ABSTRACT

In this paper, a novel solution is proposed for verifying difference flatness of a nonlinear discrete-time control system. A necessary and sufficient condition is proved under which a discrete-time control system is flat. The condition is based on a sequence of vector spaces of differential 1-forms. A more general definition of flatness is considered than in most cases, since the flat output is allowed to depend on the backward shifts of the states and inputs. Also, unlike most conditions that check flatness of a discrete-time system, the one proposed in the current paper does not require actually computing the flat output. Although, the flat output can be found from the vector spaces based on which the necessary and sufficient condition is presented. Algorithms are provided in order to compute all the necessary vector spaces. Two examples illustrate the results.

摘要

在本文中，提出了一种新的解决方案来验证非线性离散时间控制系统的差分平坦度。证明了离散时间控制系统是平坦的一个充要条件。该条件基于微分 1 形式的向量空间序列。与大多数情况相比，考虑了更一般的平坦度定义，因为平坦输出允许依赖于状态和输入的向后移动。此外，与检查离散时间系统平坦度的大多数条件不同，当前论文中提出的条件不需要实际计算平坦输出。虽然，可以从向量空间中找到平坦的输出，基于该向量空间提出了必要和充分条件。提供算法以计算所有必要的向量空间。