CCE Faculty Articles
Identification of Bilinear Systems with White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach
Document Type
Article
Publication Title
IEEE Transactions on Control Systems Technology
ISSN
1063-6536
Publication Date
2009
Abstract
In this technical brief, a new subspace state space system identification algorithm for multi input multi output bilinear systems driven by white noise inputs is introduced. The new algorithm is based on a uniformly convergent Picard sequence of linear deterministic stochastic state space subsystems which are easily identifiable by any linear deterministic stochastic subspace algorithm such as MOESP, N4SID, CVA, or CCA. The key to the proposed algorithm is the fact that the bilinear term is a second order white noise process. Using a standard linear Kalman filter model, the bilinear term can be estimated and combined with the system inputs at each iteration, thus leading to a linear system with extended inputs of dimension m(n + 1), where n is the system order and m is the dimension of the inputs. It is also shown that the model parameters obtained with the new algorithm converge to those of the true bilinear model. Moreover, the proposed algorithm has the same consistency conditions as the linear subspace identification algorithms when i, where i is the number of block rows in the past/future block Hankel data matrices. Typical bilinear subspace identification algorithms available in the literature cannot handle large values of i, thus leading to biased parameter estimates. Unlike existing bilinear subspace identification algorithms whose row dimensions in the data matrices grow exponentially, and hence suffer from the curse of dimensionality, in the proposed algorithm the dimensions of the data matrices are comparable to those of a linear subspace identification algorithm. A case study is presented with data from a heat exchanger experiment.
DOI
10.1109/TCST.2008.2002041
Volume
17
Issue
5
First Page
1145
Last Page
1153
NSUWorks Citation
Ramos, Jose A.; Lopes dos Santos, Paulo; and Martins de Carvalho, Jorge L., "Identification of Bilinear Systems with White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach" (2009). CCE Faculty Articles. 431.
https://nsuworks.nova.edu/gscis_facarticles/431
