Identification of Continuous-Time Dynamic Systems With Uncertainties Measured by Fuzzy Sets Subject to Model Structure Errors - Wang, Jiandong; Xing, Xiaotong (IEEE transactions on fuzzy systems, 2024)
Continuous-time dynamic models are indispensable for many disciplines of science and engineering. This article proposes a new approach for estimating unknown parameters of continuous-time dynamic models. The proposed approach is composed of three main steps: a searching grid of model parameters is formulated in certain step sizes, objective functions of all grid points are calculated, and optimal model parameters are found as the ones corresponding to the minimum value of the objective function. Compared with existing identification approaches, the proposed approach has one new feature that model uncertainties are measured based on the fuzzy set theory by a number of companion model parameters that are associated with objective functions close to the minimum one. The proposed approach does not require a restrictive assumption for existing approaches that the true unknown system must be enclosed by the model set being considered, and provides model uncertainties in the presence of model structure errors. The main obstacle of the grid search is a high computation cost in calculating objective functions for all grid points. This obstacle is overcome to an acceptable level via parallel computation using a number of CPUs in multiple computers. The proposed approach is validated and compared with the existing approach through numerical and experimental examples.