Explicit synchronisation of heterogeneous dynamics networks via three-layer communication framework

This paper addresses the explicit synchronisation of heterogeneous dynamics networks via three layer communication framework. The main contribution is to propose an explicit synchronisation algorithm, in which the synchronisation errors of all the agents are decoupled. By constructing a three-layer node model, the proposed algorithm removes the assumptions that the topology is fixed and the synchronisation process is coupled. By introducing appropriate assumptions, the algorithm leads to a class of explicit synchronisation protocols based on the states of agents in different layers. It is proved in the sense of Lyapunov that, if the dwell time is larger than a threshold, the explicit synchronisation can be achieved for closed-loop heterogeneous dynamics networks under switching topologies. The results are further extended to the cases in which the switching topologies are only frequently but not always connected. Simulation results are presented with four single-link manipulators to verify the theoretical analysis.