Data-driven Estimation of Finite-time Controllability Gramians

In networked control, one of the fundamental problems is to select control nodes. When the plant is unknown, the data-driven approach plays a key role in the problem. This paper presents a data-driven estimation of finite-time controllability Gramians of unknown linear systems. First, we develop a method for calculating a solution to a class of Lyapunov equations associated with the system by using the state trajectories. Based on this result, we propose a data-driven estimation method of the finite-time controllability Gramians. The proposed method is demonstrated through numerical simulation.