Comparative Study of Probabilistic Model Selection

Model-free predictive control stands out from conventional methods by relying exclusively solely on measured input/output data rather than mathematical models. The effectiveness of order selection in model-free predictive control, achieved through the integration of Singular Value Decomposition (SVD) along with Bayesian Information Criterion (BIC), has already been well-documented. This paper explores alternative probabilistic model selection methods, such as Akaike information criterion (AIC) and Generalized information criterion (GIC), in comparison with the previously proposed BIC technique from earlier research and analyzes the number of data limitations and noise levels of each probabilistic model selection method. Our numerical simulations show that GIC exhibits a notable proximity to BIC compared to AIC. However, BIC demonstrates superior performance compared to other methods, particularly with the number of data and noise levels changing.