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**Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies.**
*(English)*
Zbl 1259.93008

Summary: This paper considers the consensus problem for multi-agent systems with inherent nonlinear dynamics under directed topologies. A variable transformation method is used to convert the consensus problem to a partial stability problem. Both first-order and second-order systems are investigated under fixed and switching topologies, respectively. It is assumed that the inherent nonlinear terms satisfy the Lipschitz condition. Sufficient conditions on the feedback gains are given based on a Lyapunov function method. For first-order systems under a fixed topology, the consensus is achieved if the feedback gain related to the agents’ positions is large enough. For first-order systems under switching topologies, the effect of the minimum dwell time for the switching signal on the consensus achievement is considered. For second-order systems under a fixed topology, the consensus is achieved if the feedback gains related to the agents’ positions and velocities, respectively, are both large enough. For second-order systems under switching topologies, a switching variable transformation is given. Then, the consensus problem is investigated when all the digraphs are strongly connected and weighted balanced with a common weighted vector. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

### MSC:

93A14 | Decentralized systems |

68T42 | Agent technology and artificial intelligence |

94C15 | Applications of graph theory to circuits and networks |