On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths
On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths
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DOI：
10.1016/j.cam.2015.10.028
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
Shengda Liu;A. Debbouche;Jinrong Wang
中科院分区：
文献类型：
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作者：
Shengda Liu;A. Debbouche;Jinrong Wang
本文介绍了一类新的涉及伯努利分布的随机脉冲微分方程。为了跟踪随机不连续轨迹，通过零阶保持器定义了与分段连续变量相关的修正跟踪误差。随后，还设计了一种采用全局和局部迭代平均算子的随机ILC方案。利用数学分析工具通过脉冲Gronwall不等式获得了保证修正跟踪误差收敛的充分条件。最后，提出了两个说明性示例来证明平均 ILC 方案跟踪随机不连续轨迹的性能和有效性。
In this paper, a new class of stochastic impulsive differential equations involving Bernoulli distribution is introduced. For tracking the random discontinuous trajectory, a modified tracking error associated with a piecewise continuous variable by zero-order holder is defined. In the sequel, a new random ILC scheme by adopting global and local iteration average operators is designed too. Sufficient conditions to guarantee the convergence of modified tracking error are obtained by using the tools of mathematical analysis via an impulsive Gronwall inequality. Finally, two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ILC scheme to track the random discontinuous trajectory.