Identification of Bilinear Systems Using an Iterative Deterministic-Stochastic Subspace Approach
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005
ISSN or ISBN
In this paper we introduce a new identification algorithm for MIMO bilinear systems driven by white noise inputs. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state space approximations, thus considered a Picard based method. The key to the algorithm is the fact that the bilinear terms behave like white noise processes. Using a linear Kalman filter, the bilinear terms can be estimated and combined with the system inputs at each iteration, leading to a linear system which can be identified with a linear-deterministic subspace algorithm such as MOESP, N4SID, or CVA. Furthermore, the model parameters obtained with the new algorithm converge to those of a bilinear model. Finally, the dimensions of the data matrices are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality.
Ramos, Jose A.; Lopes dos Santos, Paulo; and Martins de Carvalho, Jorge L., "Identification of Bilinear Systems Using an Iterative Deterministic-Stochastic Subspace Approach" (2005). CEC Faculty Articles. 392.