System Identification and Filtering of Nonlinear Controlled Markov Processes by Canonical Variate Analysis.

摘要

In this Phase I SBIR study, new methods are developed for the system identification and stochastic filtering of nonlinear controlled Markov processes. Currently available methods are restricted to very special forms or provide poor approximations to optimal procedures. The feasibility of using state space Markov process models and canonical variate analysis (CVA) for obtaining optimal nonlinear procedures for system identification and stochastic filtering is demonstrated. The theory of nonlinear CVA of Markov processes is developed in terms of a Hilbert space of nonlinear functions, and the multivariate nonlinear CVA is reduced to a sequential selection problem involving a univariate nonlinear CVA - the maximal correlation problem. The theory of maximal correlation, previously developed for Hilbert spaces of nonlinear functions, guarantees the existence of solutions to the multivariate CVA problem. A state space innovations representation for the Markov process is developed in terms of the canonical variable states. Extensions to the selection of a minimal rank state and interpretation of the canonical variable in terms of optimal normalizing transformations is developed. Computational algorithms are developed for determination of the canonical variable states, state space model fitting, and construction of nonlinear stochastic filters. (KR)