Qualitative modeling of dynamical systems employing continuous-time recurrent fuzzy systems

Entwurf robuster modellbasierter Fehlerisolationsfilter

“…Liegt qualitatives Wissen vor, so lässt sich die Dynamik mithilfe rekurrenter Fuzzy-Systeme beschreiben. Diese erlauben es, die Dynamik von Systemen wissensbasiert zu modellieren [2,3,71,120,198], was es ermöglicht, rekurrente Fuzzy-Systeme auch zur Fehlererkennung und -isolation einzusetzen [198,199]. Dies ist insbesondere dann sinnvoll, wenn eine analytische Beschreibung des Modellverhaltens nicht oder nur mit sehr großem Aufwand möglich ist, Expertenwissenüber das qualitative Verhalten des Systems jedoch vorhanden ist.…”

Modeling with discrete-time recurrent fuzzy systems via mixed-integer optimization

“…This is especially suitable in application areas of DTRFS such as pattern recognition [27] or fault isolation [40], for which only the rule base identification is required, since the core positions are known a priori. The second possibility is the use of structure optimization algorithms for DTRFS without FBC as introduced in [3] which yields an initial partitioning based on given data sets. Then, both the number and initial values of the core positions are determined.…”

“…In general, the parameter optimization problem is nonconvex and multimodal. In [3] a gradient-based algorithm for continuous-time RFS (CTRFS) is developed. Basically, the parameter optimization of DTRFS is similar to the case of CTRFS.…”

“…Hence, we have to solve a multi-objective optimization problem which is according to [3] transferred to a single optimization problem…”

“…The derivatives of * (j,q) with respect to s x j and s u q are omitted for brevity and can be found in [3].…”