Tuning Nonlinear Controllers with the Virtual Reference Approach

Virtual Reference Feedback Tuning (VRFT) is a well established method for data-driven tuning of linear controllers. In VRFT the design is performed in “one-shot”, that is, with only one batch of input-output data, without the need of iterative data collection procedures. Its core concept consists in treating input-output data collected from the plant to be controlled as if they had been obtained from a virtual experiment, in which a particular reference signal - the virtual reference - would have been applied to the closed-loop system. A key feature of the VRFT method is that it greatly simplifies the design procedure with respect to standard model reference design: for linear and linearly parametrized controllers, it results in convexification of the design, so that its solution can be found by a single least squares method. In this paper this paradigm is applied to the tuning of nonlinear controllers. We propose specific design procedures for two classes of nonlinear plants: rational plants and plants of the Wiener type. Statistical properties of the controllers thus designed in noisy environments are also illustrated.