On Driftless Systems with m controls and 2m or 2m-1 states that are Flat by Pure Prolongation
Jean Lévine, Jaume Franch
人们普遍认为,对于确定一个系统是否总体上是分差的,没有任何必要和充分的条件。 但是,具体案例确实提供了这样的条件。 例如,有两个输入的无漂移系统已经知道必要和充分的条件。 对于具有三个或更多输入的无漂系统,可用的条件仅足够。 本文提出了确定具有m输入和2m或2m-1状态的系统是否通过纯延长(差异平坦度的特定子类)平整的新发现。 虽然这种情况比一般差分扁平度更具限制性,但计算平面输出的算法仍然非常简单,验证要求相对宽松。 此外,这项工作中提出的条件扩大了公认的差异平坦的系统类别,因为我们的充分条件与现有标准不同。
It is widely recognized that no tractable necessary and sufficient conditions exist for determining whether a system is, in general, differentially flat. However, specific cases do provide such conditions. For instance, driftless systems with two inputs have known necessary and sufficient conditions. For driftless systems with three or more inputs, the available conditions are only sufficient. This paper presents new findings on determining whether a system with m inputs and 2m or 2m-1 states is...