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为加快迭代学习控制律的收敛速度,针对线性时不变(LTI)系统,以PD-型学习律为例,提出一种区间可调节的具有指数加速的迭代学习控制算法.首先,根据每次学习效果确定下一次迭代需要修正的区间并在该区间内修正控制律增益;然后,在Lebesgue-p范数意义下分析所提出算法的收敛性并给出其收敛条件;最后,通过理论分析表明,收敛速度主要取决于被控对象、控制律增益、修正指数和学习区间的大小.在相同仿真条件下,与传统算法相比,所提出算法具有更快的收敛速度.
In order to speed up the convergence rate of iterative learning control laws, an iterative learning control algorithm with exponential acceleration with adjustable interval is proposed for linear time-invariant (LTI) systems, taking PD-type learning law as an example. Firstly, The learning effect determines the interval to be corrected in the next iteration and corrects the control law gain in the interval. Then, the convergence of the proposed algorithm is analyzed and its convergence condition is given in the Lebesgue-p norm. Finally, the theoretical analysis shows that , The convergence speed depends on the controlled object, the control law gain, the correction index and the size of the learning interval.Compared with the traditional algorithm, the proposed algorithm has a faster convergence rate under the same simulation conditions.