Stable manifolds of saddle equilibria for pendulum dynamics on S2 and SO(3)
Stable manifolds of saddle equilibria for pendulum dynamics on S2 and SO(3)
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S2 和 SO(3) 上摆动力学鞍平衡的稳定流形
DOI：
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发表时间：
2011
期刊：
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通讯作者：
N. McClamroch
中科院分区：
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作者：
Taeyoung Lee;M. Leok;N. McClamroch
姿态控制系统自然地在非线性配置上演化，例如 S2 和 SO(3)。在研究相应的闭环姿态控制系统时，这些配置的重要拓扑特性会导致有趣且复杂的非线性动力学。在本文中，我们回顾了一些全局分析和模拟技术，这些技术使我们能够描述这些闭环系统的双曲平衡的全局非线性稳定流形。更深入地理解这些不变流形结构对于理解闭环姿态控制系统的全局稳定特性至关重要，并且这些全局分析技术适用于非线性配置流形的广泛问题。
Attitude control systems naturally evolve on nonlinear configurations, such as S2 and SO(3). The nontrivial topological properties of these configurations result in interesting and complicated nonlinear dynamics when studying the corresponding closed loop attitude control systems. In this paper, we review some global analysis and simulation techniques that allow us to describe the global nonlinear stable manifolds of the hyperbolic equilibria of these closed loop systems. A deeper understanding of these invariant manifold structures are critical to understanding the global stabilization properties of closed loop attitude control systems, and these global analysis techniques are applicable to a broad range of problems on nonlinear configuration manifolds.