A Novel Error-Compensation Control for a Class of High-Order Nonlinear Systems With Input Delay

A novel tracking error-compensation-based adaptive neural control scheme is proposed for a class of high-order nonlinear systems with completely unknown nonlinearities and input delay. In the tracking errors of existing papers, there exist the following difficulties: first, output curve always lags behind the desired trajectory, second, some big peak errors cause a decrease in tracking precision, and third, a big initial value of the modified tracking error can make the closed-loop system unstable. To tackle them, three corresponding error-compensation terms are constructed, including a prediction and compensation term, an auxiliary signal produced by the constructed auxiliary system, and a damping term. However, inequality amplification caused by high order will weaken the effectiveness of the proposed error-compensation scheme, and the control precision will decrease under an assumption that the lower bounds of the unknown control coefficients should be exactly known. To overcome aforementioned difficulties, in the derivation of the first virtual control law, the radial basis function neural network is used to approximate a hybrid term online constructed by unknown nonlinearities, a lumped control coefficient achieved by state transformation, and the dynamic of the proposed error-compensation terms and desired signal. Meanwhile, input delay is coped with a robust compensation signal constructed based on a finite integral of the past control values. Finally, it is proven that all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the proposed method.