Optimal Control of Hyperbolic H-Hemivariational Inequalities With State Constraints

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

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LU Wei-gang, GUO Xing-ming, ZHOU Shi-xing. Optimal Control of Hyperbolic H-Hemivariational Inequalities With State Constraints[J]. Applied Mathematics and Mechanics, 2004, 25(7): 661-666.

Citation:

LU Wei-gang, GUO Xing-ming, ZHOU Shi-xing. Optimal Control of Hyperbolic H-Hemivariational Inequalities With State Constraints[J]. Applied Mathematics and Mechanics, 2004, 25(7): 661-666.

Citation:

LU Wei-gang, GUO Xing-ming, ZHOU Shi-xing. Optimal Control of Hyperbolic H-Hemivariational Inequalities With State Constraints[J]. Applied Mathematics and Mechanics, 2004, 25(7): 661-666.

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Optimal Control of Hyperbolic H-Hemivariational Inequalities With State Constraints

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

Received Date: 2003-01-16
Rev Recd Date: 2004-03-20
Publish Date: 2004-07-15

Abstract

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.
- H-hemivariational inequality,
- optimal control,
- state constraint,
- nonnomotone multivalued mapping

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References(16)

References

[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. doi: 10.1016/0362-546X(91)90224-O
[3]	Friedman A.Optimal control for variational inequalities[J].SIAM J Control Optim,1986,24:439—451. doi: 10.1137/0324025
[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. doi: 10.1016/0362-546X(93)E0022-U
[7]	WANG Geng-sheng.Optimal control of parabolic variational inequality involving state constraint[J].Nonlinear Anal,2000,42(5):789—801. doi: 10.1016/S0362-546X(99)00124-8
[8]	Arada N,Raymond J P.Optimal control problems with mixed control-state constraints[J].SIAM J Control Optim,2000,39(5):1391—1407. doi: 10.1137/S0363012999357926
[9]	HE Zheng-xu.State constrained control problems governed by variational inequality[J].SIAM J Control Optim,1987,25(5):1119—1144. doi: 10.1137/0325061
[10]	Tiba D.Optimality conditions for distributed control problems with nonlinear state equation[J].SIAM J Control Optim,1985,23(1):85—110. doi: 10.1137/0323008
[11]	Mignot F,Puel J P.Optimal control in some variational inequalities[J].SIAM J Control Optim,1984,22(3):466—476. doi: 10.1137/0322028
[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]	郭兴明，周世兴.抛物型变分不等式的最优控制[J].应用数学和力学，2003,24(7):669—674.
[14]	CHANG Kung-ching.Variational methods for non-differentiable functionals and their applications to partial differential equations[J].J Math Anal Appl,1981,80(1):102—129. doi: 10.1016/0022-247X(81)90095-0
[15]	GUO Xing-ming.On existence and uniqueness of solution of hyperbolic differential inclusion with discontinuous nonlinearity[J].J Math Anal Appl,2000,241(2):198—213. doi: 10.1006/jmaa.1999.6637
[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. doi: 10.1155/S0161171201003994