Linear optimal control problem for discrete 2-D systems with constraints

Optimal control problem for linear two-dimensional (2-D) discrete systems with mixed constraints is investigated. The problem under consideration is reduced to a linear programming problem in appropriate Hilbert space. The main duality relation for this problem is derived such that the optimality conditions for the control problem are specified by using methods of the linear operator theory. Optimality conditions are expressed in terms of solutions for conjugate system.