论文标题
具有NO（X，U）-Flat输出的平面系统
A Flat System Possessing no (x,u)-Flat Output
论文作者
论文摘要
通常，非线性系统的平面输出可能取决于系统的状态和输入以及后者的任意时间衍生物。如果知道输入的时间导数的平坦输出，则可能会提出一个问题，是否也存在一个平坦的输出，该输出与这些时间衍生物无关，即AN（X，U）-Flat Output。到目前为止，每个平面系统是否还具有（x，u）-flat输出的问题已经打开。在这一贡献中，这种猜想是通过反例子反驳的。我们提出了一个两输入系统，该系统在差异上平坦，取决于状态，输入和一阶时间派生词，但没有任何（x，u）-flat输出。证明依赖于这样一个事实，即在应用合适的输入转换后，每个（x，u）-flat两输入系统最多可以在最多昏暗（x）折叠延长之后进行线性性化。
In general, flat outputs of a nonlinear system may depend on the system's state and input as well as on an arbitrary number of time derivatives of the latter. If a flat output which also depends on time derivatives of the input is known, one may pose the question whether there also exists a flat output which is independent of these time derivatives, i.e., an (x,u)-flat output. Until now, the question whether every flat system also possesses an (x,u)-flat output has been open. In this contribution, this conjecture is disproved by means of a counterexample. We present a two-input system which is differentially flat with a flat output depending on the state, the input and first-order time derivatives of the input, but which does not possess any (x,u)-flat output. The proof relies on the fact that every (x,u)-flat two-input system can be exactly linearized after an at most dim(x)-fold prolongation of one of its (new) inputs after a suitable input transformation has been applied.
