Distributed adaptive consensus protocols for linearly coupled Lur'e systems over a directed topology

This study solves the consensus problem of networked Lue' system over a directed graph. First, a novel unified framework for multi-agent systems and complex networks is proposed, where the inner-linking function is given in advance, while the control protocols have to be designed through a communication topology. Then, for both leaderless and leader–follower situations, adaptive consensus protocols are designed in a fully distributed fashion, without using any global information of the communication graphs. Sufficient conditions are provided to design distributed protocols to ensure consensus. Furthermore, compared with other works, the simulation result of a coupled Chua's circuit shows that these conditions can be further released, since the consensus can be achieved with the union graph of the inherent connections and communication graph containing a directed spanning tree. In particular, special case of first-order system is discussed, where specific threshold is given to show how the ‘positive’ or ‘negative’ inherent interactions affect the choice of the communication graph and the feedback gain. Finally, a more practical flexible link robotic arm example is provided to illustrate the effectiveness of the theoretical analysis.