关于周期运动轨道稳定的过横坐标
On Excessive Transverse Coordinates for Orbital Stabilization of Periodic Motions
摘要：
本文探讨了横坐标的目的，轨道稳定的周期运动的非线性，控制仿射动力系统。它示出的动态的任何（最小或过多）的横向坐标，这是定义在一个特定的参数化的运动和一个严格依赖于状态的投影算子恢复的参数化变量，承认（横向）线性化沿目标运动，与明确的表达式。特别的重点是，然后放在一个通用的过度设置的正交坐标，揭示了一定的限制的“过度”的横向线性化控制设计的目的。为了克服这一限制，引入了一个线性比较系统，并说明了当其原点的渐近稳定性对应于线性化横向动力学的原点的渐近稳定性的条件。这允许利用该比较系统来构造反馈控制器，当在动力系统上实现该比较系统时，该比较系统使得期望的运动在轨道意义上渐近稳定。
英文摘要：
This paper explores transverse coordinates for the purpose of orbitally stabilizing periodic motions of nonlinear, control-affine dynamical systems. It is shown that the dynamics of any (minimal or excessive) set of transverse coordinates, which are defined in terms of a particular parameterization of the motion and a strictly state-dependent projection operator recovering the parameterizing variable, admits a (transverse) linearization along the target motion, with explicit expressions stated. Special focus is then placed on a generic excessive set of orthogonal coordinates, revealing a certain limitation of the "excessive" transverse linearization for the purpose of control design. To overcome this limitation, a linear comparison system is introduced, and conditions are stated for when the asymptotic stability of its origin corresponds to the asymptotic stability of the origin of linearized transverse dynamics. This allows for the construction of feedback controllers utilizing this comparison system which, when implemented on the dynamical system, renders the desired motion asymptotically stable in the orbital sense.
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