Event-triggered average consensus for multi-agent systems with nonlinear dynamics and switching topology.

*(English)*Zbl 1307.93258Summary: The average consensus problem for a multi-agent system with nonlinear dynamics is studied in this paper by employing a distributed event-triggered control strategy. The strategy uses a piecewise continuous control law and an event-triggering function to control the system. The piecewise continuous control law only updates at infrequent instants and keeps steady at the previous value in the period between two instants. The event-triggering function determines these instants based on the state information of the agents at current and previous instants. This control approach is first applied to a first-order system under a connected topology in a centralized pattern. Then, the switching topology case is considered. At last, both the first-order and the second-order system are considered under distributed event-triggered strategy. The distributed event-triggering function, which only employs the information of the corresponding agent and the states of its neighbors, is designed for each agent in the system. By utilizing Lyapunov method and graph theory, it is proven that the systems can reach consensus by using the event-triggered control strategy. Numerical examples are provided to show the efficacy of the proposed control strategy.

##### MSC:

93C65 | Discrete event control/observation systems |

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

93C10 | Nonlinear systems in control theory |

05C90 | Applications of graph theory |

##### Keywords:

average consensus problem; multi-agent system; nonlinear dynamics; event-triggering function; Lyapunov method; graph theor##### Software:

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\textit{D. Xie} et al., J. Franklin Inst. 352, No. 3, 1080--1098 (2015; Zbl 1307.93258)

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