OPTIMAL CONTROL WITH Lp(Ω), p ε [0,1), CONTROL COST

被引：35

作者：

Ito, Kazufumi ^{[1
]}

Kunisch, Karl ^{[2
]}

机构：

[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[2] Karl Franzens Univ Graz, Inst Math & Wissenscahftl Rechnen, A-8010 Graz, Austria

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2014年 / 52卷 / 02期

基金：

奥地利科学基金会;

关键词：

L-0; minimization; optimal control; bang-bang control; sparsity optimization; maximum principle; nonsmooth optimization; primal-dual active set method; ELLIPTIC CONTROL-PROBLEMS; ALGORITHM;

D O I：

10.1137/120896529

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

L-p optimal control with p is an element of [0, 1) is investigated. The difficulty of natural lack of convexity and thus of weak lower semicontinuity is addressed by introducing appropriately chosen regularization terms. Existence results and necessary optimality conditions are obtained, and convergence of a monotone scheme is proved. Special attention is given to the particular case of optimal control problems with quadratic tracking and regularized L-0 control costs are given. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved, and an estimate on the consequences of relaxation are estimated.

引用

页码：1251 / 1275

页数：25

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