Optimized Backstepping Combined With Dynamic Surface Technique for Single-Input–Single-Output Nonlinear Strict-Feedback System
针对单输入单输出非线性严格反馈系统，提出将优化反步控制与动态面技术结合，通过简化强化学习算法避免微分爆炸问题，并用理论和仿真验证可行性。
In this article, for the single-input–single-output (SISO) nonlinear strict-feedback system, optimized backstepping (OB) control combined with the dynamic surface (DS) technique is developed. OB is to make every subsystem control of backstepping as the optimized one so as to ensure the entire backstepping control being optimized. However, the original design of OB still needs to repeatedly calculate the derivative of virtual controls, as a result, it will inevitably cause the problem of “differential explosion.” In order to alleviate the phenomenon, the OB control is combined with the DS technique. Furthermore, OB control needs to conduct with reinforcement learning (RL) in every backstepping step, hence simplifying the algorithm of RL is very necessary and substantive for achieving the combination. In this work, because the optimized control derives both critic and actor training laws by utilizing a simple positive function instead of the square of approximation of Hamilton–Jacobi–Bellman (HJB) equation, it can obviously simplify the RL algorithm to compare with the traditional optimizing methods. Finally, the feasibility is illustrated via both theory and simulation.