Data-driven Optimal Output Feedback Control of Linear Systems from Input-Output Data

We design optimal output feedback controllers for linear systems where only outputs are available for measurement and control actuation. The goal is to render the closed-loop system stable while minimizing a quadratic cost function balancing performance and control effort. We first provide a model-based solution to this problem, where an optimal dynamic output feedback controller is computed by solving a semidefinite program. Then, we shift our attention to data-based solutions, bypassing the system identification step. We derive semidefinite programs that are explicitly stated in terms of input-output data. The effectiveness of the method is illustrated via a power system case study.