含有参数化和非参数化不确定性系统重复学习控制

Repetitive learning control for nonlinear systems with both parametric and non-parametric uncertainties systems

针对含有参数化和非参数化的高阶非线性系统,设计了一种重复学习控制方案.假设未知时变参数和参考信号的共同周期是已知的,通过参数重组技巧,将所有未知时变项合并为一个周期时变向量.将改进Backstepping方法与分段积分机制相结合,构造了微分-差分参数自适应律和重复学习控制律,使跟踪误差在误差平方范数意义下渐近收敛于零.利用Lyapunov泛函,给出了闭环系统收敛的充分条件.仿真结果验证了该方法的有效性.

A repetitive learning control scheme is designed for high-order nonlinear systems with parametric and nonparametric uncertainties.It is assumed that the common periodicity of unknown time-varying parameter and reference signal are known.By regrouping the system parameters,all unknown time-varying terms are combined into a periodically time-varying vector.Combining the modifying backstepping approach with the pointwise integral mechanism,a differentialdifference mixed-type adaptive law and an adaptive repetitive learning control one are constructed to ensure the asymptotic convergence of the tracking error in the sense of square error norm.Also,a sufficient condition of the convergence of the method is given.A simulation example shows the effectiveness of the proposed method.