A functional analytic optimization technique is applied to the Problem of optimum scheduling of hydro-thermal power systems. The power system considered contains two hydro-plants on the same stream. The time delay of flow between upstream and downstream plants is taken into consideration. The problem is formulated as an abstract minimum norm problem. The optimal solution found here satisfies the necessary conditions of variational calculus for control problems with delayed arguments. A generalized contraction mapping technique is applied to a sample system to illustrate the results obtained.