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<p>This paper introduces KANtrol, a Kolmogorov–Arnold Network (KAN)-based framework for solving optimal control problems in continuous-time systems. The method leverages Gaussian quadrature to approximate integral components, including cost function and integro-differential state equations. Exact derivatives for integer-order dynamics are computed via automatic differentiation, while fractional Caputo derivatives are approximated through a matrix–vector product representation within KANtrol. To enhance computational efficiency, fractional derivative approximation is performed using a non-uniform discretization scheme that integrates into any forward pass of the network, including those used for integral approximation, eliminating the need for an additional forward phase. Additionally, a neural architecture search algorithm is used for automated hyperparameter tuning. The effectiveness of KANtrol is evaluated on various forward and parameter identification problems, including an infinite-horizon control problem and the optimal control of a two-dimensional heat equation. Simulation results demonstrate superior accuracy compared to classical multi-layer perceptrons, fractional KANs, and rational KANs.</p>

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KANtrol: a physics-informed Kolmogorov–Arnold network framework for solving multi-dimensional and fractional optimal control problems

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Alireza Afzal Aghaei

摘要

This paper introduces KANtrol, a Kolmogorov–Arnold Network (KAN)-based framework for solving optimal control problems in continuous-time systems. The method leverages Gaussian quadrature to approximate integral components, including cost function and integro-differential state equations. Exact derivatives for integer-order dynamics are computed via automatic differentiation, while fractional Caputo derivatives are approximated through a matrix–vector product representation within KANtrol. To enhance computational efficiency, fractional derivative approximation is performed using a non-uniform discretization scheme that integrates into any forward pass of the network, including those used for integral approximation, eliminating the need for an additional forward phase. Additionally, a neural architecture search algorithm is used for automated hyperparameter tuning. The effectiveness of KANtrol is evaluated on various forward and parameter identification problems, including an infinite-horizon control problem and the optimal control of a two-dimensional heat equation. Simulation results demonstrate superior accuracy compared to classical multi-layer perceptrons, fractional KANs, and rational KANs.