Data-driven design of structured sparse feedback controllers

This article proposes a data-driven design method of structured sparse feedback controllers. In situations where the system model is unavailable but the measurement data are available, we address the problem of finding a feedback controller which minimizes the number of nonzero rows in the feedback gain such that the closed-loop system has stability with the guaranteed rate of convergence. It is shown that this problem can be reduced to a nonconvex optimization problem with a constraint described by a linear matrix inequality. Moreover, its convex relaxation problem is also considered. To demonstrate the effectiveness of our approach, a numerical example is provided. Furthermore, as an application of the above results, we develop a data-driven design method of block-structured sparse feedback controllers.