严格反馈非线性系统预设性能backstepping 控制器设计

针对一类具有一般形式的严格反馈非线性系统,提出一种基于预设性能的backstepping控制器设计方法.所谓预设性能是指在保证跟踪误差收敛到一个预先设定的任意小的区域的同时,保证收敛速度及超调量满足预先设定的条件.首先引入性能函数的概念,通过误差转化将原始的受限系统转换为等价的非受限系统;然后基于Lyapunov理论进行backstepping控制器的设计,并进行了稳定性分析;最后通过仿真实验验证了所提出方法的正确性.

Prescribed performance backstepping control of strict feedback nonlinear systems

For a class of strick feedback nonlinear systems with guaranteed prescribed performance, a backstepping controller is designed. The prescribed performance means that the tracking error should converge to an arbitrarily predefined small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. A performance function and an output error transformation are introduced to transform the original ‘constrained’ system into an equivalent ‘unconstrained’ one. Based on the Lyapunov stability theory, a backstepping controller is designed and the system is stable according to the stability analysis. The simulation results show the correctness of proposed scheme.