Minimal realizations of nonlinear systems
Minimal realizations of nonlinear systems
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非线性系统的最小实现
DOI：
10.1016/j.automatica.2018.05.007
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Tõnso
中科院分区：
文献类型：
--
作者：
Ü. Kotta;C. Moog;M. Tõnso
对时变单输入单输出非线性系统的非线性实现理论进行了改造。实现的概念也被推广到阶数大于输入输出方程阶数的实现。研究了最小实现问题。状态实现被称为最小的，如果它是可访问和可观察的，或者它的状态维数是最小的。在线性情况下，这两个定义是等价的，但对于非线性时不变系统则不然。它表明，这两个定义仍然是等价的非线性系统在一定的技术假设。给出了求最小实现的两种方法。
The nonlinear realization theory is recasted for time-varying single-input single-output nonlinear systems. The concept of realization has been extended to cover also the realizations with order greater than the order of input–output equation. The minimal realization problem is studied. The state realization is said to be minimal if it is either accessible and observable or its state dimension is minimal. In the linear case the two definitions are equivalent, but not for nonlinear time-invariant systems. It is shown that the two definitions remain equivalent for nonlinear systems under certain technical assumptions. Two alternative methods are presented for finding the minimal realization.