On optimal computer control

This paper is concerned with the optimal computer control of a linear dynamic element of plant. It is required that the outputs of the plant exactly equal a set of desired outputs at the uniformly spaced time instants,
t, t_{N}, t_{2N}, ...
. The system is optimal in the sense that a quadratic form of the control effort, which is proportional to the control energy, is a minimum. The optimal system is shown to be a linear, periodically time-varying feedback system, in which the generation of the control input is related to the solution of the adjoint equations of the plant. The paper concludes with a discussion of the effects of uncontrolled inputs and certain problems encountered in making the system adapt to slow parameter variations. This paper is to be published in the Proceedings of the First IFAC Moscow Congress by Butterworth Scientific Publications in 1960.