Model complexity optimization of equivalent dynamical linearization data models used in model‐free adaptive control

Abstract

This paper discusses a strategy for optimizing the complexity of time‐varying data models as used in model‐free adaptive control (MFAC). Here the dynamic linearization in compact form (CFDL), partial form (PFDL), and full form (FFDL) are considered as data models used to describe input/output (I/O) data sets. These data models are built only for control purpose and can have various degrees of complexity depending on the size of the considered time‐window as well as the underlying algorithms. The methodology is to compare the performance of the data models according to an evaluation criterion, to analyze the order of different data models based on bias‐variance trade‐off, and to select the best‐performing model. The complexity of the selected model is compared with the reduced linear time‐invariant (LTI) model obtained by applying a combination of the eigensystem realization algorithm (ERA) and observer/Kalman filter identification (OKID) on the same I/O dataset. The I/O data are obtained from applying the MFAC controllers on a nonlinear three‐tank system (3TS) to track various desired references. The results indicate that the model complexity optimization can also be used for selecting an appropriate MFAC data model with optimal order to reduce the complexity and computational burden of the MFAC control algorithms.