2024/09/10 by Alireza Afzal Aghaei, Aghaei, Alireza Afzal · 1 citation
Computer Science · Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Neural Networks and Applications #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2409.06649
openalex publication_date 2024/09/10 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28
In this paper, we introduce the KANtrol framework, which utilizes Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving continuous time variables. We explain how Gaussian quadrature can be employed to approximate the integral parts within the problem, particularly for integro-differential state equations. We also demonstrate how automatic differentiation is utilized to compute exact derivatives for integer-order dynamics, while for fractional derivatives of non-integer order, we employ matrix-vector product discretization within the KAN framework. We tackle multi-dimensional problems, including the optimal control of a 2D heat partial differential equation. The results of our simulations, which cover both forward and parameter identification problems, show that the KANtrol framework outperforms classical MLPs in terms of accuracy and efficiency.