A discussion of the occurrence of processes having state vectors of high dimension, a major difficulty in achieving a successful systematic approach to the study of control processes by means of dynamic-programming theory. However difficult the problem is for systems ruled by a finite set of differential equations, it is several orders of magnitude more complex for systems of infinite dimensionality and for systems with time lags. By combining a technique for dealing with finite- dimensional systems and various methods of successive approximations and quasilinearization, certain classes of control processes associated with infinite dimensional systems can be treated. The ideas are illustrated by examining not only the control of a system involving a time lag, but also the control of a thermal system. 12 pp.
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