
Accession Number : ADA135134
Title : Algorithms, Modeling and Estimation for Linear Systems.
Descriptive Note : Final technical rept. 1 Apr 7931 May 83,
Corporate Author : KENTUCKY UNIV LEXINGTON DEPT OF MATHEMATICS
Personal Author(s) : Lindquist,A
PDF Url : ADA135134
Report Date : May 1983
Pagination or Media Count : 27
Abstract : Modeling of linear stochastic systems leads to the stochastic realization problem. In this project the author develops a comprehensive theory of stochastic realization. Such a theory should be the centerpiece of stochastic systems theory. First he studies the problem from a coordinatedependent point of view. Secondly, he develops a geometric theory of Markovian representation, which also accomodates infinitedimensional systems. In this framework a unified theory of smoothing is provided, the basic idea being to embed the given stochastic system in a class of similar systems all having the same output process and the same KalmanBucy filter. This approach provides stochastic interpretations of many important smoothing procedures. The factorizations of the matrix Riccati equation underlying fast (nonRiccati) algorithms are analized in the context of Hamiltonian systems, and certain aspects of the algebraic Riccati equation are studied, as is the concept of invariant directions of the matrix Riccati equation. A unified approach to the partial realization problem is taken, incorporating ideas from numerical linear algebra. Also studied are questions of stability of partial realizations. Finally, a statistical approach to stochastic optimization is presented, and convergence results for algorithms based on stationary data are obtained.
Descriptors : *Linear systems, *Stochastic processes, *Mathematical models, Algorithms, Estimates, Matrices(Mathematics), Riccati equation, Optimization, Stochastic control, Kalman filtering, Hamiltonian functions, Linear algebra, Stability, Statistical processes
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE