Model Reduction of Homogeneous Polynomial Dynamical Systems via Tensor Decomposition

• 成果类型: Article
• 署名作者: Mao, Xin; Chen, Can
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3663107
• 发表日期: 2026
• 关键词: ORDER-REDUCTION; FLUID-DYNAMICS; eigenvalues; CONTROLLABILITY; STABILITY

摘要

Model reduction plays a critical role in system control, with established methods, such as balanced truncation, widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems that are often used to model higher order interactions in physics, biology, and ecology, remains a significant challenge. In this article, we develop a novel model reduction method for homogeneous polynomial dynamical systems (HPDSs) with linear input and output grounded in tensor decomposition. Leveraging the inherent tensor structure of HPDSs, we construct reduced models by extracting dominant mode subspaces via higher order singular value decomposition. Notably, we establish that key system-theoretic properties, including trajectory behavior, controllability, and observability, are preserved in the reduced model. We demonstrate the effectiveness of our method using numerical examples.