On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths

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• 作者：Shengda Liu^a ; ^{thinksheng@foxmail.com" class="auth_mail" title="E-mail the corresponding author} ; Amar Debbouche^b ; ^{amardebbouche@yahoo.fr" class="auth_mail" title="E-mail the corresponding author} ; JinRong Wang^a ; ^{sci.jrwang@gzu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Iterative learning control ; Random impulsive differential equations ; Global average operator ; Local average operator ; Randomly varying trial length
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：312
• 期：Complete
• 页码：47-57
• 全文大小：738 K

文摘

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.