Summary: I. A synthesis is given for optimal control of processes described by a system of linear partial differential equations, some of which contain no derivatives with respect to time. Magnetohydrodynamics and several other processes are of this type. Control is based on minimizing the integral square deviation of variables characterizing the state of the object of control. We consider both finite and infinite time intervals, and the variational problem is reduced to the solution of a boundary-value problem. It is shown that the dynamic programming method and the classical Lagrange multiplier method yield the same results. Necessary and sufficient conditions for optimization are derived.
II. The general method set forth in Part I is applied to the synthesis of the optimum control of the boundary layer of an electrically conductive, incompressible fluid on a flat plate. Control is accomplished by means of a magnetic field directed perpendicularly to the plate.