Structure reconstruction for linear network systems with dynamical structure functions

The state-space model for linear network systems which represents the structure information, in general, cannot be recovered from the dynamical input-output data, since typically the realization problem does not have a unique solution. Dynamical structure functions have been introduced to represent the structural information only between the measurements. Even though, it has shown that for a given network composed of p measured individuals, in order to completely recover the relationships between the measurements, p experiments with each experiment independently controlling a measured individual must be performed. This paper will investigate the structure reconstruction for a kind of linear networks, in which all states are measurable, but only partial states can be directly controlled by external inputs. Therefore, the network structure cannot be inferred directly by making use of the dynamical structure function. A new algorithm is proposed, in which the relations between the nodes with input are obtained from the dynamical structure function; and then, the influences from the nodes with control input to the nodes without are deduced; and finally, a convex optimization algorithm with a sparsity assumption is used to infer the full structure information.