面向互联系统的一类保结构模型降阶方法

Structure-preserving model order reduction for interconnected systems

互联系统作为一类特殊的复杂系统,其物理性质与系统的拓扑结构密切相关.因此在降阶过程中同时保持原始系统的耦合结构具有重要的现实意义.基于此,本文针对互联系统研究了一类保结构的模型降阶方法.首先,利用移位Legendre多项式正交分析技术,从归一化角度提出了计算互联系统可控与可观Gram矩阵的低秩分解算法.其次,结合平衡截断与主子空间投影方法,提出了一类保结构的降阶方法,并证明了降阶模型的保稳定性.最后,通过数值实验验证了所提方法的可行性与有效性.

As a special class of complex systems, the properties of interconnected systems are related to its topology structures. It is necessary to preserve the structures of original systems during dimension reduction. As a result, this paper focus on the topic of model order reduction(MOR) for interconnected systems and presents a series structure-preserving MOR methods. The associated controllability gramian as well as observability gramian is approximately in a low-rank decomposition form, which is constructed via shifted Legendre polynomials expansions instead of Lyapunov equations. In combination of balanced truncation and dominant subspace projection method, a class of MOR algorithms are proposed, which preserve the interconnection structures. What's more, the property of stability preservation for reduced-order models is well discussed. Finally, numerical simulations are provided to illustrate the effectiveness of our proposed algorithms.