论文标题
基于轨迹的方法来离散时间平坦
A Trajectory-Based Approach to Discrete-Time Flatness
论文作者
论文摘要
对于离散的时间系统，通常是通过通过前移来替换众所周知的连续定义的时间来源来定义平坦度。通过此定义，平面系统类别完全对应于系统类别，这些系统可以通过文献中提出的离散时间内源性动态反馈线性化。最近，已经得出了该特性的必要和足够的差分几何条件。在目前的贡献中，我们也尝试考虑向后移动。这种扩展的方法是由平面系统解决方案对琐碎系统解决方案的一对一对应的动机，正如从连续时间案例中知道的那样。如果我们将此想法转移到离散时间案例中，则会导致一种方法，该方法也允许向后移动。为了通过前移和本文的方法区分经典的定义，我们将前者称为前锋。我们表明，平坦的系统（从向后移的扩展意义上）仍然具有前向灯系统系统的许多有益属性。特别是，它们仍然是可触及/可控制的，可以直接计划轨迹，并且可以通过某些动态反馈的子类线性化。
For discrete-time systems, flatness is usually defined by replacing the time-derivatives of the well-known continuous-time definition by forward-shifts. With this definition, the class of flat systems corresponds exactly to the class of systems which can be linearized by a discrete-time endogenous dynamic feedback as it is proposed in the literature. Recently, verifiable necessary and sufficient differential-geometric conditions for this property have been derived. In the present contribution, we make an attempt to take into account also backward-shifts. This extended approach is motivated by the one-to-one correspondence of solutions of flat systems to solutions of a trivial system as it is known from the continuous-time case. If we transfer this idea to the discrete-time case, this leads to an approach which also allows backward-shifts. To distinguish the classical definition with forward-shifts and the approach of the present paper, we refer to the former as forward-flatness. We show that flat systems (in the extended sense with backward-shifts) still share many beneficial properties of forward-flat systems. In particular, they still are reachable/controllable, allow a straightforward planning of trajectories and can be linearized by a certain subclass of dynamic feedbacks.
