Neural network control of discrete-time non-affine MIMO systems with disturbances

in this paper, a simple neural network (NN) control scheme is developed for a class of discrete-time multi-input multi-output (MIMO) non-affine nonlinear systems with triangular form inputs and disturbances. The system studied is described by NARMAX (Nonlinear Auto Regressive Moving Average with eXogenous inputs) model. Firstly, by using implicit function theorem, the existence of the implicit desired feedback control (IDFC) is proved. Then single layer neural networks are used as the emulators of the desired controls. The stability of the closed-loop system is rigorously proved by using Lyapunov method. Because only input and output sequences are needed to construct the approximation based controls, the method proposed is very simple to be implemented in practical applications.