Flexible model structures for LPV identification with static scheduling dependency

Abstract

A discrete-time linear parameter-varying (LPV) model can be seen as the combination of local LTI models together with a scheduling signal dependent function set, that selects one of the models to describe the continuation of the signal trajectories at every time instant. An identification strategy of LPV models is proposed that consists of the separate approximation of the local model set and the scheduling functions. The local model set is represented as a linear combination (series expansion) of orthonormal basis functions (OBFs). The expansion coefficients are dynamically dependent (weighting) functions of the scheduling parameters (depending on time shifted scheduling). To approximate this dependency class with a static one (non-shifted scheduling), a feedback-based structure of the weighting functions is introduced. The proposed model structure is identified in a two step procedure. First the OBFs, that guarantee the least asymptotic worst-case modeling error for the local models, are selected through the fuzzy Kolmogorov c-Max approach. With the resulting OBFs, the weighting functions are identified through a separable least-squares algorithm. The method is demonstrated by means of simulation examples and analyzed in terms of applicability, convergence, and consistency of the model estimates

Modeling and Identification of Linear Parameter-Varying Systems

“…This concludes research objective 3. The presented results of the chapter are based on the papers Tóth et al (2008b.…”

Identification of input-output LPV models

“…This discretized model has only one p-dependent coefficient and the linearity of the dependence is preserved, however the model equation depends now on p(k − 1) instead of p(k). This so-called dynamic dependence (dependence of the model coefficients on time-shifted versions of p) is a common result of model transformations in the LPV case and rises problems in LPV system identification and control alike (see [Tóth et al (2008)]). Furthermore, it is well-known in numerical analysis that the forward Euler approximation is more sensitive for the choice of T s in terms of numerical stability than the backward Euler approximation [Atkinson (1989)].…”

An LPV identification Framework Based on Orthonormal Basis Functions

“…To alleviate the restrictions caused by the assumption of static dependence in the suggested model structures, extensions for these structures were proposed in Tóth et al (2008). Here we only consider the Wiener case.…”

“…To overcome the nonlinear optimization problem associated with the parallel estimation of the parameters of W and V , the approach uses a separable least squares optimization scheme. For algorithmic details see Tóth et al (2008). It should be noted that the better representation capability comes at a price.…”