On L2-regularization for Virtual Reference Feedback Tuning

The Virtual Reference Feedback Tuning (VRFT) approach is a data-driven controller design method for the model-reference control problem. In this method, the controller parameters are estimated from a set of input/output (I/O) data and no model of the process is required. However, in its standard formulation, the estimator of the controller parameters is not statistically efficient. In this paper, the estimation problem is reformulated as an L₂-regularized optimization problem, by keeping the same assumptions and features, such that its statistical performance is improved using the same data. A convex optimization method is also introduced to find the best regularization matrix. The proposed strategy is finally tested on a benchmark example in digital control system design.