Controllability Maximization of Network Systems: Gradient Computation Based on Offline Data

Abstract

In the field of network systems, controllability maximization has become more important in terms of efficient control. When an exact model of a network system is not available, data-driven approaches are useful. In this paper, we establish a framework for maximizing the controllability of networked systems by using off-line data. In particular, the maximization with respect to the network topology of the network system is addressed. First, we develop a data-driven method for solving the Lyapunov equation which describes the properties of a system different from the system associated with the data. Second, based on this result, we derive a data-driven method for computing the gradient of a controllability measure (the trace of the controllability Gramian) with respect to the network topology of the network system. Finally, we show that our gradient computation can be used for controllability maximization based on off-line data. The effectiveness of the data-driven methods is numerically demonstrated.