On Adaptive Control Processes with Computing Time Delay

Abstract

In the theory of R. Bellman's adaptive control processes, computing time to yield optimal control signal from data obtained during normal operation is ideally regarded to be zero. There will be, however, cases where the computing time delay may not be neglected.
The subject of this paper is the optimal control policy for adaptive control processes in the case where certain computing time delay is assumed in advance. Functional equations to get such an optimal control policy are described in a fairly general form. These equations ara also shown to be applicable to stochastic control processes and deterministic control processes. Two simple examples are presented to illustrate the application of the method.