A Caltech Library Service

Stochastic Optimal Control


Early, Benjamin Nathaniel (1970) Stochastic Optimal Control. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2F63-GT04.


H. J. Kushner has obtained the differential equation satisfied by the optimal feedback control law for a stochastic control system in which the plant dynamics and observations are perturbed by independent additive Gaussian white noise processes. However, the differentiation includes the first and second functional derivatives and, except for a restricted set of systems, is too complex to solve with present techniques.

This investigation studies the optimal control law for the open loop system and incorporates it in a sub-optimal feedback control law. This suboptimal control law's performance is at least as good as that of the optimal control function and satisfies a differential equation involving only the first functional derivative. The solution of this equation is equivalent to solving two two-point boundary valued integro-partial differential equations. An approximate solution has advantages over the conventional approximate solution of Kushner's equation.

As a result of this study, well known results of deterministic optimal control are deduced from the analysis of optimal open loop control.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Electrical Engineering and Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Sridhar, Rangasami
Thesis Committee:
  • Unknown, Unknown
Defense Date:3 December 1969
Funding AgencyGrant Number
Record Number:CaltechTHESIS:08282015-143654533
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9122
Deposited By: Benjamin Perez
Deposited On:28 Aug 2015 21:52
Last Modified:31 Jul 2020 22:06

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page