Necessary conditions for controllability of nonlinear networked control systems

In this paper, we study the controllability of nonlinear networked systems. In particular, we describe how graph symmetries combined with dynamic symmetries result in a loss of controllability in nonlinear leader-follower networks. Our result generalizes those of Rahmani et al. (2009) who considered the case of a linear consensus-type dynamics, namely the unweighted Laplacian network flow. We consider several nonlinear network control systems that have been previously studied in the literature and characterize the presence of leader-follower graph symmetries that result in the lack of controllability.