H. J. Kushner has obtained the differential equationsatisfied by the optimal feedback control law for astochastic control system in which the plant dynamicsand observations are perturbed by independent additiveGaussian white noise processes. However, the differentiationincludes the first and second functional derivatives and,except for a restricted set of systems, is too complex tosolve with present techniques.
This investigation studies the optimal control lawfor the open loop system and incorporates it in a sub-optimal feedback control law. This suboptimal controllaw's performance is at least as good as that of theoptimal control function and satisfies a differentialequation involving only the first functional derivative.The solution of this equation is equivalent to solvingtwo two-point boundary valued integro-partial differentialequations. An approximate solution has advantages overthe conventional approximate solution of Kushner's equation.
As a result of this study, well known results ofdeterministic optimal control are deduced from the analysisof optimal open loop control.
