PID Tuning Approach Using Kolmogorov–Arnold Networks Under Varying Operational Conditions

This paper investigates the use of Kolmogorov–Arnold networks (KANs) for dynamic proportional-integral-derivative (PID) control tuning in first- and second-order linear systems under noisy conditions, time-varying reference trajectories, and varying plant parameters. Toy datasets, based on instantaneous system error, output and reference trajectory, are used for training the networks and comparing KAN results with fixed PID coefficients, taken from MATLAB’s Simulink PID Autotune, a multilayer perceptron (MLP)-based neural network (NN), trained on the same datasets, a traditional adaptive PID scheme with gain scheduling and an LMS-based online tuning approach. Results evaluate KAN performance under several scenarios, including time-varying reference trajectories, measurement noise, and changes in the controlled plant. The results show that the learning-based tuning approaches outperform gain scheduling and LMS-based adaptation under non-stationary operating conditions. The KAN-based tuner achieves comparable or improved tracking performance relative to the MLP and consistently provides reduced steady-state and integral error measures compared with the classical approaches. While KAN and MLP controllers exhibit similar performance for first-order plants, the KAN-based tuner demonstrates improved robustness for the more complex second-order systems, particularly during reference transitions and under high measurement-noise conditions. Analysis of the gain trajectories further shows that KANs provide rapid adaptation to changes in system dynamics and operating conditions, although this increased responsiveness can result in greater gain variability under noisy conditions. A parameter-matched comparison further indicates that MLP architectures with the same parameter budgets as the KAN models provide inadequate performance, whereas substantially wider MLPs are required to achieve competitive results.