Direct data-driven model-reference control for constrained systems

A central challenge in direct data-driven control design is to ensure constraint satisfaction and safe operation of the closed-loop system while maintaining certain performance. To address this, we propose a hierarchical data-driven control architecture for constrained linear time-invariant systems to track a given setpoint reference. The inner-loop consists of a model reference controller (MRC) synthesized directly from the noisy data, which ensures performance by attempting to match a user-specified reference model. The outer-loop is a robust model predictive control (RMPC), acting as a safety pre-filter which optimally modifies the reference signal given to the inner loop MRC, ensuring constraint satisfaction and improving overall tracking performance. Additionally, the RMPC scheme accounts for a potential mismatch between the achieved closed-loop and the desired reference model, in the case of imperfect matching by the inner loop controller. The effectiveness of the method is demonstrated via a numerical example.