An LMI approach for robust Iterative Learning Control with Quadratic performance criterion
An LMI approach for robust Iterative Learning Control with Quadratic performance criterion
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DOI：
10.1109/icarcv.2008.4795802
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发表时间：
2008-12
期刊：
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通讯作者：
D. H. Nguyen;D. Banjerdpongchai
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文献类型：
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作者：
D. H. Nguyen;D. Banjerdpongchai
针对具有加性不确定性的线性系统，提出了基于二次性能准则的迭代学习控制设计方法。稳健的Q-ILC设计可以归结为一个极小极大问题。我们提出了一种新的方法，它利用最坏情况误差的上界，然后建立一个非凸二次最小化问题来获得迭代控制输入的更新。应用朗格朗日对偶，非凸二次问题的拉格朗日对偶函数等价于线性矩阵不等式(LMI)上的凸优化。在此基础上，给出了鲁棒Q-ILC的一个具有收敛性质的LMI算法。最后，给出了一个数值算例，说明了该方法的有效性。
This paper presents the design of iterative learning control based on Quadratic performance criterion (Q-ILC) for linear systems subject to additive uncertainty. Robust Q-ILC design can be cast as a min-max problem. We propose a novel approach which employs an upper bound of the worst-case error, then formulates a nonconvex quadratic minimization problem to get the update of iterative control inputs. Applying Langrange duality, the Lagrange dual function of the nonconvex quadratic problem is equivalent to a convex optimization over linear matrix inequalities (LMIs). An LMI algorithm with convergence properties is then given for the robust Q-ILC. Finally, we provide a numerical example to illustrate the effectiveness of the proposed method.