Adaptive neural control of high-order uncertain nonaffine systems: A transformation to affine systems approach

This brief investigates the adaptive neural network (NN) control of a class of high-order nonaffine nonlinear systems with completely unknown dynamics. Since the control terms appear within the unknown nonlinearity, traditional control schemes and stability analysis are usually rendered extremely complicated. Our main contribution includes a novel system transformation that converts the nonaffine system into an affine system through a combination of a low-pass filter and state transformation. As a result, the state-feedback control of the nonaffine system can be viewed as the output-feedback control of an affine system in normal form. The transformed system becomes linear with respect to the new input while the traditional backstepping approach is not needed thus allowing the synthesis to be extremely simplified. It is theoretically proven that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Simulation results are provided to demonstrate the performance of the developed controller.