Data-driven virtual reference controller design for high-order nonlinear systems via neural network

This paper is concerned with data-driven methods for virtual reference controller design of high-order nonlinear systems via neural network. Virtual reference feedback tuning (VRFT) is a one-shot direct data-based method to design controller of linear or nonlinear systems. In this paper, we recall the model reference control problem of high-order nonlinear systems and design a new objective function of VRFT. In ideal conditions, the two problems are demonstrated to have the same solution. For the first time, we prove that the value of the optimization problem for model reference control is bounded by that of the objective function of VRFT. A three-layer neural network is employed as a general approximator of the designed controller and two simulations are given to verify the validity of our method.