具有未知控制方向的输出反馈自适应学习控制

针对具有未知控制方向的工作于重复条件下的参数化输出反馈高阶非线性系统,提出一种自适应重复学习控制方法.利用连续Nussbaum增益方法解决系统中控制方向即高频增益符号未知的问题.在针对高阶非线性系统的自适应反步控制器设计过程中,使用综合时域自适应以及迭代域自适应的微分-差分自适应律对未知参数进行估计.利用李雅普诺夫稳定理论证明,在所提出的重复学习控制律作用下,系统的输出轨迹沿迭代轴逐点渐近收敛于期望轨迹.数值仿真结果表明,所提出的方法能够在解决控制方向未知问题的同时,保证输出反馈高阶非线性系统的收敛性.

Output-feedback adaptive learning control with unknown control direction

An adaptive repetitive learning control method was proposed for parametric output-feedback high-order nonlinear systems with unknown control direction under the repeatable environment. The continuous Nussbaum gain method was incorporated to tackle the difficulties associated with the unknown high-frequency gain sign. A differential-difference adaptation law which combined both the time-domain and the iteration-domain adaptations was introduced to learn the unknown parameters in the backward recursive design for the high-order nonlinear systems. The rigorous proof based on Lyapunov stability theory was presented to show that the system output could converge to the desired trajectory asymptotically along the iteration axis under the proposed control scheme. A numerical simulation demonstrates that the proposed control method can not only deal with the unknown control direction but also ensure the convergence of parametric output-feedback high-order nonlinear systems.