Robust integral of neural network and sign of tracking error control of uncertain nonlinear affine systems using state and output feedback

This paper presents a novel state and output feedback control law for the tracking control of a class of multi-input-multi-output (MIMO) continuous time nonlinear systems with unknown dynamics and disturbance input. First the state feedback based control law is designed which consists of the robust integral of a neural network (NN) output plus the sign of the tracking error signal multiplied with an adaptive gain. The two-layer NN learns the system dynamics in an online manner while the NN residual reconstruction errors and the bounded system disturbances are overcome by the error sign signal. Both of the NN output and error sign signal are included into the integral to ensure the control input is a smooth function. Since certain states are not available in practice, subsequently, a high-gain observer is utilized to estimate the unmeasurable system states and output feedback based controller is designed. A semi-global asymptotic tracking performance is guaranteed in the case of state feedback while boundedness in the case of output feedback and the NN weights and all other signals are shown to be bounded by using the Lyapunov method. Finally, theoretical results are verified in the simulation environment.