Since optimal control problems for distributed parameter systems are intimately connected to optimal control problems described by partial differential equations and require a treatment in function spaces, there is a great difficulty to solve these problems directly. Consequently it is considered to be necessary to obtain approximating solutions by nummerical computation. In computing a numerical solution of a partial differential equation, an approximating method in which differential operator is replaced by a difference operator is widely used. A similar approximating procedure is commonly used in calculating an optimal control in systems with distributed parameters. Convergency conditions of a sequence of approximating solutions for the optimal control problems of distributed parameter systems are given in this paper.
Hitoshi Sasai (Fri,) studied this question.