Distributed event-driven control for finite-time consensus.

*(English)*Zbl 1415.93019Summary: This paper is concerned with how multi-agent networks achieve finite-time consensus using distributed event-driven control. Due to the hybrid nonlinearities arising from the nonsmooth control and the triggering condition, finite-time consensus analyses are more challenging with event-driven control than with continuous-time control. We study agents with single integrator dynamics and scalar states and present a distributed event-driven control protocol for the finite-time consensus, with comparison to continuous-time control. It is shown that using the proposed event-driven control scheme, agents can reach consensus within limited time and without Zeno behavior. We also obtain an estimate for the settling time and demonstrate that it is not only related to the initial condition and network connectivity, but is also linked with the event-triggering condition. Simulations are given to demonstrate the theoretical results.

##### MSC:

93A14 | Decentralized systems |

93C65 | Discrete event control/observation systems |

93D99 | Stability of control systems |

93C10 | Nonlinear systems in control theory |

##### Keywords:

nonlinear system; multi-agent network; finite-time consensus; event-driven control; distributed control##### References:

[1] | Bhat, S. P.; Bernstein, D. S., Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization, 38, 3, 751-766, (2000) · Zbl 0945.34039 |

[2] | Cai, H.; Lewis, F. L.; Hu, G.; Huang, J., The adaptive distributed observer approach to the cooperative output regulation of linear multi-agent systems, Automatica, 75, 299-305, (2017) · Zbl 1352.93058 |

[3] | Cao, Y.; Ren, W., Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics, Automatica, 50, 10, 2648-2656, (2014) · Zbl 1301.93008 |

[4] | Chen, G.; Lewis, F. L.; Xie, L., Finite-time distributed consensus via binary control protocols, Automatica, 47, 9, 1962-1968, (2011) · Zbl 1226.93008 |

[5] | Chen, C. L.P.; Wen, G. X.; Liu, Y. J.; Liu, Z., Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems, IEEE Transactions on Cybernetcis, 46, 7, 1591-1601, (2016) |

[6] | Dimarogonas, D. V.; Frazzoli, E.; Johansson, K. H., Distributed event-triggered control for multi-agent systems, IEEE Transactions on Automatic Control, 57, 5, 1291-1297, (2012) · Zbl 1369.93019 |

[7] | Ding, L.; Han, Q. L.; Ge, X.; Zhang, X. M., An overview of recent advances in event-triggered consensus of multiagent systems, IEEE Transactions on Cybernetics, 48, 4, 1110-1123, (2018) |

[8] | Ding, D.; Wang, Z.; Shen, B.; Wei, G., Event-triggered consensus control for discrete-time stochastic multi-agent systems: The input-to-state stability in probability, Automatica, 62, 284-291, (2015) · Zbl 1330.93155 |

[9] | Fan, Y.; Feng, G.; Wang, Y.; Song, C., Distributed event-triggered control of multi-agent systems with combinational measurements, Automatica, 49, 2, 671-675, (2013) · Zbl 1258.93004 |

[10] | Franceschelli, M.; Pisano, A.; Giua, A.; Usai, E., Finite-time consensus with disturbance rejection by discontinuous local interactions in directed graphs, IEEE Transactions on Automatic Control, 60, 4, 1133-1138, (2015) · Zbl 1360.93026 |

[11] | Fu, J.; Wang, J., Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties, Systems & Control Letters, 93, 1-12, (2016) · Zbl 1338.93020 |

[12] | Guan, Z. H.; Hu, B.; Chi, M.; He, D. X.; Cheng, X. M., Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control, Automatica, 50, 9, 2415-2418, (2014) · Zbl 1297.93012 |

[13] | Guan, Z. H.; Sun, F. L.; Wang, Y. W.; Li, T., Finite-time consensus for leader-following second-order multi-agent networks, IEEE Transactions on Circuits and Systems I, 59, 11, 2646-2654, (2012) |

[14] | Guo, G.; Ding, L.; Han, Q. L., A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems, Automatica, 50, 5, 1489-1496, (2014) · Zbl 1296.93108 |

[15] | Hou, W.; Fu, M.; Zhang, H.; Wu, Z., Consensus conditions for general second-order multi-agent systems with communication delay, Automatica, 75, 293-298, (2017) · Zbl 1352.93010 |

[16] | Hu, W.; Liu, L.; Feng, G., Consensus of linear multi-agent systems by distributed event-triggered strategy, IEEE Transactions on Cybernetics, 46, 1, 148-157, (2016) |

[17] | Li, H.; Liao, X.; Huang, T., Second-order locally dynamical consensus of multiagent systems with arbitrary fast switching directed topologies, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 43, 6, 1343-1353, (2013) |

[18] | Li, H.; Liao, X.; Huang, T.; Zhu, W., Event-triggering sampling based leader-following consensus in second-order multi-agent systems, IEEE Transactions on Automatic Control, 60, 7, 1998-2003, (2015) · Zbl 1360.93031 |

[19] | Li, C.; Yu, X.; Yu, W.; Huang, T.; Liu, Z. W., Distributed event-triggered scheme for economic dispatch in smart grids, IEEE Transactions on Industrial Informatics, 12, 5, 1775-1785, (2016) |

[20] | Liu, X.; Lam, J.; Yu, W.; Chen, G., Finite-time consensus of multiagent systems with a switching protocol, IEEE Transactions on Neural Networks and Learning Systems, 27, 4, 853-862, (2016) |

[21] | Lu, Q.; Han, Q. L.; Zhang, B.; Liu, D.; Liu, S., Cooperative control of mobile sensor networks for environmental monitoring: An event-triggered finite-time control scheme, IEEE Transactions on Cybernetics, 47, 12, 4134-4147, (2017) |

[22] | Meng, X.; Chen, T., Event based agreement protocols for multi-agent networks, Automatica, 49, 2125-2132, (2013) · Zbl 1364.93476 |

[23] | Meng, D.; Jia, Y.; Du, J., Finite-time consensus for multiagent systems with cooperative and antagonistic interactions, IEEE Transactions on Neural Networks and Learning Systems, 27, 4, 762-770, (2016) |

[24] | Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533, (2004) · Zbl 1365.93301 |

[25] | Parsegov, S. E.; Polyakov, A. E.; Shcherbakov, P. S., Fixed-time consensus algorithm for multi-agent systems with integrator dynamics, (4th IFAC on distributed estimation and control in networked systems, (2013)), 110-115 |

[26] | Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52, 9, 1680-1685, (2007) · Zbl 1366.90104 |

[27] | Tang, Y., Terminal sliding mode control for rigid robots, Automatica, 34, 1, 51-56, (1998) · Zbl 0908.93042 |

[28] | Wang, L.; Xiao, F., Finite-time consensus problem for network of dynamic agents, IEEE Transactions on Automatic Control, 55, 4, 950-955, (2010) · Zbl 1368.93391 |

[29] | Xie, D.; Xu, S.; Chu, Y.; Zou, Y., Event-triggered average consensus for multi-agent systems with nonlinear dynamics and switching topology, Journal of The Franklin Institute, 352, 3, 1080-1098, (2015) · Zbl 1307.93258 |

[30] | Xu, W.; Chen, G.; Ho, D. W.C., A layered event-triggered consensus scheme, IEEE Transactions on Cybernetics, 47, 8, 2334-2340, (2017) |

[31] | Zhang, H.; Feng, G.; Yan, H.; Chen, Q., Observer-based output feedback event-triggered control for consensus of multi-agent systems, IEEE Transactions on Industrial Electronics, 61, 9, 4885-4894, (2014) |

[32] | Zhu, W.; Jiang, Z. P.; Feng, G., Event-based consensus of multi-agent systems with general linear models, Automatica, 50, 2, 552-558, (2014) · Zbl 1364.93489 |

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