Lebesgue Piecewise Affine Approximation of Nonlinear Systems and Its Application to Hybrid System Modeling of Biosystems
Lebesgue Piecewise Affine Approximation of Nonlinear Systems and Its Application to Hybrid System Modeling of Biosystems
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DOI：
10.1109/cdc.2006.377726
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发表时间：
2006-12
期刊：
影响因子：
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通讯作者：
S. Azuma;J. Imura;T. Sugie
中科院分区：
文献类型：
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作者：
S. Azuma;J. Imura;T. Sugie
提出了一种用分段仿射系统模型逼近非线性系统的新方法。首先，提出了一种近似表示非线性向量场的方法，称为Lebesgue分段仿射近似。接下来，我们推导出的PWA近似系统的轨迹方面的误差界，然后展示如何构建一个PWA近似系统与预先指定的精度。最后，将所提出的方法应用于具有非线性动力学的基因调控网络，表明该方法对于获得非线性系统的PWA近似系统模型是有用的
This paper proposes a new technique for approximating nonlinear systems by piecewise affine (PWA) system models. First, a method, called the Lebesgue piecewise affine approximation, is presented for approximately expressing nonlinear vector fields. Next, we derive an error bound of the PWA approximation systems in terms of the trajectories, and then show how to construct a PWA approximation system with an accuracy specified in advance. Finally, the proposed technique is applied to a gene regulatory network with nonlinear dynamics, and it is shown that the technique is useful for obtaining a PWA approximate system model for nonlinear systems