Data-driven Kalman Decomposition Considering Controllability of Linear Time Invariant System

The model-based control technique requires an accurate system model identification process because the performance of the controller varies depending on the accuracy of the system model information. However, there is a limit to finding accurate model information of the system due to noise of measurement data or system disturbance. Recently, active research on data-based controllers has proposed a data-driven problem structure that can design a controller using only data without identifying a system model. In this paper, we propose a method for obtaining a coordinate transformation matrix that enables Kalman decomposition of a linear system within this data-driven problem structure. Using the pre-experimental data, we obtain the uncontrollable generalized left eigenvector and use it as a basis vector to span the uncontrollable subspace. Finally, the proposed algorithm was verified through an example with uncontrollable repeated eigenvalues.