
Accession Number : AD0489159
Title : OPTIMAL CONTROL OF CONTINUOUSTIME STOCHASTIC SYSTEMS.
Descriptive Note : Research rept.,
Corporate Author : CALIFORNIA UNIV BERKELEY ELECTRONICS RESEARCH LAB
Personal Author(s) : Mortensen, R. E.
Report Date : 19 AUG 1966
Pagination or Media Count : 108
Abstract : This report is concerned with determining the optimal feedback control for continuoustime, continuousstate, stochastic, nonlinear, dynamic systems when only noisy observations of the state are available. At each instant of time, the current value of the control is a functional of the entire past history of the observations. The principal mathematical apparatus used in this investigation is the following: (1) the theory of probability measures and integration on infinite dimensional function spaces, (2) the Ito stochastic calculus for differentiation and integration of random functions, (3) the Frechet derivative of a functional on an infinite dimensional function space, and (4) dynamic programming. In Sections I and II, items (1) and (2) above are used to establish rigorously sufficient conditions for the existence of a conditional probability density for the current state of the system given the entire past history of the observations. A rigorous derivation is then given of a stochastic integral equation which is obeyed by an unnormalized version of the desired conditional density. In Section III, items (3) and (4) above are used heuristically to obtain a stochastic HamiltonJacobi equation in function space. It is shown that the solution of this equation would yield the desired feedback control. (Author)
Descriptors : (*CONTROL SYSTEMS, OPTIMIZATION), FUNCTIONAL ANALYSIS, DYNAMIC PROGRAMMING, FEEDBACK, NONLINEAR SYSTEMS, PROBABILITY, STOCHASTIC PROCESSES, INTEGRAL EQUATIONS, DIFFERENTIAL EQUATIONS, INTEGRALS, STATISTICAL PROCESSES, TIME.
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE