Adaptive Tracking Control for Perturbed Strict-Feedback Nonlinear Systems Based on Optimized Backstepping Technique

In this article, an adaptive optimized control scheme based on neural networks (NNs) is developed for a class of perturbed strict-feedback nonlinear systems. An optimized backstepping (OB) technique is employed for breaking through the limitation of the matching condition. The disturbance of existing nonlinear systems may degrade system performance or even lead to instability. In order to improve the system's robustness, a disturbance observer is constructed to compensate for the impact coming from the external disturbance. Because the proposed optimized scheme needs to train the adaptive parameters not only for reinforcement learning (RL) but also for the disturbance observer, it will become more challenging no matter designing the control algorithm or deriving the adaptive updating laws. Finally, by virtue of the Lyapunov stability theory, it is proved that all internal signals of the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the validity of the devised method.