Leader-follower finite-time consensus of multiagent systems with nonlinear dynamics by intermittent protocol. (English) Zbl 1485.93534
Summary: This paper deals with the leader-follower finite-time consensus problem for multiagent systems with nonlinear dynamics via intermittent protocol. The topological structure of the followers is undirected or balanced digraph. Different from most existing works concerning nonlinear dynamics (satisfies Lipschitz continuity), the nonlinear dynamics of each agent satisfies Hölder continuity in this paper. In light of the finite-time control technique, the intermittent control protocol is designed to reach accurate leader-follower finite-time consensus. It is justified that the leader-follower finite-time consensus can be realized if the length of communication is greater than a critical value by using limit theory. Finally, two numerical examples are exhibited to validate the effectiveness of the proposed scheme.
MSC:
| 93D50 | Consensus |
| 93D40 | Finite-time stability |
| 93A16 | Multi-agent systems |
| 93A13 | Hierarchical systems |
| 93C10 | Nonlinear systems in control theory |
References:
| [1] | Wei, G.; Jia, Y., Synchronization-based image edge detection, Europhys. Lett., 59, 6, 814-819 (2002) |
| [2] | Xie, Q.; Chen, G.; Bollt, E., Hybrid chaos synchronization and its application in information processing, Math. Comput. Model., 35, 145-163 (2002) · Zbl 1022.37049 |
| [3] | Meng, D.; Jia, Y., Formation control for multi-agent systems through an iterative learning design approach, Int. J. Robust Nonlin. Control, 24, 340-361 (2014) · Zbl 1279.93010 |
| [4] | Mirollo, R.; Strogatz, S., Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50, 6, 1645-1662 (1990) · Zbl 0712.92006 |
| [5] | Ren, W.; Beard, R., Consensus seeking in multi-agent systems using dynamically changing interaction topologies, IEEE Trans. Automat. Control, 50, 5, 665-671 (2005) |
| [6] | Hong, Y.; Hu, J.; Gao, L., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182 (2006) · Zbl 1117.93300 |
| [7] | Wang, X.; Hong, Y., Distributed finite-time \(\chi \)-consensus algorithms for multi-agent systems with variable coupling topology, J. Syst. Sci. Complexity, 23, 209-218 (2010) · Zbl 1197.93097 |
| [8] | Hummel, D., Formation flight as an energy-saving mechanism, Isr. J. Zool., 41, 261-278 (1995) |
| [9] | J, Y. S., Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph, IEEE Trans. Neural Netw. Learn. Syst., 24, 4, 666-672 (2013) |
| [10] | Wen, G. H.; Zheng, W. X., On constructing multiple Lyapunov functions for tracking control of multiple agents with switching topologies, IEEE Trans. Automat. Control, 64, 9, 3796-3803 (2019) · Zbl 1482.93542 |
| [11] | Wen, G. H.; Duan, Z. S.; Chen, G. R.; Yu, W. W., Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies, IEEE Trans. Automat. Control, 61, 2, 499-511 (2014) · Zbl 1468.93037 |
| [12] | Zuo, Z.; Wang, C., Adaptive trajectory tracking control of output constrained multi-rotors systems, IET Control Theory Appl., 8, 13, 1163-1174 (2014) |
| [13] | Zhang, H.; Lewis, F. L., Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics, Automatica, 48, 7, 1432-1439 (2012) · Zbl 1348.93144 |
| [14] | Hong, Y. G.; Hu, J. P., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 1177-1182 (2006) · Zbl 1117.93300 |
| [15] | Wu, Y. M.; Wang, Z. S., Leader-follower consensus of multi-agent systems in directed networks with actuator faults, Neurocomputing, 275, 1177-1185 (2018) |
| [16] | Yu, W.; Chen, G.; Cao, M.; Kurths, J., Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Trans. Syst. Man Cybern.Part B, 40, 881-891 (2010) |
| [17] | Zhang, X. F.; Liu, L.; Feng, G., Leader-follower consensus of time-varying nonlinear multi-agent systems, Automatica, 52, 8-14 (2015) · Zbl 1309.93018 |
| [18] | Cao, Y.; Yu, W.; Ren, W.; Chen, G., Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking, Syst. Control Lett., 59, 9, 522-529 (2010) · Zbl 1207.93103 |
| [19] | Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49, 1520-1533 (2004) · Zbl 1365.93301 |
| [20] | Bhat, S. P.; Bernstein, D. S., Continuous, finite-time stabilization of the translational and rotational double integrators, IEEE Trans. Autom. Control, 43, 678-682 (1998) · Zbl 0925.93821 |
| [21] | Bhat, S. P.; Bernstein, D. S., Finite-time stability of continuous autonomous systems, SIAM J. Control Optim., 38, 751-766 (2000) · Zbl 0945.34039 |
| [22] | Wang, X.; Hong, Y., Finite-time consensus for multi-agent networks with second-order agent dynamics, Proceedings of the 17th World Congress, 15185-15190 (2008) |
| [23] | Xiao, F.; Wang, L.; Chen, J.; Gao, Y., Finite-time formation control for multi-agent systems, Automatica, 45, 2605-2611 (2009) · Zbl 1180.93006 |
| [24] | Li, S.; Du, H.; Lin, X., Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics, Automatica, 47, 1706-1712 (2011) · Zbl 1226.93014 |
| [25] | Yu, S.; Long, X., Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode, Automatica, 54, 158-165 (2015) · Zbl 1318.93009 |
| [26] | Zhang, H. P.; Yue, D.; Yin, X. X.; Hu, S. L.; Dou, C. X., Finite-time distributed event-triggered consensus control for multi-agent systems, Inf. Sci., 339, 132-142 (2016) · Zbl 1395.68268 |
| [27] | Wang, Y. J.; Yuan, Y.; Liu, J. G., Finite-time leader-following output consensus for multi-agent systems via extended state observer, Automatica, 124, 109133 (2021) · Zbl 1461.93474 |
| [28] | Wen, G.; Duan, Z.; Li, Z.; Chen, G., Consensus and its \(l_2\)-gain performance of multi-agent systems with intermittent information transmissions, Int. J. Control, 85, 4, 384-396 (2012) · Zbl 1256.93016 |
| [29] | Yang, Y.; He, Y.; Wu, M., Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method, J. Franklin Inst., 356, 8, 4648-4676 (2019) · Zbl 1412.93082 |
| [30] | Jing, T.; Zhang, D.; Mei, J., Finite-time synchronization of delayed complex dynamic networks via aperiodically intermittent control, J. Franklin Inst., 356, 10, 5464-5484 (2019) · Zbl 1415.93235 |
| [31] | Liu, M.; Jiang, H.; Hu, C., Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control, J. Franklin Inst., 354, 13, 5374-5397 (2017) · Zbl 1395.93348 |
| [32] | Xiao, F.; Wang, L., Reaching agreement in finite time via continuous local state feedback, Proceedings of the 26th Chinese Control Conference, 711-715 (2007) |
| [33] | Yu, S.; Long, X., Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode, Automatica, 54, 158-165 (2015) · Zbl 1318.93009 |
| [34] | Li, C.; Feng, G.; Liao, X., Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans. Circuits Syst. II Express Briefs, 54, 11, 1019-1023 (2007) |
| [35] | Wen, G.; Duan, Z.; Ren, W.; Chen, G., Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications, Int. J. Robust Nonlin. Control, 24, 16, 2438-2457 (2013) · Zbl 1302.93018 |
| [36] | Xia, W.; Cao, J., Pinning synchronization of delayed dynamical networks via periodically intermittent control, Chaos, 19, 1, 013120 (2009) · Zbl 1311.93061 |
| [37] | Guan, Z. H.; Wu, Y. H.; Feng, G., Consensus analysis based on impulsive systems in multi-agent networks, IEEE Trans. Circuits Syst. I, 59, 1, 170-178 (2012) · Zbl 1468.93029 |
| [38] | Guan, Z. H.; Han, G. S.; Li, J.; He, D. X.; Feng, F., Impulsive multi-consensus of second-order multiagent networks using sampled position data, IEEE Trans. Neural Netw. Learn. Syst., 26, 11, 2679-2688 (2015) |
| [39] | Dimarogonas, D. V.; Frazzoli, E.; Johansson, K. H., Distributed event-triggered control for multi-agent systems, IEEE Trans. Automat. Control, 57, 5, 1291-1297 (2012) · Zbl 1369.93019 |
| [40] | Li, H.; Su, H., Distributed consensus of multi-agent systems with nonlinear dynamics via adaptive intermittent control, J. Franklin Inst. B, 352, 4546-4564 (2015) · Zbl 1395.93015 |
| [41] | Wan, Y.; Cao, J., Distributed robust stabilization of linear multi-agent systems with intermittent control, J. Franklin Inst. B, 352, 4515-4527 (2015) · Zbl 1395.93471 |
| [42] | Hu, A.; Cao, J.; Hu, M., Consensus of leader-following multi-agent systems in time-varying networks via intermittent control, Int. J. Control Autom. Syst., 12, 5, 969-976 (2014) |
| [43] | Wen, G.; Duan, Z.; Yu, W.; Chen, G., Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications, Int. J. Control, 86, 2, 322-331 (2013) · Zbl 1278.93016 |
| [44] | Zhao, Y.; Liu, Y.; Wen, G.; Ren, W.; Chen, G., Designing distributed specified-time consensus protocols for linear multiagent systems over directed graphs, IEEE Trans. Autom. Control, 64, 7, 2945-2952 (2019) · Zbl 1482.93065 |
| [45] | Zhao, Y.; Zhou, Y.; Liu, Y. F.; Wen, G. H.; Huang, P. F., Fixed-time bipartite synchronization with a pre-appointed settling time over directed cooperative-antagonistic networks, Automatica,, 123, 1, 109301 (2021) · Zbl 1461.93197 |
| [46] | Guo, W.; Xiao, H., Distributed consensus of the nonlinear second-order multi-agent systems via mixed intermittent protocol, Nonlin. Anal. Hybrid Syst., 30, 189-198 (2018) · Zbl 1408.93003 |
| [47] | Xiao, F.; Wang, L.; Chen, J.; Gao, Y., Finite-time formation control for multi-agent systems, Automatica, 45, 2605-2611 (2009) · Zbl 1180.93006 |
| [48] | Hardy, G. H.; Littlewood, J. E.; Pólya, G., Inequalities (1952), Cambridge University · Zbl 0047.05302 |
| [49] | Hartman, P., Ordinary Differential Equations (1982), Birkhȧuser · Zbl 0125.32102 |
| [50] | Courant, R.; John, F., Introduction to Calculus and Analysis (1989), Springer · Zbl 0911.26002 |
| [51] | Jiang, J.; Liu, X., Principle of Electric Circuits (2007), Tsinghua University |
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