Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
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. © 2013 Society for Industrial and Applied Mathematics.
Control set ; Multiplicative cylindrical noise ; Relaxed control ; Stochastic PDE ; Young measure ; Convolution ; Equations of state ; Factorization ; Nonlinear equations ; Optimization ; Stochastic systems ; Banach spaces ; Multiplicative cylindrical noise ; Relaxed control ; Stochastic convolution ; Stochastic PDE ; Suslin control set ; UMD type-2 Banach spaces ; Young measures ;
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