Many systems in nature, society, and engineering naturally occur as networks exhibit topological changes with time. To study the dynamics of such networks, one has to consider the networks under the temporal framework, as opposed to static networks where the links between nodes are permanent. For example, the spread of a virus in a social network is highly influenced by the time ordering of contacts. To contain the virus spread, one needs to analyze the networks in the framework of temporal networks. Analyzing the controllability of temporal networks using classical control theory is a challenging task due to the numerical issues of computers and the lack of precise knowledge of edge weights. Therefore, structural analysis, a framework based on the sparsity (zero-nonzero) pattern of network structure, enables to study controllability of temporal network systems.

This talk will discuss the two aspects of structural controllability, namely weak structural controllability and strong structural controllability of temporal networks. We provide the graphical conditions for both notions of structural controllability of temporal networks. We present polynomial-time algorithms to compute the dimension of structural controllable subspace for the given input. Then we discuss an important problem of optimum input design of temporal networks for structural controllability. In this regard, we propose a greedy algorithm with an approximation guarantee to identify the minimum number of inputs for weak structural controllability of temporal networks. We validate the performance of the greedy algorithm on functional brain networks obtained from fMRI (functional Magnetic Resonance Imaging) data of the human brain of 100 subjects. We numerically compare the performance of the greedy algorithm in computing the minimum input set that ensures strong structural controllability of temporal networks using synthetic graphs.