Abstract: A novel control approach based on the combination of back-stepping design and nonlinear proportional control is presented for a class of uncertain pure feedback systems. Based on the double performance functions, the nonlinear proportional controller is developed. Meanwhile, during every step of back-stepping, a Nussbaum function and a nonlinear proportional controller are adopted to construct the nonlinear proportional back-stepping controller to satisfy the requirements of unknown parameters, unknown structure, unknown control direction, unknown initial states and prescribed performance. The design procedure and structure of the proposed scheme are very simple with least adjustable parameters. Finally, the stability of the close-loop system is proved based on Lyapunov stability theorem. The simulation results demonstrate the feasibility and validity of the proposed control schemes.

Key words: Non-affine pure feedback systems, back-stepping, nonlinear proportional control, prescribed performance, unknown control direction

摘要：

针对一类不确定非仿射纯反馈系统，结合反演法、Nussbaum函数和非线性比例控制器，提出了一种新的控制器设计方案。该方案基于双性能函数设计非线性函数以构建非线性比例控制器，同时在反演设计中的每一步引入Nussbaum函数以满足系统结构和参数未知、控制方向未知、初始状态未知及预设性能控制的需求。所设计的控制器结构极为简单，在线调整的参数个数极少。最后，基于Lyapunov稳定性定理证明了闭环系统所有信号一致有界。仿真结果验证了所设计控制方案的可行性与有效性。

关键词: 非仿射纯反馈系统, 反演法, 非线性比例控制, 预设性能, 控制方向未知