OPTIMAL DISTRIBUTED CONTROL OF STOCHASTIC ELLIPTIC SYSTEMS WITH CONSTRAINTS

The objective of this paper is to study the optimality for stochastic non cooperative elliptic systems. A distributed control problem for a stochastic elliptic systems with constraints on states and controls is studied. First, the existence and uniqueness of the state process for these systems are proved. The necessary and sufficient conditions of optimality are derived for the Dirichlet and Neumann problems.