具有混合控制状态约束的热方程稀疏最优控制

IF 0.9 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2020-09-01 DOI:10.3934/mcrf.2020007

E. Casas, F. Tröltzsch

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引用次数: 3

摘要

A problem of sparse optimal control for the heat equation is considered, where pointwise bounds on the control and mixed pointwise control-state constraints are given. A standard quadratic tracking type functional is to be minimized that includes a Tikhonov regularization term and the \begin{document}$ L^1 $\end{document} -norm of the control accounting for the sparsity. Special emphasis is laid on existence and regularity of Lagrange multipliers for the mixed control-state constraints. To this aim, a duality theorem for linear programming problems in Hilbert spaces is proved and applied to the given optimal control problem.

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Sparse optimal control for the heat equation with mixed control-state constraints

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.