Towards direct data-driven model-free design of optimal controllers

The most critical step in modern direct datadriven control design approaches, such as virtual reference feedback tuning and non-iterative correlation-based tuning, is the choice of an adequate closed-loop reference model. Indeed, the chosen reference model should reflect the desired closedloop performance but also be reproducible by the underlying unknown process when in closed loop with the synthesized controller. In this paper, we propose a novel approach to compute, directly from data, an ' optimal' reference model along with the corresponding controller. The performance index used to define the optimality of the reference model measures the tracking error and the actuator efforts (as it is typical in performancedriven controllers such as linear-quadratic Gaussian control and model predictive control), along with a term penalizing the expected mismatch between the reference model and the actual closed-loop system. The performance index depends on the variables used to parametrize the reference model and the controller, which are optimized through a suitable combination of particle swarm optimization and virtual reference feedback tuning.