Pontryagin's principle for state-constrained control problems governed by parabolic equations with unbounded controls

被引：75

作者：

Raymond, JP ^{[1
]}

Zidani, H ^{[1
]}

机构：

[1] Univ Toulouse 3, Lab MAP, URN CARS 9974, F-31062 Toulouse 4, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1998年 / 36卷 / 06期

关键词：

optimal control; nonlinear boundary controls; semilinear parabolic equations; state constraints; Pontryagin's minimum principle; unbounded controls;

D O I：

10.1137/S0363012996302470

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper deals with optimal control problems governed by semilinear parabolic equations with pointwise state constraints and unbounded controls. Under some strong stability assumption, we obtain necessary optimality conditions in the form of a Pontryagin's minimum principle in qualified form. A Pontryagin's principle in nonqualified form is also proved without any stability condition.

引用

页码：1853 / 1879

页数：27

共 42 条

[1] OPTIMALITY CONDITIONS FOR SOME NONQUALIFIED PROBLEMS OF DISTRIBUTED CONTROL [J].

ABERGEL, F ;

TEMAM, R .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (01) :1-12

[2]

Ahmed NU., 1981, Optimal Control of Distributed Parameter Systems

[3] Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls [J].

Alibert, JJ ;

Raymond, JP .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1997, 18 (3-4) :235-250

[4]

[Anonymous], SIAM J CONTROL OPTIM

[5]

AZE D, 1995, P 2 CAT DAYS APPL MA, P12

[6]

AZE D, IN PRESS AN STIINT U

[7]

Barbu V., 1993, ANAL CONTROL NONLINE

[8] OPTIMAL-CONTROL OF PARABOLIC PROBLEMS WITH STATE CONSTRAINTS - A PENALIZATION METHOD FOR OPTIMALITY CONDITIONS [J].

BERGOUNIOUX, M .

APPLIED MATHEMATICS AND OPTIMIZATION, 1994, 29 (03) :285-307

[9] CALMNESS AND EXACT PENALIZATION [J].

BURKE, JV .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1991, 29 (02) :493-497

[10] CONTROL OF AN ELLIPTIC PROBLEM WITH POINTWISE STATE CONSTRAINTS [J].

CASAS, E .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1986, 24 (06) :1309-1318

← 1 2 3 4 5 →