Controllability through input addition for graph-based systems

In this paper, we consider dynamical graph-based systems, which are well fitted for the structural analysis of complex systems. A significant amount of work has been devoted to the controllability of such graph based systems, e.g. for multi-agent systems or complex networks. We study here the controllability through input addition in this framework. We present several variants of this problem depending on the freedom which is left to the designer on the additional inputs. Our contribution lies in the minimal number of inputs to be added for controllability. We provide also with information on the possible location of additional inputs. We finally present some links with other approaches and we show that these results can be easily applied to complex systems.