Controlling the collective behaviour of networks of heterogenous Kuramoto oscillators with phase lags

We investigate the problem of controlling a network of heterogeneous Kuramoto oscillators affected by phase lags in the communication with their neighbours. We find analytical conditions that allow to determine the control effort required to guarantee convergence of all the oscillators towards a common collective evolution despite the presence of heterogeneities and phase lags. After presenting some numerical simulations that confirm the theoretical results, we discuss the application of the theory to the problem of inducing motor coordination in a mixed group of human players and artificial agents performing a joint task.