Efficiency of Kolmogorov-Arnold Networks for Nonlinear Systems Identification

Abstract

The identification of nonlinear systems remains a critical challenge in control engineering, requiring models that balance accuracy. This study explores Kolmogorov-Arnold Networks (KAN) as a novel solution, leveraging their inherent ability to decompose multivariate functions into hierarchical univariate operations, a property aligned with the Kolmogorov-Arnold representation theorem. KANs excel in capturing complex nonlinearities through adaptive activation functions and sparse subnetwork compositions, offering superior interpretability and parameter efficiency compared to conventional architectures. We demonstrate KAN's efficacy by identifying three nonlinear systems spanning low to high complexity and nonlinear dynamics. The identified models are further validated in Model Reference Adaptive Control (MRAC), showcasing closed-loop stability and tracking performance. Experimental results reveal that KANs achieve lower identification error and lower parameters than MLP and LSTM, while maintaining comparable computational overhead.