Set membership estimation theory for Wiener modelling using HLCPWL functions

In this paper, we propose a Wiener-like model structure where the dynamic linear part is represented by a finite set of discrete Laguerre or Kautz transfer functions, while the non-linear static part is realised by high level canonical piecewise linear basis functions (HLCPWL). In control applications, Laguerre functions are commonly used when dealing with overdamped systems, while Kautz systems are suitable for weakly damped ones. The approximation of the static non-linear functions using HLCPWL functions is based on that this representation uses the least number of parameters and the algorithm for computing the approximation is very efficient. In this model, we estimate the parameters of the HLCPWL using set membership estimation theory, under mild error constraints. It is shown that this structure allows to uniformly approximate any causal, time-invariant, non-linear discrete dynamic system with fading memory.