Data-Driven Adaptive Tracking Control for Nonlinear New Quality Productive Forces Systems with Input Constraints

This paper addresses issues such as nonlinearity, model uncertainty, and multiple policy constraints within the dynamic evolution of new quality productive forces systems. It proposes a research framework integrating data-driven modelling with adaptive tracking control. By merging control theory with economic dynamics, a closed-loop analytical system of 'theory-data-control' is constructed, providing a methodologically rigorous yet operationally feasible pathway for the precise regulation of complex economic systems. First, utilising provincial panel data, a discrete-time system model integrating linear inertia, policy effects, and nonlinear compensation is established. System parameter identification is achieved through a dual machine learning approach employing partial linear regression. Subsequently, a tracking controller integrating data-driven initial identification with online parameter adaptation is designed, incorporating a projection mechanism to strictly ensure policy variables remain within feasible adjustment ranges. Based on Lyapunov stability theory, we demonstrate that the tracking error of the closed-loop system exhibits ultimate convergence with boundedness. Simulation experiments confirm that the proposed method significantly enhances the system's tracking performance towards the target trajectory, reducing the mean absolute error by approximately 30.8% while producing smoother control signals. Comparative studies indicate that the parameter adaptation mechanism and nonlinear compensation module play crucial roles in improving control effectiveness. This research not only expands the theoretical toolkit for analysing the dynamics of new quality productive forces but also provides an interdisciplinary methodological reference for the closed-loop management of complex socioeconomic systems under data-driven conditions.