The Nonlinear Mathematical Modeling and Optimization of Distributed Control in Complex Systems

Abstract

With the widespread application of complex systems in industries such as manufacturing, transportation, and energy, their high-dimensional, strongly nonlinear, and dynamically coupled characteristics pose significant challenges to traditional centralized control. To address these complexities more efficiently, this study constructs a nonlinear mathematical model by introducing nonlinear feature mapping into a multiple linear regression framework and implements distributed optimization using the Alternating Direction Method of Multipliers (ADMM). The proposed method is validated through the simulation of the nonlinear dynamic behavior of a deep-water riser–test pipe system, with experimental designs encompassing multi-dimensional vibration responses and dynamic environmental disturbances. The results demonstrate that the proposed nonlinear model significantly outperforms other methods in terms of prediction accuracy and optimization efficiency. Under varying amplitudes and frequencies of disturbances, the model achieves lower error rates and higher robustness, with an adaptation decay rate of less than 17.6%. These findings indicate that the proposed nonlinear modeling and distributed optimization approach can effectively capture the dynamic characteristics of complex systems, making it suitable for real-time distributed control scenarios with promising engineering applications.