含有参数化和非参数化不确定性系统重复学习控制

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.

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

A repetitive learning control scheme is designed for high-order nonlinear systems with parametric and non-
parametric 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 differential-
difference 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.