基于伪逆模型的线性系统自适应迭代学习控制

Adaptive iterative learning control for linear systems based on pseudo-inverse model

为了解决因系统参数未知而导致传统的P-型、D-型ILC算法的收敛性条件无法获取和最优ILC控制律无法构建问题,提出一种基于伪逆模型的自适应迭代学习控制策略。通过最小化实际系统输出与估计系统输出之间的误差,对系统参数矩阵提出估计方案。将估计的系统参数矩阵的逆矩阵引入到控制律设计过程中。结果表明:所提算法的跟踪误差单调收敛到零。数值仿真验证了所提算法的有效性和理论分析的正确性。

In order to solve the problem that the convergence conditions of traditional P-type and D-type ILC algorithms cannot be obtained and the optimal ILC control law cannot be constructed due to unknown system parameters,an adaptive iterative learning control strategy based on pseudo-inverse model is proposed.By minimizing the error between the actual system output and the estimated system output,an estimated scheme is proposed for the system parameter matrix.The inverse matrix of the estimated system parameter matrix is introduced into the control law design process.The results show that the tracking error of the proposed algorithm converges monotonically to zero.Numerical simulation verifies the effectiveness of the proposed algorithm and the correctness of theoretical analysis.