Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

References

• Aghababa, M. P. (2012). Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. Communications in Nonlinear Science and Numerical Simulation, 17(6), 2670–2681. doi: 10.1016/j.cnsns.2011.10.028
   Web of Science ®Google Scholar
• Aubin, J. P., & Cellina, A. (1984). Differential inclusions. Berlin: Springer-Verlag.
   Google Scholar
• Bagley, R. L., & Torvik, P. J. (1986). On the fractional calculus model of viscoelastic behavior. Journal of Rheology, 30(1), 133–155. doi: 10.1122/1.549887
   Web of Science ®Google Scholar
• Baleanu, D., Gëvenc, Z. B., & Machado, J. T. (Eds.). (2010). New trends in nanotechnology and fractional calculus applications (p. C397). New York, NY: Springer.
   Google Scholar
• Cao, Y., Li, Y., Ren, W., & Chen, Y. (2010). Distributed coordination of networked fractional-order systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40(2), 362–370. doi: 10.1109/TSMCB.2009.2024647
   PubMed Web of Science ®Google Scholar
• Cao, Y., & Ren, W. (2010). Distributed formation control for fractional-order systems: Dynamic interaction and absolute/relative damping. Systems & Control Letters, 59(3–4), 233–240. doi: 10.1016/j.sysconle.2010.01.008
   Web of Science ®Google Scholar
• Cao, Y., & Ren, W. (2012). Distributed coordinated tracking with reduced interaction via a variable structure approach. IEEE Transactions on Automatic Control, 57(1), 33–48. doi: 10.1109/TAC.2011.2146830
   Web of Science ®Google Scholar
• Cao, Y., Stuart, D., Ren, W., & Meng, Z. (2011). Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments. IEEE Transactions on Control Systems Technology, 19(4), 929–938. doi: 10.1109/TCST.2010.2053542
   Web of Science ®Google Scholar
• Chen, J., Guan, Z. H., Yang, C., Li, T., He, D. X., & Zhang, X. H. (2016). Distributed containment control of fractional-order uncertain multi-agent systems. Journal of the Franklin Institute, 353(7), 1672–1688. doi: 10.1016/j.jfranklin.2016.02.002
   Web of Science ®Google Scholar
• Chen, F., Yu, H., & Xia, X. (2016). Output consensus of multi-agent systems with delayed and sampled-data. IET Control Theory & Applications, 11(5), 632–639. doi: 10.1049/iet-cta.2016.1162
   Web of Science ®Google Scholar
• Clarke, F. H., Ledyaev, Y. S., Stem, R. J., & Wolenski, R. R. (1998). Nonsmooth analysis and control theory. New York, NY: Springer.
   Google Scholar
• Cohen, I., Golding, I., Ron, I. G., & Ben-Jacob, E. (2001). Biofluiddynamics of lubricating bacteria. Mathematical Methods in the Applied Sciences, 24(17–18), 1429–1468. doi: 10.1002/mma.190
   Web of Science ®Google Scholar
• Duarte-Mermoud, M., Aguila-Camacho, N., Gallegos, J., & Castro-Linares, R. (2015). Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Communications in Nonlinear Science and Numerical Simulation, 22(1), 650–659. doi: 10.1016/j.cnsns.2014.10.008
   Web of Science ®Google Scholar
• Fax, J. A., & Murray, R. M. (2004). Information flow and cooperative control of vehicle formations. IEEE transactions on automatic control, 49(9), 1465–1476. doi: 10.1109/TAC.2004.834433
   Web of Science ®Google Scholar
• Filippov, A. F. (1988). Differential equations with discontinuous right-hand sides. Boston, MA: Kluwer.
   Google Scholar
• Gazi, V., & Passino, K. M. (2003). Stability analysis of swarms. IEEE Transactions on Automatic Control, 48(4), 692–697. doi: 10.1109/TAC.2003.809765
   Web of Science ®Google Scholar
• Gong, P. (2016). Distributed consensus of non-linear fractional-order multi-agent systems with directed topologies. IET Control Theory & Applications, 10(18), 2515–2525. doi: 10.1049/iet-cta.2016.0606
   Web of Science ®Google Scholar
• Gong, P. (2017). Distributed tracking of heterogeneous nonlinear fractional-order multi-agent systems with an unknown leader. Journal of the Franklin Institute, 354(5), 2226–2244. doi: 10.1016/j.jfranklin.2017.01.001
   Web of Science ®Google Scholar
• Gong, P., & Lan, W. (2018). Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies. Automatica, 92, 92–99. doi: 10.1016/j.automatica.2018.02.010
   Web of Science ®Google Scholar
• Gong, P., & Lan, W. (2019). Adaptive robust tracking control for multiple unknown fractional-order nonlinear systems. IEEE Transactions on Cybernetics, 49(4), 1365–1376. doi: 10.1109/TCYB.2018.2801345
   PubMed Web of Science ®Google Scholar
• Ji, M., Ferrari-Trecate, G., Egerstedt, M., & Buffa, A. (2008). Containment control in mobile networks. IEEE Transactions on Automatic Control, 53(8), 1972–1975. doi: 10.1109/TAC.2008.930098
   Web of Science ®Google Scholar
• Li, Z., Duan, Z., & Lewis, F. L. (2014). Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties. Automatica, 50(3), 883–889. doi: 10.1016/j.automatica.2013.12.008
   Web of Science ®Google Scholar
• Liang, S., Wu, R., & Chen, L. (2017). BIBO stability of fractional-order controlled nonlinear systems. International Journal of Systems Science, 48(7), 1507–1514. doi: 10.1080/00207721.2016.1269219
   Web of Science ®Google Scholar
• Liu, H., Cheng, L., Tan, M., & Hou, Z. G. (2018). Exponential finite-time consensus of fractional-order multiagent systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems. doi:10.1109/TSMC.2018.2816060.
   Web of Science ®Google Scholar
• Liu, H., Pan, Y., Li, S., & Chen, Y. (2017). Adaptive fuzzy backstepping control of fractional-order nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(8), 2209–2217. doi: 10.1109/TSMC.2016.2640950
   Web of Science ®Google Scholar
• Ma, T., Li, T., & Cui, B. (2018). Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control. International Journal of Systems Science, 49(1), 1–14. doi: 10.1080/00207721.2017.1397805
   Web of Science ®Google Scholar
• Magin, R. L. (2006). Fractional calculus in bioengineering (pp. 269–355). Redding: Begell House.
   Google Scholar
• Mei, J., Ren, W., & Chen, J. (2016). Distributed consensus of second-order multi-agent systems with heterogeneous unknown inertias and control gains under a directed graph. IEEE Transactions on Automatic Control, 61(8), 2019–2034. doi: 10.1109/TAC.2015.2480336
   Web of Science ®Google Scholar
• Mei, J., Ren, W., Li, B., & Ma, G. (2015). Distributed containment control for multiple unknown second-order nonlinear systems with application to networked Lagrangian systems. IEEE Transactions on Neural Networks and Learning Systems, 26(9), 1885–1899. doi: 10.1109/TNNLS.2014.2359955
   PubMed Web of Science ®Google Scholar
• Meng, Z., Lin, Z., & Ren, W. (2013). Robust cooperative tracking for multiple non-identical second-order nonlinear systems. Automatica, 49(8), 2363–2372. doi: 10.1016/j.automatica.2013.04.040
   Web of Science ®Google Scholar
• Meng, Z., Ren, W., & You, Z. (2010). Distributed finite-time attitude containment control for multiple rigid bodies. Automatica, 46(12), 2092–2099. doi: 10.1016/j.automatica.2010.09.005
   Web of Science ®Google Scholar
• Olfati-Saber, R. (2006). Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on Automatic Control, 51(3), 401–420. doi: 10.1109/TAC.2005.864190
   Web of Science ®Google Scholar
• Olfati-Saber, R., & Murray, R. (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
• Petras, I. (2011). Fractional-order nonlinear systems: Modeling, analysis and simulation. London: Springer Science & Business Media.
   Google Scholar
• Podlubny, I. (1999). Fractional differential equations. New York, NY: Academic Press.
   Google Scholar
• Samko, S. G., Kilbas, A. A., & Marichev, O. I. (1987). Fractional integrals and derivatives and some of their applications. Minsk: Science and Technica.
   Google Scholar
• Shen, J., & Cao, J. (2012). Necessary and sufficient conditions for consensus of delayed fractional-order systems. Asian Journal of Control, 14(6), 1690–1697. doi: 10.1002/asjc.492
   Web of Science ®Google Scholar
• Wang, P., & Jia, Y. (2014). Distributed containment control of second-order multi-agent systems with inherent non-linear dynamics. IET Control Theory & Applications, 8(4), 277–287. doi: 10.1049/iet-cta.2013.0686
   Web of Science ®Google Scholar
• Wang, Y., Song, Y., Krstic, M., & Wen, C. (2016). Fault-tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single-way directed communication interactions and actuation failures. Automatica, 63, 374–383. doi: 10.1016/j.automatica.2015.10.049
   Web of Science ®Google Scholar
• Wang, D., Wang, D., & Wang, W. (2019). Necessary and sufficient conditions for containment control of multi-agent systems with time delay. Automatica, 103, 418–423. doi: 10.1016/j.automatica.2018.12.029
   Web of Science ®Google Scholar
• Wang, F., & Yang, Y. (2017). Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control. International Journal of Systems Science, 48(3), 571–577. doi: 10.1080/00207721.2016.1193258
   Web of Science ®Google Scholar
• Wang, D., Zhang, N., Wang, J., & Wang, W. (2017). Cooperative containment control of multiagent systems based on follower observers with time delay. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(1), 13–23.
   Web of Science ®Google Scholar
• Wen, G., Duan, Z., Chen, G., & Yu, W. (2014). Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(2), 499–511. doi: 10.1109/TCSI.2013.2268091
   Web of Science ®Google Scholar
• Wen, G., Zhao, Y., Duan, Z., Yu, W., & Chen, G. (2016). Containment of higher-order multi-leader multi-agent systems: A dynamic output approach. IEEE Transactions on Automatic Control, 61(4), 1135–1140. doi: 10.1109/TAC.2015.2465071
   Web of Science ®Google Scholar
• Yoo, S. J. (2013). Distributed adaptive containment control of uncertain nonlinear multi-agent systems in strict-feedback form. Automatica, 49(7), 2145–2153. doi: 10.1016/j.automatica.2013.03.007
   Web of Science ®Google Scholar
• Young, K., Utkin, V., & Ozguner, U. (1999). A control engineer's guide to sliding mode control. IEEE Transactions on Control Systems Technology, 7(3), 328–342. doi: 10.1109/87.761053
   Web of Science ®Google Scholar
• Yu, Z., Jiang, H., Hu, C., & Yu, J. (2015). Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control. International Journal of Control, 88(9), 1746–1756. doi: 10.1080/00207179.2015.1015807
   Web of Science ®Google Scholar
• Yu, Z., Jiang, H., Hu, C., & Yu, J. (2017). Necessary and sufficient conditions for consensus of fractional-order multiagent systems via sampled-data control. IEEE Transactions on Cybernetics, 47(8), 1892–1901. doi: 10.1109/TCYB.2017.2681718
   PubMed Web of Science ®Google Scholar
• Yu, W., Li, Y., Wen, G., Yu, X., & Cao, J. (2017). Observer design for tracking consensus in second-order multi-agent systems: Fractional order less than two. IEEE Transactions on Automatic Control, 62(2), 894–900. doi: 10.1109/TAC.2016.2560145
   Web of Science ®Google Scholar
• Yu, H., Shen, Y., & Xia, X. (2013). Adaptive finite-time consensus in multi-agent networks. Systems & Control Letters, 62(10), 880–889. doi: 10.1016/j.sysconle.2013.06.011
   Web of Science ®Google Scholar
• Yu, H., & Xia, X. (2012). Adaptive consensus of multi-agents in networks with jointly connected topologies. Automatica, 48(8), 1783–1790. doi: 10.1016/j.automatica.2012.05.068
   Web of Science ®Google Scholar
• Yu, W., Zheng, W., Lü, J., & Chen, G. (2013). Designing distributed control gains for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica, 49(7), 2107–2115. doi: 10.1016/j.automatica.2013.03.005
   Web of Science ®Google Scholar
• Zhang, H., & Frank, L. (2012). Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica, 48(7), 1432–1439. doi: 10.1016/j.automatica.2012.05.008
   Web of Science ®Google Scholar