B-spline backstepping control with derivative matrix estimation and its applications

A B-spline backstepping controller is proposed for a class of multiple-input multiple-output (MIMO) nonlinear systems. The control scheme incorporates the backstepping design technique with a B-spline neural network which is utilized to estimate the system dynamics. The B-spline neural network has the advantage of locally controlling its output behavior compared with other neural networks; therefore, it is very suitable to online estimate the system dynamics by tuning its interior parameters, including control points and knot points. Based on the mean-value theorem, the derivative of B-spline basis functions in relation to parameters can be estimated to online adjust these parameters. In addition, the validity of the proposed scheme is verified through an experiment on a servo motor system which is controlled by the output voltage of the Buck DC–DC converter.