引用本文:赵清梅, 张俊容.最优控制问题的Tikhonov正则化[J].西南大学学报(自然科学版),2019,41(5):59~63
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最优控制问题的Tikhonov正则化
赵清梅, 张俊容
西南大学 数学与统计学院, 重庆 400715
摘要:
主要研究了约束线性二次最优控制问题.通过一阶最优性条件将它等价地转化为单调变分不等式问题,并利用变分不等式的Tikhonov正则化方法研究了约束线性二次最优控制问题的正则化,证明了扰动问题的解收敛到原问题的最小范数解.
关键词:  CLQ问题|变分不等式|Tikhonov正则化|扰动问题
DOI:10.13718/j.cnki.xdzk.2019.05.010
分类号:O232
基金项目:国家自然科学基金项目(11701470).
The Tikhonov Regualization of the Optimal Control Problem
ZHAO Qing-mei, ZHANG Jun-rong
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Abstract:
In this paper, the problem of linear quadratic (LQ) optimal control with constraint is discussed. First, this problem is equivalently converted to a monotonic variational inequality problem through first-order optimality conditions. Then, by the Tikhonov regularization method of variational inequalities, the regularization of the problem is studied. Finally, we prove that the solution of the perturbation problem converges to the minimum norm solution of the original problem.
Key words:  CLQ problem|variational inequality|Tikhonov regularization|perturbation problem
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