Model Reduction Based Approximation of the Output Controllability Gramian in Large-Scale Networks

In this article, we consider the problem of determining the control energy for large-scale networks. Instead of controlling all the nodes of the network, we are interested in driving the value of some outputs to the desired value, by directly controlling some of the nodes. To do this, we exploit the concept of output controllability and of output controllability Gramian that permits to analyze the properties of the system, both in single-output and multioutput cases. Based on a projection method, we show that it is possible to obtain an approximated model that makes the computation of the Gramian and its interpretation much easier. Simulations show that the reduced model is consistent with the original one and provides a reliable approximation of the control energy necessary to control the network.