Practical Nonlinear Model Predictive Control With Kolmogorov–Arnold Network Models

This paper presents a novel approach to practical nonlinear model predictive control (PNMPC) using Kolmogorov–Arnold networks (KANs) as prediction models. KANs are based on the Kolmogorov–Arnold superposition theorem, enabling efficient nonlinear system modeling with fewer parameters compared to traditional neural networks. This characteristic makes KANs particularly suitable for nonlinear model predictive control (NMPC), where computational efficiency is critical. This paper presents a method to efficiently identify nonlinear models from data, proposing a time-delay KAN (TDKAN) architecture, which consists of a KAN associated with tap delays in its input. Furthermore, it proposes the integration of this novel model architecture into a PNMPC algorithm, with the aim of improving control accuracy while reducing computational burden. The method is validated using a pH neutralization process, a benchmark for nonlinear control problems. The results show that the TDKAN-based PNMPC outperforms other PNMPC approaches, such as those that use echo-state networks and long short-term memory networks, providing better setpoint tracking, lower mean squared error, and faster computation times, which demonstrate the potential of KANs for prediction in practical NMPC applications.