Observed-Based Adaptive Neural Tracking Control for Nonlinear Systems with Unknown Control Directions and Input Delay

Enhancing the stability and performance of practical control systems in the presence of nonlinearity, time delay, and uncertainty remains a significant challenge. Particularly, a class of strict-feedback nonlinear uncertain systems characterized by unknown control directions and time-varying input delay lacks comprehensive solutions. In this paper, we propose an observer-based adaptive tracking controller to address this gap. Neural networks are utilized to handle uncertainty, and a unique coordinate transformation is employed to untangle the coupling between input delay and unknown control directions. Subsequently, a new auxiliary signal counters the impact of time-varying input delay, while a Nussbaum function is introduced to solve the problem of unknown control directions. The leverage of an advanced dynamic surface control technique avoids the “complexity explosion” and reduces boundary layer errors. Synthesizing these techniques ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small region around the origin by selecting suitable parameters. Simulation examples are provided to demonstrate the feasibility of the proposed approach.