WSINDy for model predictive control with applications to fusion, drones and chaos

Abstract The control of complex dynamical systems remains a fundamental challenge in science and engineering, where strong nonlinearities, the presence of noise and computational constraints often pose significant obstacles in traditional control approaches. Recent advances in data-driven methods, particularly system identification (SI) techniques, have shown a powerful alternative by providing fast, parsimonious, interpretable models that are well-suited for model predictive control (MPC). Building on these developments, the present article embeds weak sparse identification of nonlinear dynamics (WSINDy) with actuation control inputs (WSINDYc) within an MPC framework. Compared to benchmark data-driven methods, WSINDYc enables a more robust identification of the governing dynamics, particularly in the presence of high noise levels, resulting in more accurate and efficient control. The capabilities of the proposed WSINDY–MPC framework are demonstrated on a range of problems, including a tokamak plasma boundary model that includes main ion gas puff actuation, drone tracking and collision avoidance, the chaotic Lorenz system and a simplified flight control model for an F-8 aircraft. The proposed framework achieves superior performance in the presence of noise, enabling longer prediction horizons, lower trajectory tracking error and a more reliable obstacle clearance, while simultaneously achieving lower MPC cost values compared to the baseline methods. Furthermore, we accelerate the optimization by compiling the MPC objective and constraints into C code, approaching real-time performance.