Simplified adaptive neural control of strict-feedback nonlinear systems

This paper presents a simplified adaptive backstepping neural network control (ABNNC) strategy for a general class of uncertain strict-feedback nonlinear systems. In the backstepping design, all unknown functions at intermediate steps are passed down such that only a single neural network is needed to approximate a lumped uncertainty at the last step. The closed-loop system achieves practical asymptotic stability in the sense that all involved signals are bounded and the tracking error converges to a small neighborhood of zero. The contribution of this study is that the complexity growing problem of the traditional ABNNC design is substantially eliminated for a general class of uncertain strict-feedback nonlinear systems, where the constraints of control parameters that guarantee closed-loop stability is clearly demonstrated. An illustrative example has verified effectiveness of our approach.