论文标题
强大的轨道稳定：基于浮标理论的方法
Robust Orbital Stabilization: A Floquet Theory-based Approach
论文作者
论文摘要
考虑了强大的轨道稳定反馈的设计。从已知的无干扰系统的轨道稳定控制器中，使用滑动模式控制（SMC）方法设计了可靠的反馈扩展。本文的主要贡献是提供一个建设性的过程，用于设计SMC合成中使用的时间不变的切换功能。更具体地说，它的零级集合（滑动歧管）是使用真实的Floquet-Lyapunov变换设计的，以对应于横向线性化的单层矩阵的不变子空间。当系统局限于滑动歧管时，尽管有任何系统不确定性和满足匹配条件的外部干扰，但可以确保周期轨道的渐近稳定性。受匹配和无与伦比的扰动/不确定性的振荡控制振荡控制的挑战性任务证明了所提出的方案的功效。
The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the paper is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet-Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated Cart-Pendulum system subject to both matched and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme.
