Neural Adaptive Learning Control With Desired Approximation: An Integral Lyapunov Function Approach

ABSTRACT The inherent approximation ability of neural networks plays an essential role in adaptive neural control, with a prerequisite that for most of the controller designs, the actual system state is assumed to be restricted and remain in a compact set. In this paper, the desired approximation strategy is employed to tackle such a problem, in which only the desired state signal is used as input to the network, instead of using the actual system state. The neural adaptive learning controllers are designed for nonlinear strict‐feedback systems, in the sense of the error tracking, which ensures both approximation and tracking performance. With a novel integral Lyapunov function, the treatment of the unknown state‐dependent input gains is adopted, while an incremental adaptive mechanism for parameter learning is developed as an alternative to integral adaptation. Theoretical results for the performance analysis are presented in detail, where the boundedness of all the variables in the closed‐loop is characterized. In addition, it is shown that the proposed neural control schemes assure that the tracking error converges to a neighborhood of the origin, without any requirement on the knowledge of the region that the actual variables evolve. Numerical results demonstrate effectiveness in the compensation for system uncertainties and the tracking performance of the control scheme.