一类非线性纯反馈系统的预定性能控制器设计

Design of prescribed performance controller for a class of nonlinear pure feedback systems

研究一类非线性纯反馈系统的预定性能控制问题.首先,为了避免采用繁琐的公式计算来处理纯反馈系统中的非仿射性结构,提出一种非传统状态变换并引入关于控制输入的一阶辅助系统;然后,为了保证纯反馈系统预定性能,设计一个相对简易的Lyapunov函数,利用反步法给出一种新的控制算法.实验仿真表明,所设计的控制器可使非线性系统状态全局有界,且可保证系统的预定性能,与现有的方法相比,其跟踪误差精度有显著提高,同时也具有一定鲁棒性.

An issue with regards to the predetermined performance control of a class of non-linear pure feedback system is studied. Firstly, to avoid using thecumbersome formula to handle the non-affine structure of the pure feedback system,a type of non-traditional state transformation is proposed and a first order auxiliary system for controlling input is introduced. Secondly, to ensure the predetermined performance of the pure feedback system, a fairly simple Lyapunov function is designed and a new controlling algorithm based on the Backstepping method is proposed. Finally, the simulation results show that, the designed controller is able to make the state of the non-linear system bounded globally, and to guarantee the predetermined performance of the system. Compared with the conventional methods, the approach proposed here can significantly improve the accuracy of the tracking error and have some certain robustness.