A major difficulty in the way of a successful systematic approach to the study of control processes by way of the theory of dynamic programming is the occurrence of processes having state vectors of high dimension. 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 presented earlier for dealing with finite dimensional systems and various methods of successive approximations and quasi-linearization, certain classes of control processes associated with infinite dimensional systems can be treated. The ideas are illustrated by discussing control of a system involving a time lag and control of a thermal system.

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