Model structure simplification of Nonlinear Systems via immersion
Model structure simplification of Nonlinear Systems via immersion
复制标题
通过沉浸简化非线性系统的模型结构
DOI：
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发表时间：
2005
影响因子：
6.8
通讯作者：
T. Ohtsuka
中科院分区：
文献类型：
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作者：
T. Ohtsuka
本文讨论了非线性系统模型结构的简化问题，同时保留了系统的输入输出映射。基本的技术是系统的沉浸，这是从原始系统到另一个系统的相同的输入输出映射的初始状态的映射。给出了一个给定的系统浸入到状态空间表示的有理函数或多项式等特定结构的状态的必要和充分条件。这些条件是如此的温和，以至于许多类型的非线性系统可以用有理或多项式模型结构来表示。此外，它还表明，多项式状态空间表示总是可以被构造为最多二次的状态。
This paper concerns the simplification of model structures of nonlinear systems while preserving their input-output maps. The basic technique is an immersion of a system, which is a mapping of the initial state from the original system to another system of an identical input-output map. The necessary and sufficient conditions are presented for the immersibility of a given system into a state-space representation of such particular structures as rational functions or polynomials with respect to the state. The conditions are so mild that many types of nonlinear systems can be represented by rational or polynomial model structures. Moreover, it is also shown that a polynomial state-space representation can always be constructed to be at most quadratic with respect to the state.