Learning-based MPC of sampled-data systems with partially unknown dynamics

• Published in: ISA transactions Vol. 162; pp. 64 - 74
• Main Authors: Han, Seungyong, Guo, Xuyang, Kommuri, Suneel Kumar
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.07.2025
• Subjects: Learning-based model predictive control; Neural ordinary differential equations; Sampled-data control systems; Ultimate boundedness; Learning-based model predictive control; Neural ordinary differential equations; Sampled-data control systems; Ultimate boundedness
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2025.04.028

In this paper, a novel learning-based model predictive control (LMPC) method is proposed for sampled-data control systems with partially unknown dynamics. Many real-world processes are subject to time-varying parameters and irregular data sampling, making accurate modeling and stability guarantees extremely challenging. To address this, the proposed method uses a neural ordinary differential equation (NODE) to learn unknown time-varying parameter dynamics from irregularly observed data. This learned model is then integrated into the sampled-data MPC framework. In particular, the LMPC method guarantees the system’s ultimate boundedness by deriving conditions based on the Gronwall–Bellman inequality. Finally, two practical examples illustrate the applicability of the LMPC method to real-world systems and demonstrate its quantitative stability analysis. •A novel LMPC method is proposed for sampled-data systems with partially unknown dynamics. An incomplete dynamics model is fulfilled with the NN trained by using NODEs.•The trained NN is integrated into the finite-horizon optimal control problem, where the continuous-time parameter is predicted by the trained NN. This is helpful to adjust the future system state as it is dependent on the parameter.•Ultimate boundedness of the LMPC method is mathematically proved for the sampled-data system whose model is composed of partially known dynamics model and the trained NN.•The superiority of the proposed LMPC method is validated for two practical systems: the tracking control system for wheeled mobile robots (WMRs) and the manipulator robot control system.