Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces. (English) Zbl 1283.60092

Brzeźniak, Zdzisław; Serrano, Rafael

SIAM J. Control Optim. 51, No. 3, 2664-2703 (2013).

The authors consider controlled semilinear stochastic evolution equations in Banach spaces, driven by cylindrical Wiener processes. The drift coefficient satisfies a dissipative-type condition with respect to the state variable. To prove the existence of an optimal weak relaxed control, the authors apply a factorization method of stochastic convolutions.
The results are illustrated by examples that cover a class of stochastic reaction-diffusion equations with multiplicative noise.

Reviewer: Alexandra Rodkina (Kingston/Jamaica)

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
49J20	Existence theories for optimal control problems involving partial differential equations
93E20	Optimal stochastic control

Keywords:

relaxed control; stochastic partial differential equation; multiplicative cylindrical noise; stochastic convolution