Applying Kolmogorov-Arnold Networks to Improve Linear Quadratic Control Performance

Hegedűs, Tamás and Németh, Balázs and Fényes, Dániel and Gáspár, Péter (2026) Applying Kolmogorov-Arnold Networks to Improve Linear Quadratic Control Performance. In: 23rd IFAC World Congress, 2026.08.23-28, Busan, Republic of Korea. (In Press)

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Abstract

This paper presents a control architecture in which a Linear Quadratic Regulator (LQR) is integrated with a machine learning-based nonlinear compensator realized through a Kolmogorov- Arnold Network (KAN). The goal of the proposed approach is to achieve a balance between guaranteed closed-loop stability, computational efficiency, and enhanced control performance. First, a Reinforcement Learning (RL) framework is used to learn an effective nonlinear control policy across the entire operating range of the system. Then, the trained RL-based control method serves as the teacher network for the KAN-based algorithm. During the knowledge distillation, gradient regularization and coefficient constraints are applied to achieve a smooth and Lipschitz-bounded neural network-based controller. Stability is guaranteed for the combined LQR-KAN closed-loop system through the computation of the maximum allowable Lipschitz constant of the neural network. The proposed control structure is validated on a double inverted pendulum system. The results show that the combined KAN-based controller achieves nearly the same performance level as the RL-based method, while the Lipschitz constant and the complexity of the network are significantly reduced. This property directly supports simple stability analysis and reliable real-time implementation.

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