抛物系统时间最优控制问题有限维逼近的误差估计

刘康生,黄景芳,于欣

系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 311-325.

PDF(334 KB)
PDF(334 KB)
系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 311-325. DOI: 10.12341/jssms13590
论文

 抛物系统时间最优控制问题有限维逼近的误差估计

    刘康生1,黄景芳1,于欣2
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Error Estimates of Finite Dimensional Approximations for the Time Optimal Control Problems of Parabolic Systems

    LIU Kangsheng1 ,HUANG Jingfang1 ,YU Xin2
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摘要

论文研究了一种抽象抛物系统时间最优控制问题的有限维逼近的误差估计. 基于抽象空间到有限维空间的正交投影逼近, 文章设计了有限维逼近问题. 证明了逼近问题的最优时间和最优控制的收敛性, 得到了最优时间的误差估计. 最后给出了有限元逼近和谱逼近的应用例子.

Abstract

This paper is devoted to the study of error estimates of finite dimensional approximations for the time optimal control problems of abstract parabolic systems. Firstly, based on the orthogonal projection approximation from abstract space to finite dimensional space, we design the finite dimensional approximation problem. Then we derive the convergence of optimal time and optimal control. Moreover, the error estimate for the optimal time is obtained. Finally, we give some application examples for the finite element approximation and spectral method approximation.

关键词

时间最优控制问题 /   / 有限维逼近 / 误差估计 / Pontryagin 最大值原理 /   / 唯一延拓性.

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刘康生 , 黄景芳 , 于欣.  抛物系统时间最优控制问题有限维逼近的误差估计. 系统科学与数学, 2019, 39(2): 311-325. https://doi.org/10.12341/jssms13590
LIU Kangsheng , HUANG Jingfang , YU Xin. Error Estimates of Finite Dimensional Approximations for the Time Optimal Control Problems of Parabolic Systems. Journal of Systems Science and Mathematical Sciences, 2019, 39(2): 311-325 https://doi.org/10.12341/jssms13590
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