Accession Number : AD0696156

Title :   CONSTANT DIRECTIONS OF THE RICCATI EQUATION.

Descriptive Note : Doctoral thesis,

Corporate Author : UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF AEROSPACE ENGINEERING

Personal Author(s) : Rappaport,David

Report Date : AUG 1969

Pagination or Media Count : 40

Abstract : An examination is made of the Riccati equation occurring in the optimization of a linear discrete-time autonomous free-control (noise-free) quadratic regulator with a scalar input, or equivalently by the duality of optimal control and optimal filtering problems, that Riccati equation arising in the optimal filtering of a linear discrete-time autonomous augmented-state system driven by Gaussian white noise being observed by a noiseless scalar output (the colored noise problem). The research problem is defined as a search for 'constant directions' of the Riccati equation. A constant direction is a direction in which the Riccati equation reaches an equilibrium point in a finite time interval. Each such direction corresponds to a reduction in the dimension of the Riccati iteration. Necessary and sufficient conditions for the existence of constant directions are determined. These conditions comprise linear relations between the inner products of the system moments. It is shown that the existence of constant directions implies that in these directions dead-beat controls are optimal. In the dual optimal filtering problem constant directions are shown to correspond to a tapped delay line with constant tap gains. (Author)

Descriptors :   (*CONTROL SYSTEMS, OPTIMIZATION), (*DIFFERENTIAL EQUATIONS, NONLINEAR SYSTEMS), DIFFERENCE EQUATIONS, INFORMATION THEORY, MATRICES(MATHEMATICS), THEOREMS, THESES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE