A Class of Hybrid Geometric Controllers for Robust Global Asymptotic Stabilization on S1

Adeel Akhtar, R. Sanfelice
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引用次数: 2

Abstract

This paper proposes a hybrid geometric control scheme for the classical problem of globally stabilizing a pointmass system on a unit circle, as it is impossible to design a smooth globally asymptotically stable controller for this problem. Unlike most existing solutions that rely on coordinates and rely on a particular controller construction, our proposed solution is coordinate free (or geometric) and belongs to a class of controllers that we also characterize. Specifically, we propose a geometric hybrid controller that uses a local geometric controller (from the said class) and an open-loop geometric controller. The system achieves global asymptotic stability when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework. Moreover, the hybrid geometric controller guarantees robust asymptotic stability. Simulations validate the stability properties of the proposed hybrid geometric controller.
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一类鲁棒全局渐近镇定的混合几何控制器
针对单位圆上点质量系统全局稳定的经典问题,由于不可能设计出光滑全局渐近稳定控制器,本文提出了一种混合几何控制方案。与大多数依赖坐标和特定控制器结构的现有解决方案不同,我们提出的解决方案是无坐标的(或几何的),并且属于我们也描述的一类控制器。具体来说,我们提出了一个几何混合控制器,它使用一个局部几何控制器(来自上述类)和一个开环几何控制器。采用混合系统框架将局部几何类的控制器与几何开环控制器相结合,使系统达到全局渐近稳定。此外,混合几何控制器保证了鲁棒渐近稳定性。仿真验证了所提混合几何控制器的稳定性。
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