Robust adaptive NN tracking control for MIMO uncertain nonlinear systems with completely unknown control gains under input saturations

This paper focuses on the study of tracking control problem for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems with completely unknown control gains under input saturations. A hyperbolic tangent function is introduced to approximate the input saturation nonlinearity. Based on the above, a novel robust adaptive neural network (NN) tracking control scheme is proposed combining finite-time nonlinear tracking differentiator (FTNTD), Nussbaum-type function and adaptive NN with backstepping design tool. Within our scheme, a constructed novel nonlinear function featured by “small-error large-gain and large-error small-gain” is inset into virtual and actual control laws to achieve a balance between the feedback control gain and the system control performance and prevent the over-learning of parameter adaptive laws caused by the input saturation. By means of a newly constructed non-quadratic Lyapunov function, it is theoretically shown that all the signals in the closed-loop control system are semi-globally uniformly ultimately bounded. Finally, the effectiveness of our proposed scheme is verified by the simulations of two simulation examples.