Integral Lyapunov Function-Based Adaptive Learning Control for Nonstrict-Feedback Nonlinear Systems

This article addresses the problem of adaptive learning control (ALC) for nonlinear systems in nonstrict-feedback form. For parameter learning, an incremental adaptive mechanism is proposed and used as an alternative to integral adaptation, with which numerical integration in implementation can be avoided. Taking advantage of the error-tracking approach, a novel integral Lyapunov function, developed specifically for tackling state-dependent control gains, is incorporated into the approximation-based backstepping design. In addition, the technical challenges associated with nonstrict-feedback structures are successfully overcome, by employing the key property of neural networks in the ALC design. It is shown that with the aid of the technique lemma for robustness analysis, the proposed ALC control strategy guarantees robust convergence of the tracking error, despite the complex uncertainties involved. The design method guarantees the tracking performance and facilitates the implementation of the suggested algorithm. Illustrative examples are provided which verify the effectiveness of the presented ALC control scheme.