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The optimal control theory is an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. It has various important applications in many fields as engineering, mathematics and economics, etc. In this book, we focus on the optimal control for Neumann and Dirichlet stochastic elliptic systems in scalar case and in non-cooperative system.