OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (7): 723-729.

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OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

陆伟刚, 郭兴明, 周世兴

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

收稿日期:2003-01-06 修回日期:2004-03-20 出版日期:2004-07-18 发布日期:2004-07-18
通讯作者: GUO Xing-ming(Corresponding author, Tel:+86-21-56331453;Fax:+86-21-36033287, E-mail:xmguo@yc.shu.edu.cn) E-mail:xmguo@yc.shu.edu.cn
基金资助:
the National Natural Science Foundation of China (19802012)

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

LU Wei-gang, GUO Xing-ming, ZHOU Shi-xing

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

Received:2003-01-06 Revised:2004-03-20 Online:2004-07-18 Published:2004-07-18
Supported by:
the National Natural Science Foundation of China (19802012)

摘要/Abstract

摘要： The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

关键词: H-hemivariational inequality, optimal control, state constraint, nonnomotone multivalued mapping

Abstract: The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnomotone multivalued mapping term are considered.The optimal solutions are obtained.In addition,their approximating problems are also studied.

Key words: H-hemivariational inequality, optimal control, state constraint, nonnomotone multivalued mapping

中图分类号:

陆伟刚;郭兴明;周世兴. OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 723-729.

LU Wei-gang;GUO Xing-ming;ZHOU Shi-xing . OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 723-729.

参考文献

[1] Panagiotopous P D. Hemivariational Inequalities, Applications in Mechanics and Engineering[M]. Berlin:Springer-Verlag, 1993.
[2] Panagiotopoulos P D. Coercive and semicoercive hemivariational inequalitis[J]. Nonlinear Anal, 1991, 16(3):209-231.
[3] Friedman A. Optimal control for variational inequalities[J]. SIAM J Control Optim, 1986, 24:439-451.
[4] Barbu V. Optimal Control of Variational Inequalities[M]. London:Pitman, 1983.
[5] Barbu V. Analysis and Control of Nonlinear Infinite Dimensional Sysems[M]. Academic Press:inc, 1993.
[6] Haslinger J, Panagiotopoulos P D. Optimal control of systems governed by hemivariational inequalities existence and approximation results[J]. Nonlinear Anal, 1995, 24(1):105-119.
[7] WANG Geng-sheng. Optimal control of parabolic variational inequality involving state constraint[J]. Nonlinear Anal, 2000, 42:789-801.
[8] Arada N, Raymond J P. Optimal control problems with mixed control-state constraints[J]. SIAM J Control Optim, 2000, 39(5):1391-1407.
[9] HE Zheng-xu. State constrained control problems governed by variational inequality[J]. SIAM J Control Optim, 1987, 25(5):1119-1144.
[10] Tiba D. Optimality conditions for distributed control problems with nonlinear state equation[J]. SIAM J Control Optim, 1985, 23(1):85-110.
[11] Mignot F, Puel J P. Optimal control in some variational inequalities[J]. SIAM J Control Optim, 1984, 22:466-476.
[12] Frederic Bonnans, Eduardo Casas. An extension of pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities[J]. SIAM J Control Optim, 1995, 33(1):271-298.
[13] GUO Xing-ming, ZHOU Shi-xing. Optimal control of parabolic variational inequalities with state constraints[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(7):756- 762.
[14] CHANG Kung-ching. Variational methods for non-differentiable functionals and their applications to partial differential equations[J]. J Math Anal Appl, 1981, 80:102-129.
[15] GUO Xing-ming. On existence and uniqueness of solution of hyperbolic differential inclusion with discontinuous nonlinearity[J]. J Math Anal Appl, 2000, 241:198-213.
[16] GUO Xing-ming. The initial boundary value problem of a mixed-typed hemivariational inequality[J]. Internat J Math Math Sci, 2001, 25(1):43-52

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

OPTIMAL CONTROL OF HYPERBOLIC H-HEMIVARIATIONAL INEQUALITIES WITH STATE CONSTRAINTS

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