Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics

References

• Bacciotti, A., & Ceragioli, F. (1999). Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions. ESAIM: Control, Optimisation and Calculus of Variations, 4, 361–376.
   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.
   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.
   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.
   Web of Science ®Google Scholar
• Chen, G., Lewis, F. L., & Xie, L. (2011). Finite-time distributed consensus via binary control protocols. Automatica, 47(9), 1962–1968.
   Web of Science ®Google Scholar
• Cortés, J. (2006). Finite-time convergent gradient flows with applications to network consensus. Automatica, 42(11), 1993–2000.
   Web of Science ®Google Scholar
• Cortés, J. (2008). Discontinuous dynamical systems. IEEE Control Systems, 28(3), 36–73.
   Web of Science ®Google Scholar
• Defoort, M., Demesure, G., Zuo, Z., Polyakov, A., & Djemai, M. (2016). Fixed-time stabilisation and consensus of non-holonomic systems. IET Control Theory & Applications, 10(18), 2497–2505.
   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.
   Web of Science ®Google Scholar
• Filippov, A. F., & Arscott, F. M. (1988). Differential equations with discontinuous righthand sides. Springer.
   Google Scholar
• Fu, J., & Wang, J. (2016). Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties. Systems & Control Letters, 93, 1–12.
   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 I: Regular Papers, 59(11), 2646–2654.
   Web of Science ®Google Scholar
• Guo, M., & Dimarogonas, D. V. (2013). Nonlinear consensus via continuous, sampled, and aperiodic updates. International Journal of Control, 86(4), 567–578.
   Web of Science ®Google Scholar
• Hardy, G. H., Littlewood, J. E., & Polya, G. (1988). Inequalities. Cambridge University Press.
   Google Scholar
• Hartman, P. (1982). Ordinary differential equations. Birkhauser.
   Google Scholar
• Horn, R. A., & Johnson, C. R. (2012). Matrix analysis (2nd ed.). Cambridge University Press.
   Google Scholar
• Khoo, S., Xie, L., & Man, Z. (2009). Robust finite-time consensus tracking algorithm for multirobot systems. IEEE/ASME Transactions on Mechatronics, 14(2), 219–228.
   Web of Science ®Google Scholar
• Kim, Y., & Mesbahi, M. (2006). On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian. IEEE Transactions on Automatic Control, 51(1),116–120.
   Web of Science ®Google Scholar
• Li, H., Liao, X., Chen, G., Hill, D.J., Dong, Z., & Huang, T. (2015b). Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks. Neural Networks, 66, 1–10.
   PubMed Web of Science ®Google Scholar
• Li, H., Liao, X., Huang, T., & Zhu, W. (2015c). Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE Transactions on Automatic Control, 60(7), 1998–2003.
   Web of Science ®Google Scholar
• Li, H., Liao, X., Huang, T., Zhu, W., & Liu, Y. (2015a). Second-order global consensus in multiagent networks with random directional link failure. IEEE Transactions on Neural Networks and Learning Systems, 26(3), 565–575.
   PubMed Web of Science ®Google Scholar
• Liu, H., Cheng, L., Tan, M., Hou, Z., & Wang, Y. (2015). Distributed exponential finite-time coordination of multi-agent systems: containment control and consensus. International Journal of Control, 88(2), 237–247.
   Web of Science ®Google Scholar
• Liu, X., Cao, J., Yu, W., & Song, Q. (2016). Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Transactions on Cybernetics, 46(10), 2360–2371.
   PubMed 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.
   PubMed Web of Science ®Google Scholar
• Liu, X., Park, J.H., Jiang, N., & Cao, J. (2014). Nonsmooth finite-time stabilization of neural networks with discontinuous activations. Neural Networks, 52, 25–32.
   PubMed Web of Science ®Google Scholar
• Liu, X., Yu, W., Cao, J., & Alsaadi, F. (2015). Finite-time synchronisation control of complex networks via non-smooth analysis. IET Control Theory & Applications, 9(8), 1245–1253.
   Web of Science ®Google Scholar
• Meng, D., Jia, Y., & Du, J. (2016). Finite-time consensus for multiagent systems with cooperative and antagonistic interactions. IEEE Transactions on Neural Networks and Learning Systems, 27(4), 762–770.
   PubMed Web of Science ®Google Scholar
• Ni, J., Liu, L., Liu, C., Hu, X., & Li, S. (2017). Fast Fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Transactions on Circuits and Systems II: Express Briefs, 64(2), 151–155.
   Web of Science ®Google Scholar
• Olfati-Saber, R., Fax, J.A., & Murray, R.M. (2007). Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1), 215–233.
   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.
   Web of Science ®Google Scholar
• Parsegov, S., Polyakov, A., & Shcherbakov, P. (2013). Fixed-time consensus algorithm for multi-agent systems with integrator dynamics. In Proceeding of the 4th IFAC workshop on distributed estimation and control in networked systems (pp. 110–115).
   Google Scholar
• Polyakov, A. (2012). Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, 57(8), 2106–2110.
   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.
   Web of Science ®Google Scholar
• Shang, Y. (2014). Average consensus in multi-agent systems with uncertain topologies and multiple time-varying delays. Linear Algebra and its Applications, 459,411–429.
   Web of Science ®Google Scholar
• Shang, Y. (2016). Finite-time weighted average consensus and generalized consensus over a subset. IEEE Access, 4, 2615–2620.
   Web of Science ®Google Scholar
• Shevitz, D., & Paden, B. (1994). Lyapunov stability theory of nonsmooth systems. IEEE Transactions on Automatic Control, 39(9), 1910–1914.
   Web of Science ®Google Scholar
• Wang, L., & Xiao, F. (2010). Finite-time consensus problems for networks of dynamic agents. IEEE Transactions on Automatic Control, 55(4), 950–955.
   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.
   Web of Science ®Google Scholar
• Wen, G., Yu, Y., Peng, Z., & Rahmani, A. (2016). Consensus tracking for second-order nonlinear multi-agent systems with switching topologies and time-varying reference state. International Journal of Control, 89(10), 2096–2106.
   Web of Science ®Google Scholar
• Xiao, F., Wang, L., Chen, J., & Gao, Y. (2009). Finite-time formation control for multi-agent systems. Automatica, 45(11), 2605–2611.
   Web of Science ®Google Scholar
• Xu, W., Cao, J., Yu, W., & Lu, J. (2014). Leader-following consensus of non-linear multi-agent systems with jointly connected topology. IET Control Theory & Applications, 8(6), 432–440.
   Web of Science ®Google Scholar
• Yang, X., & Cao, J. (2013). Exponential synchronization of delayed neural networks with discontinuous activations. IEEE Transactions on Circuits and Systems I: Regular Papers, 60(9), 2431–2439.
   Web of Science ®Google Scholar
• Zhang, Y., Yang, Y., Zhao, Y., & Wen, G. (2013). Distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances. International Journal of Control, 86(1), 29–40.
   Web of Science ®Google Scholar
• Zhao, Y., Li, Z., & Duan, Z. (2013). Distributed consensus tracking of multi-agent systems with nonlinear dynamics under a reference leader. International Journal of Control, 86(10), 1859–1869.
   Web of Science ®Google Scholar
• Zuo, Z. (2015a). Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory & Applications, 9(4), 545–552.
   Web of Science ®Google Scholar
• Zuo, Z. (2015b). Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, 54, 305–309.
   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.
   Web of Science ®Google Scholar
• Zuo, Z., & Tie, L. (2016). Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. International Journal of Systems Science, 47(6), 1366–1375.
   Web of Science ®Google Scholar