Controllability of Large-Scale Networks: An Output Controllability Approach

In this paper we consider the problem of controllability and energy consumption for large scale networks. Instead of controlling separately all the nodes of the network we control an output which is defined as some measurement (for instance the average) of the nodes which are not directly controlled. We thus exploit the concept of Output Controllability and the Output Controllability Gramian to analyze the properties of the system. In this context, we show that it is possible to obtain a reduced-order approximated model which makes the Gramian computation and control design much easier. Simulations show that the reduced model is consistent with the original one and for low ratios of controlled nodes, more robust with respect to the original.