Towards Wiener system identification with minimum a priori information

The ability to construct accurate mathematical models of real systems is an important part of control systems design. A block oriented systems identification approach models the unknown system as interconnected linear and nonlinear blocks. The subject of this thesis is a particular configuration of these blocks referred to as a Wiener model. The Wiener model studied here is a cascade of a one input linear block followed by a nonlinear block which then provides one output. We assume that the signal between the linear and nonlinear block is always unknown, only the Wiener model input and output can be sampled. This thesis investigates identification of the linear transfer function in a Wiener model. The question examined throughout the thesis is: given some small amount of a priori information on the nonlinear part, what can we determine about the linear part? Examples of minimal a priori information are knowledge of only one point on the nonlinear transfer characteristic, or simply that the transfer characteristic is monotonic over a certain range. Nonlinear blocks with and without memory are discussed. Several algorithms for identifying the linear transfer function of a block oriented Wiener system are presented and analyzed in detail. Linear blocks identified have both finite and infinite impulse response (i.e. FIR and IIR). Each algorithm has a carefully defined set of minimal a priori information on the nonlinearity. Also, each approach has a minimally restrictive set of assumptions on the input excitation.

The universal applicability of each algorithm is established by providing rigorous proofs of identifiability and in some cases convergence. Extensive simulation testing of each algorithm has been performed. Simulation techniques and results are discussed in detail.