Accession Number : AD0489159

Title :   OPTIMAL CONTROL OF CONTINUOUS-TIME 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 continuous-time, continuous-state, 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 Hamilton-Jacobi 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