On Hybrid Adaptive and Pinning Consensus for Multiagent Networks

The consensus problems for both continuous-time and discrete-time multiagent networks are deeply investigated by adopting hybrid adaptive and pinning control laws, respectively. Particularly, the topology of the networks needs to neither be symmetric nor contain a directed spanning tree and some useful criteria are addressed analytically. Simultaneously, a comprehensive pinning scheme is proposed as well which shows that the nodes with zero in-degree need to be pinned primarily in order to guarantee the system to achieve consensus, and then the nodes whose out-degrees are bigger than their in-degrees can give priority to be pinned compared to other nodes for improving the convergence rate of the system, whereas it is also interesting to find out that the regular rule does not always hold, that is, the more nodes are selected to be pinned, the faster the system will converge. Finally, the validity of our theoretical findings is verified by several numerical examples.