sayyaadi, H., & Doostmohammadian, M. R. (2011). Finite-time consensus in directed switching network topologies and time-delayed communications. Scientia Iranica, 18(1), 75–85. doi: 10.1016/j.scient.2011.03.010
   Web of Science ®Google Scholar
• Seo, J. H., Shim, H., & Back, J. (2009). Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach. Automatica, 45, 2659–2664. doi: 10.1016/j.automatica.2009.07.022
   Web of Science ®Google Scholar
• Shang, Y. (2012). Finite-time consensus for multi-agent systems with fixed topologies. International Journal of Systems Science, 43(3), 499–506. doi: 10.1080/00207721.2010.517857
   Web of Science ®Google Scholar
• Shang, Y., & Ye, Y. (2017). Leader-follower fixed-time group consensus control of multiagent systems under directed topology. Complexity, 90, 1420–1427.
   Google Scholar
• Sharghi, A., Baradarannia, M., & Hashemzadeh, F. (2016). Leader-follower fixed-time consensus for multi-agent systems with heterogeneous non-linear inherent dynamics. In 2016 3rd international conference on Soft computing & machine intelligence (ISCMI) (pp. 224–228), Dubai, United Arab Emirates.
   Google Scholar
• Tian, B., Lu, H., Zuo, Z., & Yang, W. (2018). Fixed-time leader-follower output feedback consensus for second-order multiagent systems. IEEE Transactions on Cybernetics, 1–6. doi: 10.1109/TCYB.2018.2794759
   Web of Science ®Google Scholar
• Tian, B., Zuo, Z., & Wang, H. (2017). Leader-follower fixed-time consensus of multi-agent systems with high-order integrator dynamics. International Journal of Control, 90(7), 1420–1427. doi: 10.1080/00207179.2016.1207101
   Web of Science ®Google Scholar
• Tu, Z., Yu, H., & Xia, X. (2017). Decentralized finite-time adaptive consensus of multiagent systems with fixed and switching network topologies. Neurocomputing, 219, 59–67. doi: 10.1016/j.neucom.2016.09.013
   Web of Science ®Google Scholar
• Wang, X., Li, J., Xing, J., Wang, R., Xie, L., & Zhang, X. (2018). A novel finite-time average consensus protocol for multi-agent systems with switching topology. Transactions of the Institute of Measurement and Control, 40(2), 606–614. doi: 10.1177/0142331216663617
   Web of Science ®Google Scholar
• Wang, L., & Xiao, F. (2010, April). Finite-time consensus problems for networks of dynamic agents. IEEE Transactions on Automatic Control, 55(4), 950–955. doi: 10.1109/TAC.2010.2041610
   Web of Science ®Google Scholar
• Xiao, F., Wang, L., & Chen, J. (2009). General distributed protocols for finite-time consensus of multi-agent systems. In Decision and control, 2009 held jointly with the 2009 28th Chinese control conference. Proceedings of the 48th ieee conference on CDC/CCC 2009 (pp. 4741–4746), Shanghai, China.
   Google Scholar
• Xu, Y., Han, T., Cai, K., Lin, Z., Yan, G., & Fu, M. (2017). A distributed algorithm for resource allocation over dynamic digraphs. IEEE Transactions on Signal Processing, 65(10), 2600–2612. doi: 10.1109/TSP.2017.2669896
   Web of Science ®Google Scholar
• Xu, Y., Yan, G., Cai, K., & Lin, Z. (2017). Fast centralized integer resource allocation algorithm and its distributed extension over digraphs. Neurocomputing, 270, 91–100. doi: 10.1016/j.neucom.2017.03.089
   Web of Science ®Google Scholar
• Yong, C., Guangming, X., & Huiyang, L. (2012). Reaching consensus at a preset time: Single-integrator dynamics case. In 31st Chinese control conference (CCC) (pp. 6220–6225), Hefei, China.
   Google Scholar
• You, K., Li, Z., & Xie, L. (2013). Consensus condition for linear multi-agent systems over randomly switching topologies. Automatica, 49, 3125–3132. doi: 10.1016/j.automatica.2013.07.024
   Web of Science ®Google Scholar
• Zhao, Y., Duan, Z., Wen, G., & Zhang, Y. (2013). Distributed finite-time tracking control for multi-agent systems: an observer-based approach. Systems & Control Letters, 62, 22–28. doi: 10.1016/j.sysconle.2012.10.012
   Web of Science ®Google Scholar
• Zhao, L. W., & Hua, C. C. (2014). Finite-time consensus tracking of second-order multi-agent systems via nonsingular tsm. Nonlinear Dynamics, 75, 311–318. doi: 10.1007/s11071-013-1067-5
   Web of Science ®Google Scholar
• Zhu, Y.-K., Guan, X.-P. & Luo, X.-Y. (2013). Finite-time consensus for multi-agent systems via nonlinear control protocols. International Journal of Automation and Computing, 10(5), 455–462. doi: 10.1007/s11633-013-0742-9
   Google Scholar
• Zuo, Z., Tian, B., Defoort, M., & Ding, Z. (2018, February). Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics. IEEE Transactions on Automatic Control, 63(2), 563–570. doi: 10.1109/TAC.2017.2729502
   Web of Science ®Google Scholar
• Zuo, Z., & Tie, L. (2014). A new class of finite-time nonlinear consensus protocols for multi-agent systems. International Journal of Control, 87(2), 363–370. doi: 10.1080/00207179.2013.834484
   Web of Science ®Google Scholar
• Zuo, Z., Yang, W., Tie, L., & Meng, D. (2014, June). Fixed-time consensus for multi-agent systems under directed and switching interaction topology. In American control conference (ACC), 2014 (pp. 5133–5138), Portland, USA.
   Google Scholar