A Decomposition Technique for Nonlinear Dynamical System Analysis
A Decomposition Technique for Nonlinear Dynamical System Analysis
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DOI：
10.1109/tac.2011.2175058
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发表时间：
2012-06
影响因子：
6.8
通讯作者：
James Anderson;A. Papachristodoulou
中科院分区：
文献类型：
--
作者：
James Anderson;A. Papachristodoulou
本文提出了一种分析大规模非线性动力系统的方法，即把它们分解成耦合的低阶子系统，这些子系统对于计算分析来说足够简单。结果表明，分解方法可以用来衡量非线性系统分析的平方和规划框架。该方法构造子系统的李雅普诺夫函数，用于形成整个系统的复合李雅普诺夫函数。如果使用基于稀疏性最大化的方法来获得子系统的李雅普诺夫函数，则可以实现进一步的计算节省。
A method for analyzing large-scale nonlinear dynamical systems by decomposing them into coupled lower order subsystems that are sufficiently simple for computational analysis is presented. It is shown that the decomposition approach can be used to scale the Sum of Squares programming framework for nonlinear systems analysis. The method constructs subsystem Lyapunov functions which are used to form a composite Lyapunov function for the whole system. Further computational savings are achieved if a method based on sparsity maximization is used to obtain the subsystem Lyapunov functions.