Data-Driven Controller Tuning for MIMO Systems: A Set-Membership Approach

Over time, Single-Input Single-Output systems have received significant attention in the field of data-driven control. However, real-world applications often involve Multi-Input Multi-Output systems, where the challenges associated with multivariable control are considerably greater. This paper presents an innovative extension of the Set Membership Data-Driven approach from Single-Input Single-Output to Multi-Input Multi-Output systems. Exploiting unknown but bounded assumptions on process noise and fixed bases controllers parametrization, an efficient batch algorithm for controller tuning is developed, relying on low dimensional convex optimization problems. Through a comparative analysis with Virtual Reference Feedback Tuning, it is quantitatively demonstrated that the Set Membership Data-Driven approach significantly outperforms existing solutions, achieving reductions in Integral Square Error and Integral Absolute Error by up to 6% and 27%, respectively, thereby reducing coupling errors. Furthermore, the designed controllers exhibit faster rise and settling times, with improvements of up to 20% and 39%, eliminating the overshoots. These findings indicate that the SMDD approach effectively enhances decoupling and error minimization, making it a reliable solution for managing the complexities of MIMO systems.