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<p>This paper presents a novel model predictive control(MPC) strategy for nonlinear dynamical systems by integrating the Sparse Identification of Nonlinear Dynamics with Control(SINDYc) framework with fourth-order Runge–Kutta(RK) numerical integration. The proposed Runge–Kutta Sparse Identification of Nonlinear Dynamics with Control(RK-SINDYc) formulation enables accurate multi-step prediction of system behavior, while also delivering the sensitivity information required for MPC optimization. Unlike traditional SINDYc-based approaches, the proposed RK-SINDYc-MPC framework comprises EKF-based state reconstruction from input-output data and an online adaptation mechanism to adjust sparse model coefficients, enhancing both control accuracy and robustness. The controller’s effectiveness is demonstrated through comprehensive simulations on the nonlinear Continuous Stirred Tank Reactor(CSTR) and two degree of fredom(2-DOF) helicopter benchmark systems. Control performance has been examined in detail under nominal, measurement noise, and parametric uncertainty conditions for both staircase and sinusoidal reference signals. Moreover, the introduced RK-SINDYc-MPC is compared with the Function Tuner–based model-free adaptive PID and RK-NARMA-L2 controllers. Additionally, a Lyapunov-based stability analysis has been conducted, indicating that the closed-loop system is uniformly ultimately bounded (UUB). The attained results show that the proposed RK-SINDYc based MPC(RK-SINDYc-MPC) scheme achieves stable, robust and accurate control performance for nonlinear systems, highlighting its potential as a data-driven predictive control tool.</p>

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A novel data-driven model predictive controller for nonlinear dynamical systems based on Runge-Kutta sparse identification

  • 期刊论文

  • 发表日期：

    2026年7月18日

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  • Kemal Uçak

摘要

This paper presents a novel model predictive control(MPC) strategy for nonlinear dynamical systems by integrating the Sparse Identification of Nonlinear Dynamics with Control(SINDYc) framework with fourth-order Runge–Kutta(RK) numerical integration. The proposed Runge–Kutta Sparse Identification of Nonlinear Dynamics with Control(RK-SINDYc) formulation enables accurate multi-step prediction of system behavior, while also delivering the sensitivity information required for MPC optimization. Unlike traditional SINDYc-based approaches, the proposed RK-SINDYc-MPC framework comprises EKF-based state reconstruction from input-output data and an online adaptation mechanism to adjust sparse model coefficients, enhancing both control accuracy and robustness. The controller’s effectiveness is demonstrated through comprehensive simulations on the nonlinear Continuous Stirred Tank Reactor(CSTR) and two degree of fredom(2-DOF) helicopter benchmark systems. Control performance has been examined in detail under nominal, measurement noise, and parametric uncertainty conditions for both staircase and sinusoidal reference signals. Moreover, the introduced RK-SINDYc-MPC is compared with the Function Tuner–based model-free adaptive PID and RK-NARMA-L2 controllers. Additionally, a Lyapunov-based stability analysis has been conducted, indicating that the closed-loop system is uniformly ultimately bounded (UUB). The attained results show that the proposed RK-SINDYc based MPC(RK-SINDYc-MPC) scheme achieves stable, robust and accurate control performance for nonlinear systems, highlighting its potential as a data-driven predictive control tool.