Data-driven reference model selection and application to L-DDC design
This work addresses the critical problem of reference model selection in data-driven control for LTI systems, but the method is incremental as it builds on existing stability analysis and L-DDC techniques.
The paper proposes a data-driven method to select a reference model for LTI monovariable systems that is both achievable by the plant and meets desired performance, using a stability analysis technique. The approach is validated with the L-DDC algorithm and enables controller validation via the small-gain theorem.
The choice of a reference model in data-driven control techniques is a critical step. Indeed, it should represent the desired closed-loop performances and be achievable by the plant at the same time. In this paper, we propose a method to build such a reference model, both reproducible by the system and having a desired behaviour. It is applicable to Linear Time-Invariant (LTI) monovariable systems and relies on the estimation of the plant's instabilities through a data-driven stability analysis technique. The L-DDC (Loewner Data Driven Control) algorithm is used to illustrate the impact of the choice of the reference model on the control design process. Finally, the proposed choice of specifications allows to use a controller validation technique based on the small-gain theorem.