ABSTRACT
Unless the system equations, the performance index, and the constraints are quite simple, we must employ numerical methods to solve optimal programming and control problems. However, the amount of numerical computation required for even a relatively simple problem is forbidding if it must be done by hand. This is why the calculus of variations found very little use in engineering and applied science until quite recently. The development of economical, highspeed computers in the mid-1950’s has dramatically changed this situation. It is now possible to solve complicated optimal programming and control problems in a reasonable length of time and at a reasonable cost.
