Title :
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
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;
Conference_Titel :
American Control Conference, 2003. Proceedings of the 2003
Print_ISBN :
0-7803-7896-2
DOI :
10.1109/ACC.2003.1244099
