论文标题
强大的单调收敛迭代学习控制设计：一种基于LMI的方法
Robust Monotonic Convergent Iterative Learning Control Design: an LMI-based Method
论文作者
论文摘要
这项工作研究了在时间和频域中不确定的线性系统的强大单调收敛迭代学习控制（ILC），并以$ L_ {2} $误差信号规范来优化收敛速度的ILC算法。首先，证明ILC系统的鲁棒单调收敛可以通过在某些集合上的矩阵多项式的正面确定性等效地建立。然后，提出了以正方形总和（SOS）形式进行正定确定性的必要条件，这是对线性矩阵不平等（LMI）的可行性的修正。基于这种条件，通过解决一组凸优化问题获得最大化收敛速度的最佳ILC算法。此外，可以任意选择学习函数的顺序，以便设计人员可以灵活地决定学习算法的复杂性。
This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error signals is derived. Firstly, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares (SOS) for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities (LMIs). Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.
