Model reduction and system identification for master equation control systems

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,...

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Bibliographic Details
Main Authors: Gallivan, M.A., Murray, R.M.
Format: Conference Proceeding
Language:English
Subjects:
Control system synthesis
Differential equations
Ear
Fluctuations
Kinetic theory
Monte Carlo methods
Probability distribution
Reduced order systems
Stochastic processes
System identification
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Summary: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.
ISSN:0743-1619
2378-5861
DOI:10.1109/ACC.2003.1244099