Identication and Prediction of Discrete-Time Bilinear State-Space Models: Interaction Matrices and Superstates
Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
In this master thesis, an extension of the interaction matrix formulation to the discrete-time bilinear state-space model is derived. Several identication techniques are presented from this formulation to identify the bilinear state-space matrices using a superstate vector, derived from a single set of su-ciently rich input-output measurements. The initial state can be non-zero and unknown. Unlike other approaches, no specialized inputs are required, such as sinusoidal or white inputs, or duration-varying unit pulses involving multiple experiments. For that reason, the bilinear state-space identication problem is di-cult to solve, since it can be seen as a linear time-varying system with input-dependent system matrix or state-dependent input-influence matrix.
The resultant input-output map from this state-space formulation can be used for output prediction. A relationship between the coe-cients of this input-output map and the bilinear state-space model matrices is obtained via two interaction matrices, corresponding to the linear and bilinear portions of the model, respectively.
Numerical examples are provided to illustrate these bilinear state-space model identication techniques and the input-output model identication method. It is concluded that the proposed identication algorithms can correctly identify the original bilinear state-space model, and the identied input-output map correctly predict its system output response, despite the fact that the interaction matrices are only implicitly assumed to exist.
Place, publisher, year, edition, pages
2010. , 51 p.
IdentifiersURN: urn:nbn:se:kth:diva-105141OAI: oai:DiVA.org:kth-105141DiVA: diva2:570096
Master of Science in Engineering - Electrical Engineering
Fischione, Carlo, Univ lektor