On Distributed Control Based Second-order Multi-agent System Consensus And Formation

In order to overcome the disadvantage of single agent and the defect of centralized control, in recent years, distributed coordination control of multi-agent has attracted many scholars'attention. On one hand, it contributes to the execution of complex task, for example, in civil and commercial field, independent dug mining, environmental monitoring, disaster monitoring and precision agriculture can be realized by autonomous vehicle. On the military domain, reconnaissance, surveillance and battle damage assessment can be achieved. In family protection realm, district on patrol, guardianship and rescue can be completed. On the other hand, the parallelism and redundancy can improve fault tolerance and robustness of the system. Therefore, consensus and formation control should be paid more attention to due to their significance.In sharp contrast to the first-order consensus problem, consensus may fail to be achieved for agents with second-order dynamics even if the network topology has a directed spanning tree. So it is still a challenging problem to identify sufficient and necessary conditions of consensus problem for the second-order multi-agent system. As the practical application of consensus problem, formation control can effectively imitate cluster and coordinate control phenomenon in biology, so there is more practical value for further study.The paper mainly includes:(a) Using algebraic graph theory and matrix theory, distributed consensus problems for the second-order multi-agent system are discussed under a variety of assumptions on the network topology(being fixed without delay, fixed with delay and switching).(b) It is found that both the real and imaginary parts of eigenvalues of the Laplace matrix of the network play key roles in reaching consensus when it is fixed network topology without delay. Meanwhile, it is proved that the system can reach consensus faster using the proposed algorithm in the paper.(c) In fixed network topology with delay, the maximum delay is given.(d) In switching network topology case, it shows that switching network topology can also reach consensus when the networks topology keep long enough.(e) Formation controller of three agents is designed based on behavior method, given different parameters, different simulation results are showed.(f) Using artificial potential function method, formation controller of second-order multi-agent system is designed, which includes both the leader and the follower. The result indicates that formation control performs well.