An optimal control is giyen for regulating power distribution in a nuclear power reactor which has cylindrical geometry. The space dependence of the system is
described by expanding space depenident variables by
Helmholtz modes. Results are obtained through the principle
of optimality and are described by the Riccati-type algebraic equation that the optimal feedback coefficients
should satisfy. Use of an integral equation as the system
equation makes it possible to deal with actual controlling
apparatuses: control rods or rod clusters.