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The purpose of this paper is to find the optimal control for a class of distributed parameter systems modeled by a stochastic partial differential equation of parabolic type. Uncertainties existing in both system parameters and the boundary state are considered. First, existence and uniqueness properties of the solution to the state equation are discussed within the framework of the function space concept. Secondly, the optimal, control signal is derived so as to minimize the quadratic cost functional. Furthermore, mathematical properties of the control gain function determined by solving the operator differential equation are studied in detail. Finally, for the purpose of supporting the theoretical aspects developed here, an example is shown including results of digital simulation experiments.