Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces

Zdzislaw Brzeźniak, Rafael Serrano

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2664-2703
Number of pages40
JournalSIAM Journal on Control and Optimization
Volume51
Issue number3
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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