OPTIMAL RELAXED CONTROL OF DISSIPATIVE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN BANACH SPACES

被引：17

作者：

Brzezniak, Zdzislaw ^{[1
]}

Serrano, Rafael ^{[2
]}

机构：

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Univ Rosario, Fac Econ, Bogota, Colombia

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 03期

关键词：

relaxed control; stochastic PDE; multiplicative cylindrical noise; stochastic convolution; UMD type-2 Banach spaces; Young measures; Suslin control set; EVOLUTION-EQUATIONS; EXPONENTIAL ERGODICITY; PARABOLIC EQUATIONS; EXISTENCE; RELAXATION; CONVERGENCE; POWERS;

D O I：

10.1137/100788574

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type condition with respect to the state variable. The main tools of our study are the factorization method for stochastic convolutions in UMD type-2 Banach spaces and certain compactness properties of the factorization operator and of the class of Young measures on Suslin metrizable control sets.

引用

页码：2664 / 2703

页数：40

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