Cooperative Control of Heterogeneous Uncertain Dynamical Networks: An Adaptive Explicit Synchronization Framework

This paper proposes an adaptive explicit synchronization framework to address the cooperative control for heterogeneous uncertain dynamical networks under switching communication topologies. The main contribution is to develop an adaptive explicit synchronization algorithm, in which the synchronization state can be completely tracked by each agent in real time rather than only be measured after the synchronization process of all agents is over. By introducing appropriate assumptions, a class of adaptive explicit synchronization protocols is designed by using a combination of the virtual leader's states, the neighboring agents' relative information, distributed feedback gain, and distributed average weighted parameters. It is proved in the sense of Lyapunov that, if the dwell time is larger than a positive threshold, the cooperative control problem for the closed-loop heterogeneous uncertain dynamical networks under switching of strongly-connected communication topologies can be solved by the proposed adaptive explicit synchronization algorithm. Furthermore, by assuming that the topology is frequently strongly-connected, it shows that intermittent adaptive explicit synchronization can be achieved with well-designed control parameters. Two examples are presented to demonstrate the effectiveness of the proposed theory.