Control scheme based on the inverse system method online learning BP neural network adaptive compensate

In this paper, an online BP neural network (BPNN) compensate control scheme based on inverse system method is presented for a class of single-input—single-output nonlinear systems. Firstly, the error between the α-th derivative of the system output and the pseudo-control is analyzed and a BPNN is designed to compensate the error. Then, an adaptive algorithm of the BPNN, designed based on the Lyapunov stability theory, proves that tracking error of closed-loop system and weight estimation error of BPNN are uniform ultimate boundedness. Simulations for three nonlinear systems demonstrate the validity of the proposed control scheme??