Model reduction and system identification for master equation control systems

Author

Gallivan, MarthaA ; Murray, RichardM

Author_Institution

Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA, USA

Volume

4

fYear

2003

fDate

4-6 June 2003

Firstpage

3561

Abstract

A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear-like structure and an often-high dimension. We develop a model reduction approach in which the number of possible configurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones. Error bounds for the reduction are derived based on a minimum and maximum time scale of interest. An analogous linear identification procedure is then presented, which computes the state and output matrices for a predetermined configuration set. These ideas are demonstrated first in a finite-dimensional model inspired by problems in surface evolution, and then in an infinite-dimensional film growth master equation.

Keywords

identification; master equation; matrix algebra; nonlinear control systems; reduced order systems; statistical distributions; analogous linear identification procedure; bilinear-like structure; continuous time evolution; error bound; finite-dimensional model; master equation control system; model reduction; probability distribution; surface evolution; system identification; Control system synthesis; Differential equations; Ear; Fluctuations; Kinetic theory; Monte Carlo methods; Probability distribution; Reduced order systems; Stochastic processes; System identification;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2003. Proceedings of the 2003

ISSN

0743-1619

Print_ISBN

0-7803-7896-2

Type

conf

DOI

10.1109/ACC.2003.1244099

Filename

1244099