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.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-105141 |
| Date | January 2010 |
| Creators | Celik, Haris |
| Publisher | KTH, Reglerteknik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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