Data-driven controller design for general MIMO nonlinear systems via virtual reference feedback tuning and neural networks

In this paper, we develop a novel data-driven multivariate nonlinear controller design method for multi-input-multi-output (MIMO) nonlinear systems via virtual reference feedback tuning (VRFT) and neural networks. To the best of authors' knowledge, it is the first time to introduce VRFT to MIMO nonlinear systems in theory. Unlike the standard VRFT for linear systems, we restate the model reference control problem with time-domain model in the absence of transfer functions and simplify the objective function of VRFT without a linear filter. Then, we prove that the objective function of VRFT reaches the minimum at the same point as the optimization problem of model reference control and give the relationship between the bounds of the two optimization problems of model reference control and VRFT. A three-layer neural network is used to implement the developed method. Finally, two simulations are conducted to verify the validity of our method.