Decentralised adaptive synchronisation of a class of discrete-time and nonlinearly parametrised coupled multi-agent systems

In this paper, the adaptive decentralised control problem of the multi-agent system is considered. Each agent is described by a discrete-time nonlinear inverse model with the unknown parameter. The output of each agent has an influence from the history outputs of its neighbour agents. To deal with uncertainty, a projection-type parameter estimation algorithm is adopted to identify parameter. According to the certainty equivalence principle, the local control law of each agent is designed only using the history outputs of its own and neighbour agents. Under the parameter update law and the local dual control, it is shown that the output of each agent tracks the average value of history outputs from its neighbour agents, and the closed-loop system eventually achieves strong synchronisation. Finally, two simulations for an example are provided to illustrated the validity of the results.