In recent years considerable advances in the field of “optimal control” have been made. The impetus behind many of these advances has been derived from a growing demand that not only is it desirable, but also essential, that the design of a control system be optimised. This is particularly true of the aerospace industry in which the specification laid before the control systems designer usually demands the best possible performance for minimum cost (be that cost financial, on fuel, or on weight). Short of a major technological innovation, the problem becomes one of finding some means of meeting an ever increasing demand for performance, using existing technology. More attention has therefore been given in recent years to the study of optimal control, particularly since the advent of high speed, sophisticated scientific digital computers. Two of the major areas which have been explored have been the optimal design of systems, according to a quadratic performance criterion, and non-linear programming techniques. These are briefly discussed in Section 3 of this paper.