This paper continues our previous hierarchical consensus work by considering a nonlinear case. All agents are partitioned into a set of groups, each of which contains a value called group information, representing a convex combination of all agents' states inside. The control input for each agent consists of two parts, i.e., agent state inside its associated group and its group information. When the received group information is a nonlinear transformation, it is shown that the consensus can be achieved under the proposed scheme in both discrete time and continuous time. Finally, the numerical simulations are performed to validate the theoretical results.INDEX TERMS Consensus, multi-agent systems, hierarchical structure, nonlinear consensus.

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This paper addresses the distributed consensus problem in the presence of faulty nodes. A novel weight learning algorithm is introduced such that neither network connectivity nor a sequence of history records is required to achieve resilient consensus. The critical idea is to dynamically update the interaction weights among neighbors learnt from their credibility measurement. Basically, we define a reward function that is inversely proportional to the distance to its neighbor, and then adjust the credibility based on the reward derived at the present step and the previous credibility. In such a way, the interaction weights are updated at every step, which integrates the historic information and degrades the influences from faulty nodes. Both fixed and stochastic topologies are considered in this paper. Furthermore, we apply this novel approach in clock synchronization problem. By updating the logical clock skew and offset via the corresponding weight learning algorithms, respectively, the logical clock synchronization is eventually achieved regardless of faulty nodes. Simulations are provided to illustrate the effectiveness of the strategy.