On L2-Regularization for Virtual Reference Feedback Tuning

The Virtual Reference Feedback Tuning (VRFT) approach is a design method that allow optimal feedback control laws to be derived from input-output (I/O) data only, without need of a model of the process. A drawback of this methods is that, in its standard formulation, it is not statistically efficient. In this paper, it is shown that it can be reformulated as a L2-regularized optimization problem, by keeping the same assumptions and features, such that its statistical performance can be 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.