Order Selection Using Kernel-SVD in Model-Free Predictive Control

Model-Free Predictive Control is widely adopted due to its ability to control complex systems without explicit mathematical models. However, determining the appropriate order that accurately represents the actual order of the system remains a significant challenge. Previous research has explored the combination of Singular Value Decomposition (SVD) with the Bayesian Information Criterion (BIC) for optimal order selection, the limitations of this approach become apparent in nonlinear systems by inherent complexity. This paper proposes an order selection method that integrates Kernel Singular Value Decomposition (Kernel-SVD) with BIC to improve the effectiveness of order selection, particularly in systems exhibiting nonlinear behavior. The proposed kernel-based approach demonstrates a superior ability to capture nonlinear relationships across various operating conditions. To evaluate the efficacy of proposed method, we compare the performance of conventional SVD-based and kernel-SVD-based through simulations in nonlinear systems. The results demonstrate that kernel-SVD significantly improves the accuracy of order selection in model-free predictive control.